D7(1):S3^2
order := 36,
length := 1209600,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 3^2
Generators:
[ 5 2 2 2 0 2 0 2 2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 0 0 -1 -1]
[11 3 4 2 5 5 4 3 4]
[-3 -1 -1 0 -1 -2 -1 -1 -1]
[-4 -1 -2 -1 -2 -2 -1 -1 -1]
[-2 0 -1 0 -1 -1 -1 0 -1]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-4 -1 -1 -1 -2 -2 -2 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 9 4 2 3 5 3 2 3 2]
[-1 -1 0 0 -1 0 0 0 0]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-4 -2 -1 -1 -2 -1 -1 -2 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-4 -2 -1 -1 -2 -2 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]>
Orbit type:{2,2,3,3,3,3,4,4,6,6,6,6,6,6,12,12,12,12,12,12,36,36,36}
Orbit:
1
{@
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
C3:S3
MatrixGroup(9, Integer Ring)
Generators:
[11 3 4 2 5 5 4 3 4]
[-3 -1 -1 0 -1 -2 -1 -1 -1]
[-4 -1 -2 -1 -2 -2 -1 -1 -1]
[-2 0 -1 0 -1 -1 -1 0 -1]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-4 -1 -1 -1 -2 -2 -2 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 9 4 2 3 5 3 2 3 2]
[-1 -1 0 0 -1 0 0 0 0]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-4 -2 -1 -1 -2 -1 -1 -2 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-4 -2 -1 -1 -2 -2 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
2
{@
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
C3:S3
MatrixGroup(9, Integer Ring)
Generators:
[11 3 4 2 5 5 4 3 4]
[-3 -1 -1 0 -1 -2 -1 -1 -1]
[-4 -1 -2 -1 -2 -2 -1 -1 -1]
[-2 0 -1 0 -1 -1 -1 0 -1]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-4 -1 -1 -1 -2 -2 -2 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 9 4 2 3 5 3 2 3 2]
[-1 -1 0 0 -1 0 0 0 0]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-4 -2 -1 -1 -2 -1 -1 -2 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-4 -2 -1 -1 -2 -2 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
3
{@
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2)
@}
Intersection Matrix:
[-1 2 2]
[ 2 -1 2]
[ 2 2 -1]
Stabilizer Group Name:
D6
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 2 0 2 0 2 2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 0 0 -1 -1]
[11 3 4 2 5 5 4 3 4]
[-3 -1 -1 0 -1 -2 -1 -1 -1]
[-4 -1 -2 -1 -2 -2 -1 -1 -1]
[-2 0 -1 0 -1 -1 -1 0 -1]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-4 -1 -1 -1 -2 -2 -2 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 2 2]
[ 2 -1 2]
[ 2 2 -1]
Stabilizer Group Name:
D6
MatrixGroup(9, Integer Ring)
Generators:
[12 3 4 3 5 4 4 4 6]
[-3 0 -1 -1 -1 -1 -1 -1 -2]
[-4 -1 -1 -1 -2 -1 -1 -2 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-4 -1 -1 -1 -2 -1 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-4 -1 -2 -1 -2 -1 -1 -1 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
[ 8 3 2 3 5 2 2 2 2]
[-1 0 0 -1 -1 0 0 0 0]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-1 -1 0 0 -1 0 0 0 0]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-3 -1 -1 -1 -2 0 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 0 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[11 4 4 5 5 3 2 3 4]
[-2 -1 -1 -1 -1 0 0 0 -1]
[-5 -2 -2 -2 -2 -2 -1 -1 -2]
[-3 -1 -1 -2 -1 -1 0 -1 -1]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-4 -1 -2 -2 -2 -1 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-4 -1 -1 -2 -2 -1 -1 -1 -2]
[-5 -2 -2 -2 -2 -1 -1 -2 -2]
5
{@
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2),
Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1 2 2]
[ 2 -1 2]
[ 2 2 -1]
Stabilizer Group Name:
D6
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 2 0 2 0 2 2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 0 0 -1 -1]
[11 3 4 2 5 5 4 3 4]
[-3 -1 -1 0 -1 -2 -1 -1 -1]
[-4 -1 -2 -1 -2 -2 -1 -1 -1]
[-2 0 -1 0 -1 -1 -1 0 -1]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-4 -1 -1 -1 -2 -2 -2 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
6
{@
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1)
@}
Intersection Matrix:
[-1 2 2]
[ 2 -1 2]
[ 2 2 -1]
Stabilizer Group Name:
D6
MatrixGroup(9, Integer Ring)
Generators:
[11 3 4 2 5 5 4 3 4]
[-3 -1 -1 0 -1 -2 -1 -1 -1]
[-4 -1 -2 -1 -2 -2 -1 -1 -1]
[-2 0 -1 0 -1 -1 -1 0 -1]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-4 -1 -1 -1 -2 -2 -2 -1 -1]
[ 3 1 1 0 0 2 1 0 1]
[-1 -1 0 0 0 -1 0 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 0 -1 -1 0 0]
[ 4 2 2 1 0 1 0 1 2]
[-2 -1 -1 0 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-1 0 -1 0 0 0 0 0 -1]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 -1 0 0 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 0 0 -1 -1]
7
{@
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 1 1 2]
[ 1 -1 2 1]
[ 1 2 -1 1]
[ 2 1 1 -1]
Stabilizer Group Name:
C3^2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 9 4 2 3 5 3 2 3 2]
[-1 -1 0 0 -1 0 0 0 0]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-4 -2 -1 -1 -2 -1 -1 -2 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-4 -2 -1 -1 -2 -2 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
8
{@
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2)
@}
Intersection Matrix:
[-1 1 1 2]
[ 1 -1 2 1]
[ 1 2 -1 1]
[ 2 1 1 -1]
Stabilizer Group Name:
C3^2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 9 4 2 3 5 3 2 3 2]
[-1 -1 0 0 -1 0 0 0 0]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-2 -1 0 -1 -1 -1 0 -1 0]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-4 -2 -1 -1 -2 -1 -1 -2 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-4 -2 -1 -1 -2 -2 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
9
{@
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1)
@}
Intersection Matrix:
[-1 2 3 0 0 2]
[ 2 -1 0 3 2 0]
[ 3 0 -1 2 2 0]
[ 0 3 2 -1 0 2]
[ 0 2 2 0 -1 3]
[ 2 0 0 2 3 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[12 3 4 3 5 4 4 4 6]
[-3 0 -1 -1 -1 -1 -1 -1 -2]
[-4 -1 -1 -1 -2 -1 -1 -2 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-4 -1 -1 -1 -2 -1 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-4 -1 -2 -1 -2 -1 -1 -1 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
[ 8 3 2 3 5 2 2 2 2]
[-1 0 0 -1 -1 0 0 0 0]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-1 -1 0 0 -1 0 0 0 0]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-3 -1 -1 -1 -2 0 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 0 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
10
{@
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2)
@}
Intersection Matrix:
[-1 2 0 0 3 2]
[ 2 -1 2 3 0 0]
[ 0 2 -1 0 2 3]
[ 0 3 0 -1 2 2]
[ 3 0 2 2 -1 0]
[ 2 0 3 2 0 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 2 0 2 0 2 2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 0 0 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
11
{@
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1)
@}
Intersection Matrix:
[-1 1 0 0 0 0]
[ 1 -1 0 0 0 0]
[ 0 0 -1 0 1 0]
[ 0 0 0 -1 0 1]
[ 0 0 1 0 -1 0]
[ 0 0 0 1 0 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 2 0 2 0 2 2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 0 0 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
12
{@
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1)
@}
Intersection Matrix:
[-1 0 0 1 0 0]
[ 0 -1 0 0 0 1]
[ 0 0 -1 0 1 0]
[ 1 0 0 -1 0 0]
[ 0 0 1 0 -1 0]
[ 0 1 0 0 0 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 8 1 3 1 4 3 3 3 3]
[-3 0 -1 -1 -2 -1 -1 -1 -1]
[-2 0 0 0 -1 -1 -1 -1 -1]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-2 0 -1 0 -1 0 -1 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 -1 0 -1]
[-2 0 -1 0 -1 -1 -1 -1 0]
[ 9 4 2 4 4 2 2 2 4]
[-4 -1 -1 -2 -2 -1 -1 -1 -2]
[-2 -1 0 -1 -1 0 0 -1 -1]
[-4 -2 -1 -1 -2 -1 -1 -1 -2]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-2 -1 0 -1 -1 0 -1 0 -1]
[-2 -1 0 -1 -1 -1 0 0 -1]
[-2 -1 -1 -1 -1 0 0 0 -1]
[-4 -2 -1 -2 -1 -1 -1 -1 -2]
13
{@
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1)
@}
Intersection Matrix:
[-1 0 1 0 0 0]
[ 0 -1 0 0 1 0]
[ 1 0 -1 0 0 0]
[ 0 0 0 -1 0 1]
[ 0 1 0 0 -1 0]
[ 0 0 0 1 0 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 8 1 3 1 4 3 3 3 3]
[-3 0 -1 -1 -2 -1 -1 -1 -1]
[-2 0 0 0 -1 -1 -1 -1 -1]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-2 0 -1 0 -1 0 -1 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 -1 0 -1]
[-2 0 -1 0 -1 -1 -1 -1 0]
[ 9 4 2 4 4 2 2 2 4]
[-4 -1 -1 -2 -2 -1 -1 -1 -2]
[-2 -1 0 -1 -1 0 0 -1 -1]
[-4 -2 -1 -1 -2 -1 -1 -1 -2]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-2 -1 0 -1 -1 0 -1 0 -1]
[-2 -1 0 -1 -1 -1 0 0 -1]
[-2 -1 -1 -1 -1 0 0 0 -1]
[-4 -2 -1 -2 -1 -1 -1 -1 -2]
14
{@
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2)
@}
Intersection Matrix:
[-1 1 0 0 0 0]
[ 1 -1 0 0 0 0]
[ 0 0 -1 0 1 0]
[ 0 0 0 -1 0 1]
[ 0 0 1 0 -1 0]
[ 0 0 0 1 0 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 5 2 2 2 0 2 0 2 2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 0 -1 0 -1 -1]
[-2 -1 -1 -1 0 0 0 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
15
{@
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2)
@}
Intersection Matrix:
[-1 1 1 0 0 2 0 2 1 0 1 2]
[ 1 -1 2 0 0 1 0 1 2 0 2 1]
[ 1 2 -1 2 1 0 2 1 0 1 0 0]
[ 0 0 2 -1 0 1 0 1 1 1 2 2]
[ 0 0 1 0 -1 1 1 2 1 0 2 2]
[ 2 1 0 1 1 -1 2 0 0 2 1 0]
[ 0 0 2 0 1 2 -1 1 2 0 1 1]
[ 2 1 1 1 2 0 1 -1 0 2 0 0]
[ 1 2 0 1 1 0 2 0 -1 2 0 1]
[ 0 0 1 1 0 2 0 2 2 -1 1 1]
[ 1 2 0 2 2 1 1 0 0 1 -1 0]
[ 2 1 0 2 2 0 1 0 1 1 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
16
{@
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1)
@}
Intersection Matrix:
[-1 2 1 1 2 2 1 0 1 0 0 0]
[ 2 -1 0 1 0 0 1 1 0 2 1 2]
[ 1 0 -1 0 0 1 2 2 0 2 1 1]
[ 1 1 0 -1 0 0 2 2 0 1 2 1]
[ 2 0 0 0 -1 0 1 2 1 2 1 1]
[ 2 0 1 0 0 -1 1 1 0 1 2 2]
[ 1 1 2 2 1 1 -1 0 2 0 0 0]
[ 0 1 2 2 2 1 0 -1 1 0 0 1]
[ 1 0 0 0 1 0 2 1 -1 1 2 2]
[ 0 2 2 1 2 1 0 0 1 -1 1 0]
[ 0 1 1 2 1 2 0 0 2 1 -1 0]
[ 0 2 1 1 1 2 0 1 2 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
17
{@
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2)
@}
Intersection Matrix:
[-1 0 1 2 0 0 1 1 2 2 1 0]
[ 0 -1 2 2 1 0 1 0 1 1 2 0]
[ 1 2 -1 0 1 2 0 2 1 0 0 1]
[ 2 2 0 -1 1 1 1 1 0 0 0 2]
[ 0 1 1 1 -1 0 2 0 2 2 1 0]
[ 0 0 2 1 0 -1 2 0 1 2 1 1]
[ 1 1 0 1 2 2 -1 2 0 0 0 1]
[ 1 0 2 1 0 0 2 -1 1 1 2 0]
[ 2 1 1 0 2 1 0 1 -1 0 0 2]
[ 2 1 0 0 2 2 0 1 0 -1 1 1]
[ 1 2 0 0 1 1 0 2 0 1 -1 2]
[ 0 0 1 2 0 1 1 0 2 1 2 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 8 1 3 1 4 3 3 3 3]
[-3 0 -1 -1 -2 -1 -1 -1 -1]
[-2 0 0 0 -1 -1 -1 -1 -1]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-2 0 -1 0 -1 0 -1 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 -1 0 -1]
[-2 0 -1 0 -1 -1 -1 -1 0]
18
{@
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2),
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1)
@}
Intersection Matrix:
[-1 2 1 0 1 0 1 0 1 2 0 2]
[ 2 -1 1 2 0 2 0 1 1 0 1 0]
[ 1 1 -1 1 0 1 0 2 2 0 2 0]
[ 0 2 1 -1 1 0 2 1 0 2 0 1]
[ 1 0 0 1 -1 2 0 2 2 1 1 0]
[ 0 2 1 0 2 -1 2 0 0 1 1 1]
[ 1 0 0 2 0 2 -1 1 2 0 1 1]
[ 0 1 2 1 2 0 1 -1 0 1 0 2]
[ 1 1 2 0 2 0 2 0 -1 1 0 1]
[ 2 0 0 2 1 1 0 1 1 -1 2 0]
[ 0 1 2 0 1 1 1 0 0 2 -1 2]
[ 2 0 0 1 0 1 1 2 1 0 2 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 8 3 2 3 5 2 2 2 2]
[-1 0 0 -1 -1 0 0 0 0]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-1 -1 0 0 -1 0 0 0 0]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-3 -1 -1 -1 -2 0 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 0 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
19
{@
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0)
@}
Intersection Matrix:
[-1 2 2 1 2 0 0 0 0 1 3 2]
[ 2 -1 0 0 0 2 2 1 3 2 0 1]
[ 2 0 -1 0 1 3 1 2 2 2 0 0]
[ 1 0 0 -1 0 2 2 2 2 3 1 0]
[ 2 0 1 0 -1 1 3 2 2 2 0 0]
[ 0 2 3 2 1 -1 1 0 0 0 2 2]
[ 0 2 1 2 3 1 -1 0 0 0 2 2]
[ 0 1 2 2 2 0 0 -1 1 0 2 3]
[ 0 3 2 2 2 0 0 1 -1 0 2 1]
[ 1 2 2 3 2 0 0 0 0 -1 1 2]
[ 3 0 0 1 0 2 2 2 2 1 -1 0]
[ 2 1 0 0 0 2 2 3 1 2 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 8 3 2 3 5 2 2 2 2]
[-1 0 0 -1 -1 0 0 0 0]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-1 -1 0 0 -1 0 0 0 0]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-3 -1 -1 -1 -2 0 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 0 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
20
{@
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3)
@}
Intersection Matrix:
[-1 2 0 2 0 1 2 0 2 0 1 3]
[ 2 -1 2 0 3 2 0 1 1 2 0 0]
[ 0 2 -1 3 0 0 1 0 2 1 2 2]
[ 2 0 3 -1 2 2 1 2 0 1 0 0]
[ 0 3 0 2 -1 0 2 1 1 0 2 2]
[ 1 2 0 2 0 -1 2 0 2 0 3 1]
[ 2 0 1 1 2 2 -1 2 0 3 0 0]
[ 0 1 0 2 1 0 2 -1 3 0 2 2]
[ 2 1 2 0 1 2 0 3 -1 2 0 0]
[ 0 2 1 1 0 0 3 0 2 -1 2 2]
[ 1 0 2 0 2 3 0 2 0 2 -1 1]
[ 3 0 2 0 2 1 0 2 0 2 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
21
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2),
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 1 0 0 -1 0 0 0 0 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1)
@}
Intersection Matrix:
[-1 1 1 0 0 0 1 1 0 1 1 1 0 0 1 2 0 0 1 1 0 1 1 1 0 2 1 1 2 1 2 0 0 2 1 1]
[ 1 -1 1 1 2 1 0 2 0 1 0 0 1 1 2 0 0 1 1 0 2 1 0 2 1 1 1 1 1 1 1 0 0 0 0 1]
[ 1 1 -1 0 1 2 1 0 1 1 1 2 1 0 0 1 1 1 0 0 0 1 2 1 1 1 2 1 0 0 1 2 0 0 1 0]
[ 0 1 0 -1 1 1 2 1 1 1 1 1 0 1 0 1 0 1 0 0 0 0 2 1 1 1 2 2 1 1 2 1 0 1 0 0]
[ 0 2 1 1 -1 0 1 0 1 1 1 1 0 0 0 2 1 0 1 2 0 1 1 0 0 1 0 0 1 1 1 1 1 2 2 1]
[ 0 1 2 1 0 -1 1 1 1 1 0 0 0 1 1 1 1 1 1 2 1 0 0 0 0 1 0 0 1 2 1 0 1 2 1 2]
[ 1 0 1 2 1 1 -1 1 0 0 1 1 2 0 2 1 1 0 2 1 1 2 0 1 1 1 0 0 1 0 0 0 1 0 1 1]
[ 1 2 0 1 0 1 1 -1 1 1 1 2 1 0 0 1 2 1 0 1 0 1 1 0 0 1 1 0 0 0 0 2 1 1 2 1]
[ 0 0 1 1 1 1 0 1 -1 1 1 1 1 0 2 1 0 0 1 0 1 2 0 2 0 2 1 1 2 0 1 0 0 1 1 1]
[ 1 1 1 1 1 1 0 1 1 -1 2 1 2 1 1 1 1 0 2 1 0 1 1 0 2 0 0 1 1 0 0 0 2 0 0 0]
[ 1 0 1 1 1 0 1 1 1 2 -1 0 0 1 1 0 1 2 0 1 2 0 0 1 0 1 1 0 0 2 1 1 0 1 1 2]
[ 1 0 2 1 1 0 1 2 1 1 0 -1 0 2 1 0 0 1 1 1 2 0 0 1 1 0 0 1 1 2 1 0 1 1 0 1]
[ 0 1 1 0 0 0 2 1 1 2 0 0 -1 1 0 1 0 1 0 1 1 0 1 1 0 1 1 1 1 2 2 1 0 2 1 1]
[ 0 1 0 1 0 1 0 0 0 1 1 2 1 -1 1 2 1 0 1 1 0 2 1 1 0 2 1 0 1 0 1 1 0 1 2 1]
[ 1 2 0 0 0 1 2 0 2 1 1 1 0 1 -1 1 1 1 0 1 0 0 2 0 1 0 1 1 0 1 1 2 1 1 1 0]
[ 2 0 1 1 2 1 1 1 1 1 0 0 1 2 1 -1 1 2 0 0 2 0 0 1 1 0 1 1 0 1 0 1 1 0 0 1]
[ 0 0 1 0 1 1 1 2 0 1 1 0 0 1 1 1 -1 0 1 0 1 1 1 2 1 1 1 2 2 1 2 0 0 1 0 0]
[ 0 1 1 1 0 1 0 1 0 0 2 1 1 0 1 2 0 -1 2 1 0 2 1 1 1 1 0 1 2 0 1 0 1 1 1 0]
[ 1 1 0 0 1 1 2 0 1 2 0 1 0 1 0 0 1 2 -1 0 1 0 1 1 0 1 2 1 0 1 1 2 0 1 1 1]
[ 1 0 0 0 2 2 1 1 0 1 1 1 1 1 1 0 0 1 0 -1 1 1 1 2 1 1 2 2 1 0 1 1 0 0 0 0]
[ 0 2 0 0 0 1 1 0 1 0 2 2 1 0 0 2 1 0 1 1 -1 1 2 0 1 1 1 1 1 0 1 1 1 1 1 0]
[ 1 1 1 0 1 0 2 1 2 1 0 0 0 2 0 0 1 2 0 1 1 -1 1 0 1 0 1 1 0 2 1 1 1 1 0 1]
[ 1 0 2 2 1 0 0 1 0 1 0 0 1 1 2 0 1 1 1 1 2 1 -1 1 0 1 0 0 1 1 0 0 1 1 1 2]
[ 1 2 1 1 0 0 1 0 2 0 1 1 1 1 0 1 2 1 1 2 0 0 1 -1 1 0 0 0 0 1 0 1 2 1 1 1]
[ 0 1 1 1 0 0 1 0 0 2 0 1 0 0 1 1 1 1 0 1 1 1 0 1 -1 2 1 0 1 1 1 1 0 2 2 2]
[ 2 1 1 1 1 1 1 1 2 0 1 0 1 2 0 0 1 1 1 1 1 0 1 0 2 -1 0 1 0 1 0 1 2 0 0 0]
[ 1 1 2 2 0 0 0 1 1 0 1 0 1 1 1 1 1 0 2 2 1 1 0 0 1 0 -1 0 1 1 0 0 2 1 1 1]
[ 1 1 1 2 0 0 0 0 1 1 0 1 1 0 1 1 2 1 1 2 1 1 0 0 0 1 0 -1 0 1 0 1 1 1 2 2]
[ 2 1 0 1 1 1 1 0 2 1 0 1 1 1 0 0 2 2 0 1 1 0 1 0 1 0 1 0 -1 1 0 2 1 0 1 1]
[ 1 1 0 1 1 2 0 0 0 0 2 2 2 0 1 1 1 0 1 0 0 2 1 1 1 1 1 1 1 -1 0 1 1 0 1 0]
[ 2 1 1 2 1 1 0 0 1 0 1 1 2 1 1 0 2 1 1 1 1 1 0 0 1 0 0 0 0 0 -1 1 2 0 1 1]
[ 0 0 2 1 1 0 0 2 0 0 1 0 1 1 2 1 0 0 2 1 1 1 0 1 1 1 0 1 2 1 1 -1 1 1 0 1]
[ 0 0 0 0 1 1 1 1 0 2 0 1 0 0 1 1 0 1 0 0 1 1 1 2 0 2 2 1 1 1 2 1 -1 1 1 1]
[ 2 0 0 1 2 2 0 1 1 0 1 1 2 1 1 0 1 1 1 0 1 1 1 1 2 0 1 1 0 0 0 1 1 -1 0 0]
[ 1 0 1 0 2 1 1 2 1 0 1 0 1 2 1 0 0 1 1 0 1 0 1 1 2 0 1 2 1 1 1 0 1 0 -1 0]
[ 1 1 0 0 1 2 1 1 1 0 2 1 1 1 0 1 0 0 1 0 0 1 2 1 2 0 1 2 1 0 1 1 1 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
22
{@
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2),
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 0 1 1 1 1 2 1 1 2 1 1 1 0 1 0 0 2 1 1 0 1 0 0 2 0 1 0 2 0 1 0 1 1 0]
[ 1 -1 1 2 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1 0 2 0 0 0 0 1 2 2 1 1 1 1 2 0 0]
[ 0 1 -1 1 0 2 1 1 0 0 1 2 0 1 0 0 1 0 2 1 1 0 1 0 1 1 1 1 0 2 1 1 1 1 2 0]
[ 1 2 1 -1 1 1 1 0 1 1 0 0 0 2 1 0 0 2 1 1 1 0 1 1 2 1 1 0 0 0 1 0 1 0 1 2]
[ 1 1 0 1 -1 1 1 0 0 0 1 2 1 0 0 0 2 0 1 0 1 0 2 1 1 0 1 1 1 1 1 1 2 0 2 1]
[ 1 1 2 1 1 -1 1 1 2 1 1 0 2 0 1 2 1 1 0 0 1 1 1 2 0 1 0 0 1 0 0 1 0 0 0 1]
[ 1 0 1 1 1 1 -1 1 1 0 0 0 1 0 2 0 1 1 0 1 1 1 0 0 1 0 0 1 2 1 2 2 1 2 1 0]
[ 2 1 1 0 0 1 1 -1 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 2 0 2 1 1 0 1 0 2 0 1 2]
[ 1 0 0 1 0 2 1 0 -1 1 1 2 0 1 0 0 1 0 1 1 0 1 1 0 1 0 2 2 1 1 1 0 2 1 1 1]
[ 1 1 0 1 0 1 0 1 1 -1 0 1 1 0 1 0 2 1 1 0 2 0 1 1 1 0 0 0 1 1 2 2 1 1 2 0]
[ 2 1 1 0 1 1 0 0 1 0 -1 0 0 1 2 0 1 2 0 1 1 1 0 1 2 0 1 0 1 0 2 1 1 1 1 1]
[ 1 1 2 0 2 0 0 1 2 1 0 -1 1 1 2 1 0 2 0 1 1 1 0 1 1 1 0 0 1 0 1 1 0 1 0 1]
[ 1 1 0 0 1 2 1 0 0 1 0 1 -1 2 1 0 0 1 1 2 0 1 0 0 2 1 2 1 0 1 1 0 1 1 1 1]
[ 1 0 1 2 0 0 0 1 1 0 1 1 2 -1 1 1 2 0 0 0 1 1 1 1 0 0 0 1 2 1 1 2 1 1 1 0]
[ 0 1 0 1 0 1 2 1 0 1 2 2 1 1 -1 1 1 0 2 0 1 0 2 1 0 1 1 1 0 1 0 0 1 0 1 1]
[ 1 1 0 0 0 2 0 0 0 0 0 1 0 1 1 -1 1 1 1 1 1 0 1 0 2 0 1 1 1 1 2 1 2 1 2 1]
[ 0 1 1 0 2 1 1 1 1 2 1 0 0 2 1 1 -1 1 1 2 0 1 0 0 1 2 1 1 0 1 0 0 0 1 0 1]
[ 0 0 0 2 0 1 1 1 0 1 2 2 1 0 0 1 1 -1 1 1 0 1 1 0 0 1 1 2 1 2 0 1 1 1 1 0]
[ 2 0 2 1 1 0 0 0 1 1 0 0 1 0 2 1 1 1 -1 1 0 2 0 1 1 0 1 1 2 0 1 1 1 1 0 1]
[ 1 1 1 1 0 0 1 1 1 0 1 1 2 0 0 1 2 1 1 -1 2 0 2 2 0 0 0 0 1 0 1 1 1 0 1 1]
[ 1 0 1 1 1 1 1 0 0 2 1 1 0 1 1 1 0 0 0 2 -1 2 0 0 1 1 2 2 1 1 0 0 1 1 0 1]
[ 0 2 0 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 2 0 2 -1 2 1 1 1 0 0 0 1 1 1 1 0 2 1]
[ 1 0 1 1 2 1 0 1 1 1 0 0 0 1 2 1 0 1 0 2 0 2 -1 0 1 1 1 1 1 1 1 1 0 2 0 0]
[ 0 0 0 1 1 2 0 1 0 1 1 1 0 1 1 0 0 0 1 2 0 1 0 -1 1 1 1 2 1 2 1 1 1 2 1 0]
[ 0 0 1 2 1 0 1 2 1 1 2 1 2 0 0 2 1 0 1 0 1 1 1 1 -1 1 0 1 1 1 0 1 0 1 0 0]
[ 2 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 2 1 0 0 1 1 1 1 1 -1 1 1 2 0 2 1 2 1 1 1]
[ 0 1 1 1 1 0 0 2 2 0 1 0 2 0 1 1 1 1 1 0 2 0 1 1 0 1 -1 0 1 1 1 2 0 1 1 0]
[ 1 2 1 0 1 0 1 1 2 0 0 0 1 1 1 1 1 2 1 0 2 0 1 2 1 1 0 -1 0 0 1 1 0 0 1 1]
[ 0 2 0 0 1 1 2 1 1 1 1 1 0 2 0 1 0 1 2 1 1 0 1 1 1 2 1 0 -1 1 0 0 0 0 1 1]
[ 2 1 2 0 1 0 1 0 1 1 0 0 1 1 1 1 1 2 0 0 1 1 1 2 1 0 1 0 1 -1 1 0 1 0 0 2]
[ 0 1 1 1 1 0 2 1 1 2 2 1 1 1 0 2 0 0 1 1 0 1 1 1 0 2 1 1 0 1 -1 0 0 0 0 1]
[ 1 1 1 0 1 1 2 0 0 2 1 1 0 2 0 1 0 1 1 1 0 1 1 1 1 1 2 1 0 0 0 -1 1 0 0 2]
[ 0 1 1 1 2 0 1 2 2 1 1 0 1 1 1 2 0 1 1 1 1 1 0 1 0 2 0 0 0 1 0 1 -1 1 0 0]
[ 1 2 1 0 0 0 2 0 1 1 1 1 1 1 0 1 1 1 1 0 1 0 2 2 1 1 1 0 0 0 0 0 1 -1 1 2]
[ 1 0 2 1 2 0 1 1 1 2 1 0 1 1 1 2 0 1 0 1 0 2 0 1 0 1 1 1 1 0 0 0 0 1 -1 1]
[ 0 0 0 2 1 1 0 2 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 1 0 1 1 2 1 2 0 2 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
23
{@
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 2 1 2 1 1 0 1 0 1 1 1 1 1 3 0 2 2 1 2 0 1 0 0 0 1 1 2 1 2 1 1 1 2 0]
[ 1 -1 2 1 0 1 1 2 1 2 1 1 1 1 3 1 0 2 2 1 0 0 1 2 2 0 1 1 2 1 0 1 1 1 0 0]
[ 2 2 -1 1 1 0 1 1 1 1 1 2 0 1 0 0 2 1 0 0 1 3 1 1 1 1 2 2 0 0 1 1 1 2 1 2]
[ 1 1 1 -1 0 2 0 1 2 0 3 1 1 1 1 1 0 1 0 0 1 1 2 2 1 1 1 2 2 1 2 0 1 0 1 2]
[ 2 0 1 0 -1 2 1 2 1 1 2 1 1 0 2 0 1 1 1 0 0 1 1 3 2 1 1 2 1 1 1 1 2 0 0 1]
[ 1 1 0 2 2 -1 1 1 1 2 0 2 0 2 1 1 1 2 1 1 1 2 1 0 1 0 2 1 1 0 0 1 0 3 1 1]
[ 1 1 1 0 1 1 -1 2 3 1 2 0 2 2 1 1 0 1 0 1 0 1 1 1 0 1 2 1 2 0 1 1 0 1 2 2]
[ 0 2 1 1 2 1 2 -1 0 0 1 2 0 1 0 2 1 1 1 1 3 1 2 0 1 1 0 1 1 2 2 0 1 1 1 1]
[ 1 1 1 2 1 1 3 0 -1 1 0 2 0 0 1 1 2 1 2 1 2 1 1 1 2 1 0 1 0 2 1 1 2 1 0 0]
[ 0 2 1 0 1 2 1 0 1 -1 2 1 1 0 0 2 1 1 1 0 2 1 1 1 0 1 1 2 1 1 3 1 2 0 2 1]
[ 1 1 1 3 2 0 2 1 0 2 -1 1 1 1 1 1 2 1 2 2 1 1 0 0 1 1 1 0 0 1 0 2 1 2 1 0]
[ 1 1 2 1 1 2 0 2 2 1 1 -1 3 1 1 1 1 0 1 2 0 0 0 1 0 2 1 0 1 1 1 2 1 0 2 1]
[ 1 1 0 1 1 0 2 0 0 1 1 3 -1 1 1 1 1 2 1 0 2 2 2 1 2 0 1 2 1 1 1 0 1 2 0 1]
[ 1 1 1 1 0 2 2 1 0 0 1 1 1 -1 1 1 2 1 2 0 1 1 0 2 1 1 1 2 0 1 2 2 3 0 1 0]
[ 1 3 0 1 2 1 1 0 1 0 1 1 1 1 -1 1 2 0 0 1 2 2 1 0 0 2 1 1 0 1 2 1 1 1 2 2]
[ 3 1 0 1 0 1 1 2 1 2 1 1 1 1 1 -1 2 0 0 1 0 2 1 2 2 2 1 1 0 1 0 1 1 1 0 2]
[ 0 0 2 0 1 1 0 1 2 1 2 1 1 2 2 2 -1 2 1 1 1 0 2 1 1 0 1 1 3 1 1 0 0 1 1 1]
[ 2 2 1 1 1 2 1 1 1 1 1 0 2 1 0 0 2 -1 0 2 1 1 1 1 1 3 0 0 0 2 1 1 1 0 1 2]
[ 2 2 0 0 1 1 0 1 2 1 2 1 1 2 0 0 1 0 -1 1 1 2 2 1 1 2 1 1 1 1 1 0 0 1 1 3]
[ 1 1 0 0 0 1 1 1 1 0 2 2 0 0 1 1 1 2 1 -1 1 2 1 2 1 0 2 3 1 0 2 1 2 1 1 1]
[ 2 0 1 1 0 1 0 3 2 2 1 0 2 1 2 0 1 1 1 1 -1 1 0 2 1 1 2 1 1 0 0 2 1 1 1 1]
[ 0 0 3 1 1 2 1 1 1 1 1 0 2 1 2 2 0 1 2 2 1 -1 1 1 1 1 0 0 2 2 1 1 1 0 1 0]
[ 1 1 1 2 1 1 1 2 1 1 0 0 2 0 1 1 2 1 2 1 0 1 -1 1 0 1 2 1 0 0 1 3 2 1 2 0]
[ 0 2 1 2 3 0 1 0 1 1 0 1 1 2 0 2 1 1 1 2 2 1 1 -1 0 1 1 0 1 1 1 1 0 2 2 1]
[ 0 2 1 1 2 1 0 1 2 0 1 0 2 1 0 2 1 1 1 1 1 1 0 0 -1 1 2 1 1 0 2 2 1 1 3 1]
[ 0 0 1 1 1 0 1 1 1 1 1 2 0 1 2 2 0 3 2 0 1 1 1 1 1 -1 2 2 2 0 1 1 1 2 1 0]
[ 1 1 2 1 1 2 2 0 0 1 1 1 1 1 1 1 1 0 1 2 2 0 2 1 2 2 -1 0 1 3 1 0 1 0 0 1]
[ 1 1 2 2 2 1 1 1 1 2 0 0 2 2 1 1 1 0 1 3 1 0 1 0 1 2 0 -1 1 2 0 1 0 1 1 1]
[ 2 2 0 2 1 1 2 1 0 1 0 1 1 0 0 0 3 0 1 1 1 2 0 1 1 2 1 1 -1 1 1 2 2 1 1 1]
[ 1 1 0 1 1 0 0 2 2 1 1 1 1 1 1 1 1 2 1 0 0 2 0 1 0 0 3 2 1 -1 1 2 1 2 2 1]
[ 2 0 1 2 1 0 1 2 1 3 0 1 1 2 2 0 1 1 1 2 0 1 1 1 2 1 1 0 1 1 -1 1 0 2 0 1]
[ 1 1 1 0 1 1 1 0 1 1 2 2 0 2 1 1 0 1 0 1 2 1 3 1 2 1 0 1 2 2 1 -1 0 1 0 2]
[ 1 1 1 1 2 0 0 1 2 2 1 1 1 3 1 1 0 1 0 2 1 1 2 0 1 1 1 0 2 1 0 0 -1 2 1 2]
[ 1 1 2 0 0 3 1 1 1 0 2 0 2 0 1 1 1 0 1 1 1 0 1 2 1 2 0 1 1 2 2 1 2 -1 1 1]
[ 2 0 1 1 0 1 2 1 0 2 1 2 0 1 2 0 1 1 1 1 1 1 2 2 3 1 0 1 1 2 0 0 1 1 -1 1]
[ 0 0 2 2 1 1 2 1 0 1 0 1 1 0 2 2 1 2 3 1 1 0 0 1 1 0 1 1 1 1 1 2 2 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D7(2):D10
order := 20,
length := 2177280,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 5
Generators:
[13 5 4 4 5 5 4 3 6]
[-5 -2 -1 -2 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-5 -2 -2 -2 -2 -2 -1 -1 -2]
[-4 -2 -1 -1 -2 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
[ 8 1 4 4 2 3 2 2 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-1 0 -1 -1 0 0 0 0 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[ 3 1 1 0 2 1 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,2,2,2,4,4,4,5,5,5,5,10,10,10,10,20,20,20,20,20,20,20,20}
Orbit:
1
{@
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 8 1 4 4 2 3 2 2 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-1 0 -1 -1 0 0 0 0 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[13 5 4 4 5 5 4 3 6]
[-5 -2 -1 -2 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-5 -2 -2 -2 -2 -2 -1 -1 -2]
[-4 -2 -1 -1 -2 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
2
{@
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[11 4 3 4 3 4 3 3 6]
[-4 -2 -1 -2 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 0 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -1 -1 -2 -1 -2 -1 -1 -2]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
[ 8 1 4 4 2 3 2 2 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-1 0 -1 -1 0 0 0 0 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
3
{@
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 8 1 4 4 2 3 2 2 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-1 0 -1 -1 0 0 0 0 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[13 5 4 4 5 5 4 3 6]
[-5 -2 -1 -2 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-5 -2 -2 -2 -2 -2 -1 -1 -2]
[-4 -2 -1 -1 -2 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
4
{@
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 1 0 0 -1 0 0 0 0 -1)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[11 4 3 4 3 4 3 3 6]
[-4 -2 -1 -2 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 0 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -1 -1 -2 -1 -2 -1 -1 -2]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
[ 8 1 4 4 2 3 2 2 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-1 0 -1 -1 0 0 0 0 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
5
{@
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2)
@}
Intersection Matrix:
[-1 2 0 2]
[ 2 -1 2 0]
[ 0 2 -1 2]
[ 2 0 2 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 8 1 4 4 2 3 2 2 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-1 0 -1 -1 0 0 0 0 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
6
{@
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 0 2 2]
[ 0 -1 2 2]
[ 2 2 -1 0]
[ 2 2 0 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 8 1 4 4 2 3 2 2 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-1 0 -1 -1 0 0 0 0 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
7
{@
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 3]
[ 1 -1 3 1]
[ 1 3 -1 1]
[ 3 1 1 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 8 1 4 4 2 3 2 2 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-1 0 -1 -1 0 0 0 0 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
8
{@
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 1 2 1 2]
[ 1 -1 2 2 1]
[ 2 2 -1 1 1]
[ 1 2 1 -1 2]
[ 2 1 1 2 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 2 1 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 0 0 1 0 1 1 2]
[-1 -1 0 0 0 0 0 0 -1]
[ 0 0 0 0 0 1 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 0 0 0 0 0 -1 -1]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 0 -1]
[-1 0 0 0 -1 0 0 0 -1]
[-2 -1 0 0 -1 0 -1 -1 -1]
9
{@
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1)
@}
Intersection Matrix:
[-1 1 2 2 1]
[ 1 -1 1 2 2]
[ 2 1 -1 1 2]
[ 2 2 1 -1 1]
[ 1 2 2 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 2 1 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 8 3 2 4 2 1 4 2 3]
[-3 -1 -1 -2 -1 0 -1 -1 -1]
[-2 -1 -1 -1 0 0 -1 0 -1]
[-4 -2 -1 -2 -1 -1 -2 -1 -1]
[-2 -1 0 -1 0 0 -1 -1 -1]
[-1 0 0 -1 0 0 -1 0 0]
[-4 -1 -1 -2 -1 -1 -2 -1 -2]
[-2 -1 0 -1 -1 0 -1 0 -1]
[-3 -1 -1 -1 -1 0 -2 -1 -1]
10
{@
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1),
Mod: (0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1 2 2 1]
[ 1 -1 2 1 2]
[ 2 2 -1 1 1]
[ 2 1 1 -1 2]
[ 1 2 1 2 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 2 1 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[10 4 3 4 4 2 5 2 3]
[-4 -1 -1 -2 -2 -1 -2 -1 -1]
[-3 -1 -1 -1 -1 -1 -2 0 -1]
[-4 -2 -1 -2 -1 -1 -2 -1 -1]
[-4 -2 -1 -1 -2 -1 -2 -1 -1]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-5 -2 -2 -2 -2 -1 -2 -1 -2]
[-2 -1 0 -1 -1 0 -1 0 -1]
[-3 -1 -1 -1 -1 0 -2 -1 -1]
11
{@
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2)
@}
Intersection Matrix:
[-1 1 2 1 2]
[ 1 -1 2 2 1]
[ 2 2 -1 1 1]
[ 1 2 1 -1 2]
[ 2 1 1 2 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 2 1 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[13 5 4 4 5 5 4 3 6]
[-5 -2 -1 -2 -2 -2 -2 -1 -2]
[-4 -1 -1 -1 -2 -2 -1 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
[-5 -2 -2 -1 -2 -2 -2 -1 -2]
[-5 -2 -2 -2 -2 -2 -1 -1 -2]
[-4 -2 -1 -1 -2 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
12
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 1 1 0 2 1 2 0 3 1]
[ 1 -1 2 2 1 0 0 1 1 3]
[ 1 2 -1 1 2 3 1 0 1 0]
[ 0 2 1 -1 1 1 3 1 2 0]
[ 2 1 2 1 -1 0 1 3 0 1]
[ 1 0 3 1 0 -1 1 2 1 2]
[ 2 0 1 3 1 1 -1 1 0 2]
[ 0 1 0 1 3 2 1 -1 2 1]
[ 3 1 1 2 0 1 0 2 -1 1]
[ 1 3 0 0 1 2 2 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 2 1 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
13
{@
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1)
@}
Intersection Matrix:
[-1 2 3 0 1 1 2 1 0 1]
[ 2 -1 0 3 1 2 1 0 1 1]
[ 3 0 -1 2 1 1 0 1 2 1]
[ 0 3 2 -1 1 0 1 2 1 1]
[ 1 1 1 1 -1 0 2 2 0 3]
[ 1 2 1 0 0 -1 1 3 1 2]
[ 2 1 0 1 2 1 -1 1 3 0]
[ 1 0 1 2 2 3 1 -1 1 0]
[ 0 1 2 1 0 1 3 1 -1 2]
[ 1 1 1 1 3 2 0 0 2 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 2 1 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
14
{@
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2)
@}
Intersection Matrix:
[-1 0 0 1 0 0 0 0 0 0]
[ 0 -1 0 0 0 0 0 1 0 0]
[ 0 0 -1 0 0 0 1 0 0 0]
[ 1 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 0 -1 1 0 0 0 0]
[ 0 0 0 0 1 -1 0 0 0 0]
[ 0 0 1 0 0 0 -1 0 0 0]
[ 0 1 0 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 -1 1]
[ 0 0 0 0 0 0 0 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 2 1 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
15
{@
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1)
@}
Intersection Matrix:
[-1 1 0 0 0 0 0 0 0 0]
[ 1 -1 0 0 0 0 0 0 0 0]
[ 0 0 -1 0 0 0 1 0 0 0]
[ 0 0 0 -1 0 0 0 1 0 0]
[ 0 0 0 0 -1 0 0 0 0 1]
[ 0 0 0 0 0 -1 0 0 1 0]
[ 0 0 1 0 0 0 -1 0 0 0]
[ 0 0 0 1 0 0 0 -1 0 0]
[ 0 0 0 0 0 1 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 2 1 1 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[-1 -1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-1 0 0 0 -1 0 -1 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
16
{@
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1)
@}
Intersection Matrix:
[-1 3 2 0 0 2 0 2 2 1 2 0 2 0 2 2 1 0 0 0]
[ 3 -1 0 2 2 0 2 0 0 1 0 2 0 2 0 0 1 2 2 2]
[ 2 0 -1 2 2 0 2 0 0 0 0 2 1 2 0 0 2 2 1 3]
[ 0 2 2 -1 0 3 0 2 2 2 1 0 2 0 2 2 0 1 0 0]
[ 0 2 2 0 -1 2 0 2 2 2 2 0 2 1 1 3 0 0 0 0]
[ 2 0 0 3 2 -1 2 0 0 0 1 2 0 2 0 0 2 1 2 2]
[ 0 2 2 0 0 2 -1 3 1 2 2 1 2 0 2 2 0 0 0 0]
[ 2 0 0 2 2 0 3 -1 1 0 0 1 0 2 0 0 2 2 2 2]
[ 2 0 0 2 2 0 1 1 -1 0 0 3 0 2 0 0 2 2 2 2]
[ 1 1 0 2 2 0 2 0 0 -1 0 2 0 2 0 0 3 2 2 2]
[ 2 0 0 1 2 1 2 0 0 0 -1 2 0 2 0 0 2 3 2 2]
[ 0 2 2 0 0 2 1 1 3 2 2 -1 2 0 2 2 0 0 0 0]
[ 2 0 1 2 2 0 2 0 0 0 0 2 -1 2 0 0 2 2 3 1]
[ 0 2 2 0 1 2 0 2 2 2 2 0 2 -1 3 1 0 0 0 0]
[ 2 0 0 2 1 0 2 0 0 0 0 2 0 3 -1 1 2 2 2 2]
[ 2 0 0 2 3 0 2 0 0 0 0 2 0 1 1 -1 2 2 2 2]
[ 1 1 2 0 0 2 0 2 2 3 2 0 2 0 2 2 -1 0 0 0]
[ 0 2 2 1 0 1 0 2 2 2 3 0 2 0 2 2 0 -1 0 0]
[ 0 2 1 0 0 2 0 2 2 2 2 0 3 0 2 2 0 0 -1 1]
[ 0 2 3 0 0 2 0 2 2 2 2 0 1 0 2 2 0 0 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
17
{@
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 3 2 2 0 1 0 2 0 2 2 2 0 2 0 1 0 0 2 0]
[ 3 -1 0 0 2 1 2 0 2 0 0 0 2 0 2 1 2 2 0 2]
[ 2 0 -1 0 2 2 2 0 2 0 0 0 2 1 2 0 1 3 0 2]
[ 2 0 0 -1 1 2 2 0 2 0 0 0 2 0 2 0 2 2 1 3]
[ 0 2 2 1 -1 0 0 2 0 2 2 2 0 2 0 2 0 0 3 1]
[ 1 1 2 2 0 -1 0 2 0 2 2 2 0 2 0 3 0 0 2 0]
[ 0 2 2 2 0 0 -1 2 0 2 1 3 0 2 1 2 0 0 2 0]
[ 2 0 0 0 2 2 2 -1 1 1 0 0 3 0 2 0 2 2 0 2]
[ 0 2 2 2 0 0 0 1 -1 3 2 2 1 2 0 2 0 0 2 0]
[ 2 0 0 0 2 2 2 1 3 -1 0 0 1 0 2 0 2 2 0 2]
[ 2 0 0 0 2 2 1 0 2 0 -1 1 2 0 3 0 2 2 0 2]
[ 2 0 0 0 2 2 3 0 2 0 1 -1 2 0 1 0 2 2 0 2]
[ 0 2 2 2 0 0 0 3 1 1 2 2 -1 2 0 2 0 0 2 0]
[ 2 0 1 0 2 2 2 0 2 0 0 0 2 -1 2 0 3 1 0 2]
[ 0 2 2 2 0 0 1 2 0 2 3 1 0 2 -1 2 0 0 2 0]
[ 1 1 0 0 2 3 2 0 2 0 0 0 2 0 2 -1 2 2 0 2]
[ 0 2 1 2 0 0 0 2 0 2 2 2 0 3 0 2 -1 1 2 0]
[ 0 2 3 2 0 0 0 2 0 2 2 2 0 1 0 2 1 -1 2 0]
[ 2 0 0 1 3 2 2 0 2 0 0 0 2 0 2 0 2 2 -1 1]
[ 0 2 2 3 1 0 0 2 0 2 2 2 0 2 0 2 0 0 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
18
{@
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1),
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 2 2 1 1 1 0 0 0 2 0 1 0 1 2 1 1 0 1]
[ 0 -1 2 1 0 2 0 1 1 0 1 0 2 1 0 1 2 1 1 0]
[ 2 2 -1 0 1 0 1 1 1 2 0 2 0 1 1 0 0 0 1 1]
[ 2 1 0 -1 1 1 0 2 1 2 0 1 1 1 1 0 0 0 2 0]
[ 1 0 1 1 -1 1 0 1 2 0 0 1 2 2 0 0 2 1 1 0]
[ 1 2 0 1 1 -1 2 1 1 1 0 2 0 0 2 1 0 0 0 1]
[ 1 0 1 0 0 2 -1 1 1 1 1 0 2 2 0 0 1 1 2 0]
[ 0 1 1 2 1 1 1 -1 0 0 2 0 0 1 0 1 1 2 0 2]
[ 0 1 1 1 2 1 1 0 -1 1 2 0 0 0 1 2 0 1 0 2]
[ 0 0 2 2 0 1 1 0 1 -1 1 0 1 1 0 1 2 2 0 1]
[ 2 1 0 0 0 0 1 2 2 1 -1 2 1 1 1 0 1 0 1 0]
[ 0 0 2 1 1 2 0 0 0 0 2 -1 1 1 0 1 1 2 1 1]
[ 1 2 0 1 2 0 2 0 0 1 1 1 -1 0 1 1 0 1 0 2]
[ 0 1 1 1 2 0 2 1 0 1 1 1 0 -1 2 2 0 0 0 1]
[ 1 0 1 1 0 2 0 0 1 0 1 0 1 2 -1 0 2 2 1 1]
[ 2 1 0 0 0 1 0 1 2 1 0 1 1 2 0 -1 1 1 2 0]
[ 1 2 0 0 2 0 1 1 0 2 1 1 0 0 2 1 -1 0 1 1]
[ 1 1 0 0 1 0 1 2 1 2 0 2 1 0 2 1 0 -1 1 0]
[ 0 1 1 2 1 0 2 0 0 0 1 1 0 0 1 2 1 1 -1 2]
[ 1 0 1 0 0 1 0 2 2 1 0 1 2 1 1 0 1 0 2 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
19
{@
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 2 1 1 1 2 0 1 1 0 1 0 1 0 2 0 1 0 2 0]
[ 2 -1 0 1 0 0 1 1 0 1 0 1 1 2 0 2 1 1 0 2]
[ 1 0 -1 0 0 0 1 1 0 0 1 1 1 2 1 2 2 2 0 1]
[ 1 1 0 -1 1 0 2 0 1 1 2 2 0 1 0 1 1 2 0 0]
[ 1 0 0 1 -1 0 0 1 0 0 0 1 2 1 1 2 2 1 1 2]
[ 2 0 0 0 0 -1 1 0 1 1 1 2 1 1 0 2 1 2 0 1]
[ 0 1 1 2 0 1 -1 1 1 0 0 0 2 0 2 1 1 0 2 1]
[ 1 1 1 0 1 0 1 -1 2 2 2 2 0 0 0 1 0 1 1 0]
[ 1 0 0 1 0 1 1 2 -1 0 0 0 1 2 1 1 2 1 0 2]
[ 0 1 0 1 0 1 0 2 0 -1 0 0 2 1 2 1 2 1 1 1]
[ 1 0 1 2 0 1 0 2 0 0 -1 0 2 1 1 1 1 0 1 2]
[ 0 1 1 2 1 2 0 2 0 0 0 -1 1 1 2 0 1 0 1 1]
[ 1 1 1 0 2 1 2 0 1 2 2 1 -1 1 0 0 0 1 0 0]
[ 0 2 2 1 1 1 0 0 2 1 1 1 1 -1 1 0 0 0 2 0]
[ 2 0 1 0 1 0 2 0 1 2 1 2 0 1 -1 1 0 1 0 1]
[ 0 2 2 1 2 2 1 1 1 1 1 0 0 0 1 -1 0 0 1 0]
[ 1 1 2 1 2 1 1 0 2 2 1 1 0 0 0 0 -1 0 1 0]
[ 0 1 2 2 1 2 0 1 1 1 0 0 1 0 1 0 0 -1 2 1]
[ 2 0 0 0 1 0 2 1 0 1 1 1 0 2 0 1 1 2 -1 1]
[ 0 2 1 0 2 1 1 0 2 1 2 1 0 0 1 0 0 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
20
{@
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0)
@}
Intersection Matrix:
[-1 1 1 0 1 1 0 2 1 1 0 2 2 2 0 0 1 1 0 0]
[ 1 -1 1 0 0 2 2 0 1 0 1 0 1 1 2 0 0 2 1 1]
[ 1 1 -1 2 1 0 1 0 0 2 1 1 0 0 0 1 0 1 2 2]
[ 0 0 2 -1 1 2 1 1 1 0 0 1 2 2 1 0 1 1 0 0]
[ 1 0 1 1 -1 1 1 1 2 0 2 0 0 1 2 0 0 2 0 1]
[ 1 2 0 2 1 -1 0 1 0 2 1 1 0 0 0 2 1 0 1 1]
[ 0 2 1 1 1 0 -1 2 1 1 0 2 1 1 0 1 2 0 0 0]
[ 2 0 0 1 1 1 2 -1 0 1 1 0 0 0 1 1 0 1 2 2]
[ 1 1 0 1 2 0 1 0 -1 2 0 1 1 0 0 2 1 0 2 1]
[ 1 0 2 0 0 2 1 1 2 -1 1 0 1 1 2 0 1 1 0 0]
[ 0 1 1 0 2 1 0 1 0 1 -1 2 2 1 0 1 2 0 1 0]
[ 2 0 1 1 0 1 2 0 1 0 2 -1 0 0 2 1 0 1 1 1]
[ 2 1 0 2 0 0 1 0 1 1 2 0 -1 0 1 1 0 1 1 2]
[ 2 1 0 2 1 0 1 0 0 1 1 0 0 -1 1 2 1 0 2 1]
[ 0 2 0 1 2 0 0 1 0 2 0 2 1 1 -1 1 1 0 1 1]
[ 0 0 1 0 0 2 1 1 2 0 1 1 1 2 1 -1 0 2 0 1]
[ 1 0 0 1 0 1 2 0 1 1 2 0 0 1 1 0 -1 2 1 2]
[ 1 2 1 1 2 0 0 1 0 1 0 1 1 0 0 2 2 -1 1 0]
[ 0 1 2 0 0 1 0 2 2 0 1 1 1 2 1 0 1 1 -1 0]
[ 0 1 2 0 1 1 0 2 1 0 0 1 2 1 1 1 2 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
21
{@
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1)
@}
Intersection Matrix:
[-1 1 1 0 1 1 0 1 0 2 2 0 2 2 0 0 1 1 1 0]
[ 1 -1 0 1 1 2 0 2 1 0 1 2 0 1 1 0 0 0 1 2]
[ 1 0 -1 1 2 2 0 1 0 1 1 1 0 1 0 0 1 0 2 2]
[ 0 1 1 -1 0 1 0 0 0 1 1 0 2 2 1 1 2 2 1 0]
[ 1 1 2 0 -1 0 1 0 1 0 0 1 1 1 2 2 1 2 0 0]
[ 1 2 2 1 0 -1 2 0 1 1 0 0 1 0 1 2 1 1 0 0]
[ 0 0 0 0 1 2 -1 1 0 1 2 1 1 2 0 0 1 1 2 1]
[ 1 2 1 0 0 0 1 -1 0 1 0 0 1 1 1 2 2 2 1 0]
[ 0 1 0 0 1 1 0 0 -1 2 1 0 1 2 0 1 2 1 2 1]
[ 2 0 1 1 0 1 1 1 2 -1 0 2 0 0 2 1 0 1 0 1]
[ 2 1 1 1 0 0 2 0 1 0 -1 1 0 0 2 2 1 1 0 1]
[ 0 2 1 0 1 0 1 0 0 2 1 -1 2 1 0 1 2 1 1 0]
[ 2 0 0 2 1 1 1 1 1 0 0 2 -1 0 1 1 0 0 1 2]
[ 2 1 1 2 1 0 2 1 2 0 0 1 0 -1 1 1 0 0 0 1]
[ 0 1 0 1 2 1 0 1 0 2 2 0 1 1 -1 0 1 0 2 1]
[ 0 0 0 1 2 2 0 2 1 1 2 1 1 1 0 -1 0 0 1 1]
[ 1 0 1 2 1 1 1 2 2 0 1 2 0 0 1 0 -1 0 0 1]
[ 1 0 0 2 2 1 1 2 1 1 1 1 0 0 0 0 0 -1 1 2]
[ 1 1 2 1 0 0 2 1 2 0 0 1 1 0 2 1 0 1 -1 0]
[ 0 2 2 0 0 0 1 0 1 1 1 0 2 1 1 1 1 2 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
22
{@
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2),
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 1 1 0 1 0 1 1 1 1 2 1 1 1 0 1 1 0 0 2]
[ 1 -1 1 1 1 1 0 1 2 0 0 0 1 1 1 0 1 1 2 1]
[ 1 1 -1 0 1 1 1 2 0 1 1 2 0 0 1 1 1 0 1 1]
[ 0 1 0 -1 1 1 1 1 0 1 2 1 0 0 1 1 1 1 1 2]
[ 1 1 1 1 -1 1 1 0 1 0 1 1 1 2 2 0 0 1 1 0]
[ 0 1 1 1 1 -1 2 1 1 1 1 1 0 1 0 1 2 0 0 1]
[ 1 0 1 1 1 2 -1 1 1 1 0 0 2 1 1 0 0 1 1 1]
[ 1 1 2 1 0 1 1 -1 1 0 1 0 1 1 1 1 0 2 1 0]
[ 1 2 0 0 1 1 1 1 -1 2 1 1 0 0 1 1 1 1 0 1]
[ 1 0 1 1 0 1 1 0 2 -1 1 1 1 1 1 1 0 1 2 0]
[ 2 0 1 2 1 1 0 1 1 1 -1 0 1 1 1 0 1 1 1 0]
[ 1 0 2 1 1 1 0 0 1 1 0 -1 1 1 1 0 1 2 1 1]
[ 1 1 0 0 1 0 2 1 0 1 1 1 -1 0 1 1 2 1 1 1]
[ 1 1 0 0 2 1 1 1 0 1 1 1 0 -1 0 2 1 1 1 1]
[ 0 1 1 1 2 0 1 1 1 1 1 1 1 0 -1 2 1 0 0 1]
[ 1 0 1 1 0 1 0 1 1 1 0 0 1 2 2 -1 1 1 1 1]
[ 1 1 1 1 0 2 0 0 1 0 1 1 2 1 1 1 -1 1 1 0]
[ 0 1 0 1 1 0 1 2 1 1 1 2 1 1 0 1 1 -1 0 1]
[ 0 2 1 1 1 0 1 1 0 2 1 1 1 1 0 1 1 0 -1 1]
[ 2 1 1 2 0 1 1 0 1 0 0 1 1 1 1 1 0 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
23
{@
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2)
@}
Intersection Matrix:
[-1 1 1 1 1 0 0 1 1 2 1 1 2 0 0 1 1 0 1 1]
[ 1 -1 1 0 1 1 1 1 0 1 2 0 0 2 1 0 1 1 1 1]
[ 1 1 -1 1 0 1 1 2 1 0 1 0 1 1 1 0 1 2 1 0]
[ 1 0 1 -1 1 1 1 1 0 1 1 0 0 1 2 1 2 1 1 0]
[ 1 1 0 1 -1 2 1 1 0 0 1 1 1 1 1 0 1 1 2 0]
[ 0 1 1 1 2 -1 1 1 2 1 1 1 1 0 0 1 1 0 0 1]
[ 0 1 1 1 1 1 -1 0 1 2 0 1 2 1 1 1 0 1 0 1]
[ 1 1 2 1 1 1 0 -1 1 1 0 2 1 1 1 1 0 0 0 1]
[ 1 0 1 0 0 2 1 1 -1 1 1 0 0 1 1 1 1 1 2 1]
[ 2 1 0 1 0 1 2 1 1 -1 1 1 0 1 1 0 1 1 1 0]
[ 1 2 1 1 1 1 0 0 1 1 -1 1 1 0 1 2 0 1 0 1]
[ 1 0 0 0 1 1 1 2 0 1 1 -1 0 1 1 1 1 2 1 1]
[ 2 0 1 0 1 1 2 1 0 0 1 0 -1 1 1 1 1 1 1 1]
[ 0 2 1 1 1 0 1 1 1 1 0 1 1 -1 0 2 1 0 1 1]
[ 0 1 1 2 1 0 1 1 1 1 1 1 1 0 -1 1 0 0 1 2]
[ 1 0 0 1 0 1 1 1 1 0 2 1 1 2 1 -1 1 1 1 0]
[ 1 1 1 2 1 1 0 0 1 1 0 1 1 1 0 1 -1 1 0 2]
[ 0 1 2 1 1 0 1 0 1 1 1 2 1 0 0 1 1 -1 1 1]
[ 1 1 1 1 2 0 0 0 2 1 0 1 1 1 1 1 0 1 -1 1]
[ 1 1 0 0 0 1 1 1 1 0 1 1 1 1 2 0 2 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D7(3):C2*F5
order := 40,
length := 2177280,
subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 5
Generators:
[ 6 3 2 0 2 2 3 2 1]
[-3 -2 -1 0 -1 -1 -1 -1 -1]
[-2 -1 -1 0 -1 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-3 -1 -1 0 -1 -1 -2 -1 -1]
[-1 -1 0 0 0 0 -1 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 4 1 2 2 1 2 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[-2 0 -1 -1 -1 -1 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 0 0 0 1 0]
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 1 0 0 0 0]
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{2,2,2,2,4,4,4,10,10,10,10,20,20,20,20,20,20,20,20,20}
Orbit:
1
{@
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
F5
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 1 0 0 0 0]
[ 6 3 2 0 2 2 3 2 1]
[-3 -2 -1 0 -1 -1 -1 -1 -1]
[-2 -1 -1 0 -1 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-3 -1 -1 0 -1 -1 -2 -1 -1]
[-1 -1 0 0 0 0 -1 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: (0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
F5
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 1 0 0 0 0]
[ 6 3 2 0 2 2 3 2 1]
[-3 -2 -1 0 -1 -1 -1 -1 -1]
[-2 -1 -1 0 -1 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 0 0 -1 -1 -1 -1 0]
[-3 -1 -1 0 -1 -1 -2 -1 -1]
[-1 -1 0 0 0 0 -1 0 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 0 0 0 0 -1 -1 0 0)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
F5
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 1 0 0 0 0]
[ 8 3 4 2 2 3 4 2 1]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[-4 -1 -2 -1 -1 -2 -2 -1 -1]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-1 0 -1 0 0 0 -1 0 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-4 -2 -2 -1 -1 -1 -2 -1 -1]
[-2 -1 -1 0 -1 -1 -1 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
4
{@
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
F5
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 1 0 0 0 0]
[ 8 3 4 2 1 3 4 2 2]
[-3 -1 -1 -1 0 -1 -2 -1 -1]
[-4 -1 -2 -1 -1 -2 -2 -1 -1]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-4 -2 -2 -1 -1 -1 -2 -1 -1]
[-2 -1 -1 0 0 -1 -1 0 -1]
[-1 0 -1 0 0 0 -1 0 0]
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
5
{@
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2)
@}
Intersection Matrix:
[-1 2 0 2]
[ 2 -1 2 0]
[ 0 2 -1 2]
[ 2 0 2 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 1 0 0 0 0]
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
6
{@
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 2 0 2]
[ 2 -1 2 0]
[ 0 2 -1 2]
[ 2 0 2 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 1 0 0 0 0]
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
7
{@
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 3]
[ 1 -1 3 1]
[ 1 3 -1 1]
[ 3 1 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 1 0 0 0 0]
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
8
{@
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1)
@}
Intersection Matrix:
[-1 1 0 1 2 2 2 0 2 1]
[ 1 -1 2 2 0 1 1 2 0 2]
[ 0 2 -1 1 2 2 1 1 2 0]
[ 1 2 1 -1 2 2 2 0 1 0]
[ 2 0 2 2 -1 0 1 2 1 1]
[ 2 1 2 2 0 -1 0 1 1 2]
[ 2 1 1 2 1 0 -1 2 0 2]
[ 0 2 1 0 2 1 2 -1 2 1]
[ 2 0 2 1 1 1 0 2 -1 2]
[ 1 2 0 0 1 2 2 1 2 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
9
{@
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1),
Mod: ( 1 0 0 -1 0 0 0 0 -1)
@}
Intersection Matrix:
[-1 2 0 1 1 1 2 2 2 0]
[ 2 -1 2 2 1 2 0 1 0 1]
[ 0 2 -1 0 2 1 1 2 2 1]
[ 1 2 0 -1 2 0 2 2 1 1]
[ 1 1 2 2 -1 2 1 0 0 2]
[ 1 2 1 0 2 -1 2 1 2 0]
[ 2 0 1 2 1 2 -1 0 1 2]
[ 2 1 2 2 0 1 0 -1 1 2]
[ 2 0 2 1 0 2 1 1 -1 2]
[ 0 1 1 1 2 0 2 2 2 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 4 1 2 2 1 2 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[-2 0 -1 -1 -1 -1 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 0 0 0 1 0]
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
10
{@
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0]
[ 0 -1 1 0 0 0 0 0 0 0]
[ 0 1 -1 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 0 0 0 1]
[ 1 0 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 -1 0 0 1 0]
[ 0 0 0 0 0 0 -1 1 0 0]
[ 0 0 0 0 0 0 1 -1 0 0]
[ 0 0 0 0 0 1 0 0 -1 0]
[ 0 0 0 1 0 0 0 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
11
{@
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 0 0 1 0 0 0 0 0 0]
[ 0 -1 1 0 0 0 0 0 0 0]
[ 0 1 -1 0 0 0 0 0 0 0]
[ 1 0 0 -1 0 0 0 0 0 0]
[ 0 0 0 0 -1 0 0 0 0 1]
[ 0 0 0 0 0 -1 0 0 1 0]
[ 0 0 0 0 0 0 -1 1 0 0]
[ 0 0 0 0 0 0 1 -1 0 0]
[ 0 0 0 0 0 1 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 5 2 2 2 1 3 1 0 1]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 -1 -1 -1 0 -1 -1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[-3 -1 -1 -1 -1 -2 -1 0 -1]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[-1 0 -1 0 0 -1 0 0 0]
12
{@
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1),
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1)
@}
Intersection Matrix:
[-1 3 2 1 2 0 2 2 0 1 2 0 0 2 0 0 2 0 2 0]
[ 3 -1 0 1 0 2 0 0 2 1 0 2 2 0 2 2 0 2 0 2]
[ 2 0 -1 2 0 2 0 1 2 0 0 2 2 0 1 3 0 2 0 2]
[ 1 1 2 -1 2 0 2 2 0 3 2 0 0 2 0 0 2 0 2 0]
[ 2 0 0 2 -1 1 1 0 3 0 0 2 2 0 2 2 0 2 0 2]
[ 0 2 2 0 1 -1 3 2 1 2 2 0 0 2 0 0 2 0 2 0]
[ 2 0 0 2 1 3 -1 0 1 0 0 2 2 0 2 2 0 2 0 2]
[ 2 0 1 2 0 2 0 -1 2 0 0 2 2 0 3 1 0 2 0 2]
[ 0 2 2 0 3 1 1 2 -1 2 2 0 0 2 0 0 2 0 2 0]
[ 1 1 0 3 0 2 0 0 2 -1 0 2 2 0 2 2 0 2 0 2]
[ 2 0 0 2 0 2 0 0 2 0 -1 1 2 0 2 2 0 3 1 2]
[ 0 2 2 0 2 0 2 2 0 2 1 -1 0 2 0 0 2 1 3 0]
[ 0 2 2 0 2 0 2 2 0 2 2 0 -1 1 0 0 3 0 2 1]
[ 2 0 0 2 0 2 0 0 2 0 0 2 1 -1 2 2 1 2 0 3]
[ 0 2 1 0 2 0 2 3 0 2 2 0 0 2 -1 1 2 0 2 0]
[ 0 2 3 0 2 0 2 1 0 2 2 0 0 2 1 -1 2 0 2 0]
[ 2 0 0 2 0 2 0 0 2 0 0 2 3 1 2 2 -1 2 0 1]
[ 0 2 2 0 2 0 2 2 0 2 3 1 0 2 0 0 2 -1 1 0]
[ 2 0 0 2 0 2 0 0 2 0 1 3 2 0 2 2 0 1 -1 2]
[ 0 2 2 0 2 0 2 2 0 2 2 0 1 3 0 0 1 0 2 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
13
{@
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1)
@}
Intersection Matrix:
[-1 0 0 0 0 0 2 3 2 2 2 2 0 1 0 1 2 2 2 0]
[ 0 -1 1 0 0 0 2 2 2 1 3 2 0 2 0 0 2 2 2 0]
[ 0 1 -1 0 0 0 2 2 2 3 1 2 0 2 0 0 2 2 2 0]
[ 0 0 0 -1 0 1 2 2 2 2 2 3 0 2 0 0 2 1 2 0]
[ 0 0 0 0 -1 0 2 2 3 2 2 2 1 2 0 0 1 2 2 0]
[ 0 0 0 1 0 -1 2 2 2 2 2 1 0 2 0 0 2 3 2 0]
[ 2 2 2 2 2 2 -1 0 0 0 0 0 2 0 3 2 0 0 1 1]
[ 3 2 2 2 2 2 0 -1 0 0 0 0 2 1 2 1 0 0 0 2]
[ 2 2 2 2 3 2 0 0 -1 0 0 0 1 0 2 2 1 0 0 2]
[ 2 1 3 2 2 2 0 0 0 -1 1 0 2 0 2 2 0 0 0 2]
[ 2 3 1 2 2 2 0 0 0 1 -1 0 2 0 2 2 0 0 0 2]
[ 2 2 2 3 2 1 0 0 0 0 0 -1 2 0 2 2 0 1 0 2]
[ 0 0 0 0 1 0 2 2 1 2 2 2 -1 2 0 0 3 2 2 0]
[ 1 2 2 2 2 2 0 1 0 0 0 0 2 -1 2 3 0 0 0 2]
[ 0 0 0 0 0 0 3 2 2 2 2 2 0 2 -1 0 2 2 1 1]
[ 1 0 0 0 0 0 2 1 2 2 2 2 0 3 0 -1 2 2 2 0]
[ 2 2 2 2 1 2 0 0 1 0 0 0 3 0 2 2 -1 0 0 2]
[ 2 2 2 1 2 3 0 0 0 0 0 1 2 0 2 2 0 -1 0 2]
[ 2 2 2 2 2 2 1 0 0 0 0 0 2 0 1 2 0 0 -1 3]
[ 0 0 0 0 0 0 1 2 2 2 2 2 0 2 1 0 2 2 3 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
14
{@
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2),
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 0 2 2 2 0 1 0 1 1 1 2 1 0 3 0 0 2 2]
[ 1 -1 1 0 1 1 0 3 2 2 0 2 2 0 0 1 2 1 2 0]
[ 0 1 -1 2 0 3 1 1 1 2 0 0 2 2 0 2 0 2 1 1]
[ 2 0 2 -1 1 0 0 2 1 2 0 1 0 1 2 0 3 1 2 1]
[ 2 1 0 1 -1 2 2 1 2 2 0 0 1 2 1 0 1 3 0 0]
[ 2 1 3 0 2 -1 1 1 1 0 2 2 0 0 2 0 2 0 1 1]
[ 0 0 1 0 2 1 -1 2 0 2 0 1 1 1 1 2 2 0 3 2]
[ 1 3 1 2 1 1 2 -1 0 0 2 0 0 2 2 1 0 1 0 2]
[ 0 2 1 1 2 1 0 0 -1 1 1 0 0 2 2 2 1 0 2 3]
[ 1 2 2 2 2 0 2 0 1 -1 3 2 1 0 1 1 0 0 0 1]
[ 1 0 0 0 0 2 0 2 1 3 -1 0 1 2 1 1 2 2 2 1]
[ 1 2 0 1 0 2 1 0 0 2 0 -1 0 3 2 1 1 2 1 2]
[ 2 2 2 0 1 0 1 0 0 1 1 0 -1 2 3 0 2 1 1 2]
[ 1 0 2 1 2 0 1 2 2 0 2 3 2 -1 0 1 1 0 1 0]
[ 0 0 0 2 1 2 1 2 2 1 1 2 3 0 -1 2 0 1 1 0]
[ 3 1 2 0 0 0 2 1 2 1 1 1 0 1 2 -1 2 2 0 0]
[ 0 2 0 3 1 2 2 0 1 0 2 1 2 1 0 2 -1 1 0 1]
[ 0 1 2 1 3 0 0 1 0 0 2 2 1 0 1 2 1 -1 2 2]
[ 2 2 1 2 0 1 3 0 2 0 2 1 1 1 1 0 0 2 -1 0]
[ 2 0 1 1 0 1 2 2 3 1 1 2 2 0 0 0 1 2 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
15
{@
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2)
@}
Intersection Matrix:
[-1 1 2 0 0 1 1 0 1 1 1 1 1 0 1 1 1 0 2 1]
[ 1 -1 1 0 1 1 0 2 1 2 1 1 0 1 0 1 0 1 1 1]
[ 2 1 -1 1 1 1 0 1 1 0 0 1 1 1 1 0 1 2 0 1]
[ 0 0 1 -1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 2 2]
[ 0 1 1 1 -1 1 0 0 1 1 1 2 1 0 1 2 1 1 1 0]
[ 1 1 1 1 1 -1 1 1 1 0 1 1 0 2 2 1 0 0 1 0]
[ 1 0 0 0 0 1 -1 1 1 1 1 2 0 1 1 1 1 2 1 1]
[ 0 2 1 1 0 1 1 -1 0 0 1 1 1 0 1 1 2 1 1 1]
[ 1 1 1 1 1 1 1 0 -1 1 2 0 0 1 0 1 2 1 0 1]
[ 1 2 0 1 1 0 1 0 1 -1 0 1 1 1 2 0 1 1 1 1]
[ 1 1 0 1 1 1 1 1 2 0 -1 1 2 0 1 0 0 1 1 1]
[ 1 1 1 1 2 1 2 1 0 1 1 -1 1 1 0 0 1 0 0 1]
[ 1 0 1 0 1 0 0 1 0 1 2 1 -1 2 1 1 1 1 1 1]
[ 0 1 1 1 0 2 1 0 1 1 0 1 2 -1 0 1 1 1 1 1]
[ 1 0 1 1 1 2 1 1 0 2 1 0 1 0 -1 1 1 1 0 1]
[ 1 1 0 0 2 1 1 1 1 0 0 0 1 1 1 -1 1 1 1 2]
[ 1 0 1 1 1 0 1 2 2 1 0 1 1 1 1 1 -1 0 1 0]
[ 0 1 2 1 1 0 2 1 1 1 1 0 1 1 1 1 0 -1 1 0]
[ 2 1 0 2 1 1 1 1 0 1 1 0 1 1 0 1 1 1 -1 0]
[ 1 1 1 2 0 0 1 1 1 1 1 1 1 1 1 2 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 1 1 0 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 0 0 0 1 0]
16
{@
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: (0 0 0 0 0 1 0 0 0)
@}
Intersection Matrix:
[-1 0 1 1 1 1 1 1 2 0 1 0 1 1 1 1 0 2 1 0]
[ 0 -1 0 0 2 1 1 0 1 1 1 1 1 1 0 1 1 2 1 1]
[ 1 0 -1 0 1 1 1 0 1 2 1 1 0 2 1 0 1 1 1 1]
[ 1 0 0 -1 1 2 1 0 0 1 1 2 1 1 1 1 0 1 1 1]
[ 1 2 1 1 -1 1 0 1 1 1 1 0 1 1 2 0 0 0 1 1]
[ 1 1 1 2 1 -1 1 1 1 1 0 0 0 1 0 1 2 0 1 1]
[ 1 1 1 1 0 1 -1 0 1 1 1 0 2 0 1 0 1 1 1 2]
[ 1 0 0 0 1 1 0 -1 1 1 0 1 1 1 1 1 1 1 2 2]
[ 2 1 1 0 1 1 1 1 -1 1 1 2 1 0 0 1 1 0 0 1]
[ 0 1 2 1 1 1 1 1 1 -1 0 1 1 0 1 2 0 1 1 0]
[ 1 1 1 1 1 0 1 0 1 0 -1 1 0 1 1 2 1 0 2 1]
[ 0 1 1 2 0 0 0 1 2 1 1 -1 1 1 1 0 1 1 1 1]
[ 1 1 0 1 1 0 2 1 1 1 0 1 -1 2 1 1 1 0 1 0]
[ 1 1 2 1 1 1 0 1 0 0 1 1 2 -1 0 1 1 1 0 1]
[ 1 0 1 1 2 0 1 1 0 1 1 1 1 0 -1 1 2 1 0 1]
[ 1 1 0 1 0 1 0 1 1 2 2 0 1 1 1 -1 1 1 0 1]
[ 0 1 1 0 0 2 1 1 1 0 1 1 1 1 2 1 -1 1 1 0]
[ 2 2 1 1 0 0 1 1 0 1 0 1 0 1 1 1 1 -1 1 1]
[ 1 1 1 1 1 1 1 2 0 1 2 1 1 0 0 0 1 1 -1 0]
[ 0 1 1 1 1 1 2 2 1 0 1 1 0 1 1 1 0 1 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
17
{@
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 2 1 1 1 1 1 0 1 0 1 1 2 1 1 1 1 0]
[ 0 -1 0 1 1 2 1 1 1 0 1 1 1 2 1 1 1 1 0 0]
[ 0 0 -1 1 1 1 1 1 1 0 2 1 1 1 1 2 1 0 1 0]
[ 2 1 1 -1 0 1 1 1 1 1 0 2 1 0 0 1 0 1 1 1]
[ 1 1 1 0 -1 1 1 0 2 2 0 1 1 0 1 1 0 1 1 1]
[ 1 2 1 1 1 -1 1 0 1 1 1 1 0 0 0 0 1 1 2 1]
[ 1 1 1 1 1 1 -1 1 0 1 1 0 2 1 1 1 2 0 0 0]
[ 1 1 1 1 0 0 1 -1 2 2 1 1 0 1 0 0 1 1 1 1]
[ 1 1 1 1 2 1 0 2 -1 0 1 0 1 1 1 1 1 0 0 1]
[ 0 0 0 1 2 1 1 2 0 -1 1 1 1 1 1 1 1 1 1 0]
[ 1 1 2 0 0 1 1 1 1 1 -1 1 1 0 1 0 0 2 1 1]
[ 0 1 1 2 1 1 0 1 0 1 1 -1 1 1 2 1 1 0 0 1]
[ 1 1 1 1 1 0 2 0 1 1 1 1 -1 1 0 0 0 1 1 2]
[ 1 2 1 0 0 0 1 1 1 1 0 1 1 -1 1 1 0 1 2 1]
[ 2 1 1 0 1 0 1 0 1 1 1 2 0 1 -1 0 1 1 1 1]
[ 1 1 2 1 1 0 1 0 1 1 0 1 0 1 0 -1 1 2 1 1]
[ 1 1 1 0 0 1 2 1 1 1 0 1 0 0 1 1 -1 1 1 2]
[ 1 1 0 1 1 1 0 1 0 1 2 0 1 1 1 2 1 -1 0 1]
[ 1 0 1 1 1 2 0 1 0 1 1 0 1 2 1 1 1 0 -1 1]
[ 0 0 0 1 1 1 0 1 1 0 1 1 2 1 1 1 2 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 2 0 1 1]
[-1 0 0 0 0 -1 0 0 -1]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[-1 -1 0 0 0 -1 0 0 0]
18
{@
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2)
@}
Intersection Matrix:
[-1 1 1 1 1 0 1 2 1 0 1 0 1 0 1 2 1 0 1 1]
[ 1 -1 1 1 1 1 1 1 1 1 1 2 0 1 0 0 0 1 0 2]
[ 1 1 -1 0 0 1 1 1 1 0 2 1 1 1 1 1 1 0 2 0]
[ 1 1 0 -1 0 0 1 1 2 1 1 1 1 1 1 1 2 0 1 0]
[ 1 1 0 0 -1 1 2 1 1 1 1 1 1 0 2 1 1 0 1 0]
[ 0 1 1 0 1 -1 1 1 2 0 1 0 1 0 1 1 2 1 1 1]
[ 1 1 1 1 2 1 -1 0 0 1 0 1 0 2 0 1 1 1 1 1]
[ 2 1 1 1 1 1 0 -1 0 1 0 1 0 1 1 0 1 2 1 1]
[ 1 1 1 2 1 2 0 0 -1 1 0 1 0 1 1 1 0 1 1 1]
[ 0 1 0 1 1 0 1 1 1 -1 2 0 1 0 1 1 1 1 2 1]
[ 1 1 2 1 1 1 0 0 0 2 -1 1 0 1 1 1 1 1 0 1]
[ 0 2 1 1 1 0 1 1 1 0 1 -1 2 0 1 1 1 1 1 0]
[ 1 0 1 1 1 1 0 0 0 1 0 2 -1 1 1 1 1 1 1 2]
[ 0 1 1 1 0 0 2 1 1 0 1 0 1 -1 2 1 1 1 1 1]
[ 1 0 1 1 2 1 0 1 1 1 1 1 1 2 -1 0 0 1 0 1]
[ 2 0 1 1 1 1 1 0 1 1 1 1 1 1 0 -1 0 2 0 1]
[ 1 0 1 2 1 2 1 1 0 1 1 1 1 1 0 0 -1 1 0 1]
[ 0 1 0 0 0 1 1 2 1 1 1 1 1 1 1 2 1 -1 1 0]
[ 1 0 2 1 1 1 1 1 1 2 0 1 1 1 0 0 0 1 -1 1]
[ 1 2 0 0 0 1 1 1 1 1 1 0 2 1 1 1 1 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 1 1 0 0 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 -1 -1 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 0 0 0 1 0]
19
{@
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2)
@}
Intersection Matrix:
[-1 1 0 0 2 2 0 1 1 1 0 1 1 0 1 1 1 1 1 1]
[ 1 -1 0 1 0 1 1 1 1 2 1 1 1 1 0 2 0 0 1 1]
[ 0 0 -1 1 1 1 0 1 1 1 1 1 0 0 1 2 1 1 1 2]
[ 0 1 1 -1 2 1 1 0 1 1 1 0 1 1 1 1 1 0 2 0]
[ 2 0 1 2 -1 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1]
[ 2 1 1 1 0 -1 1 0 1 0 2 0 0 1 1 1 1 1 1 1]
[ 0 1 0 1 1 1 -1 0 1 1 1 2 1 0 2 1 1 1 0 1]
[ 1 1 1 0 1 0 0 -1 1 1 2 1 1 1 2 1 1 0 1 0]
[ 1 1 1 1 1 1 1 1 -1 1 0 1 0 2 1 0 2 0 0 1]
[ 1 2 1 1 1 0 1 1 1 -1 1 0 0 0 1 0 1 2 1 1]
[ 0 1 1 1 1 2 1 2 0 1 -1 1 1 1 0 0 1 1 0 1]
[ 1 1 1 0 1 0 2 1 1 0 1 -1 0 1 0 1 1 1 2 1]
[ 1 1 0 1 1 0 1 1 0 0 1 0 -1 1 1 1 2 1 1 2]
[ 0 1 0 1 1 1 0 1 2 0 1 1 1 -1 1 1 0 2 1 1]
[ 1 0 1 1 0 1 2 2 1 1 0 0 1 1 -1 1 0 1 1 1]
[ 1 2 2 1 1 1 1 1 0 0 0 1 1 1 1 -1 1 1 0 0]
[ 1 0 1 1 0 1 1 1 2 1 1 1 2 0 0 1 -1 1 1 0]
[ 1 0 1 0 1 1 1 0 0 2 1 1 1 2 1 1 1 -1 1 0]
[ 1 1 1 2 0 1 0 1 0 1 0 2 1 1 1 0 1 1 -1 1]
[ 1 1 2 0 1 1 1 0 1 1 1 1 2 1 1 0 0 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
20
{@
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1)
@}
Intersection Matrix:
[-1 1 1 1 1 2 1 1 1 1 1 0 1 0 0 2 1 0 0 1]
[ 1 -1 0 2 1 1 1 1 1 0 0 0 1 1 1 0 1 1 2 1]
[ 1 0 -1 1 0 0 2 1 1 1 1 1 1 1 1 1 1 0 2 0]
[ 1 2 1 -1 1 0 1 0 0 1 1 2 1 1 1 1 1 0 0 1]
[ 1 1 0 1 -1 0 1 1 2 2 1 1 0 0 1 1 1 1 1 0]
[ 2 1 0 0 0 -1 1 1 1 1 1 2 1 1 1 0 1 1 1 0]
[ 1 1 2 1 1 1 -1 1 1 1 1 0 0 1 1 0 0 2 0 1]
[ 1 1 1 0 1 1 1 -1 0 1 0 1 0 1 2 1 1 0 1 2]
[ 1 1 1 0 2 1 1 0 -1 0 1 1 1 2 1 1 0 0 1 1]
[ 1 0 1 1 2 1 1 1 0 -1 0 1 2 1 0 0 1 1 1 1]
[ 1 0 1 1 1 1 1 0 1 0 -1 1 1 0 1 0 2 1 1 2]
[ 0 0 1 2 1 2 0 1 1 1 1 -1 0 1 1 1 0 1 1 1]
[ 1 1 1 1 0 1 0 0 1 2 1 0 -1 1 2 1 0 1 1 1]
[ 0 1 1 1 0 1 1 1 2 1 0 1 1 -1 0 1 2 1 0 1]
[ 0 1 1 1 1 1 1 2 1 0 1 1 2 0 -1 1 1 1 0 0]
[ 2 0 1 1 1 0 0 1 1 0 0 1 1 1 1 -1 1 2 1 1]
[ 1 1 1 1 1 1 0 1 0 1 2 0 0 2 1 1 -1 1 1 0]
[ 0 1 0 0 1 1 2 0 0 1 1 1 1 1 1 2 1 -1 1 1]
[ 0 2 2 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 -1 1]
[ 1 1 0 1 0 0 1 2 1 1 2 1 1 1 0 1 0 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 1]
D7(4):C5⋊C4
order := 20,
length := 2177280,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 5
Generators:
[14 5 5 5 6 4 6 4 4]
[-6 -2 -2 -2 -2 -2 -3 -2 -2]
[-4 -1 -1 -2 -2 -1 -2 -1 -1]
[-5 -2 -2 -2 -2 -2 -2 -1 -1]
[-6 -2 -2 -2 -3 -2 -2 -2 -2]
[-5 -2 -2 -2 -2 -1 -2 -2 -1]
[-5 -2 -2 -2 -2 -1 -2 -1 -2]
[-4 -1 -2 -1 -2 -1 -2 -1 -1]
[-4 -2 -1 -1 -2 -1 -2 -1 -1]
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{4,4,4,4,4,5,5,5,5,10,10,10,10,20,20,20,20,20,20,20,20}
Orbit:
1
{@
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 2 0 2]
[ 2 -1 2 0]
[ 0 2 -1 2]
[ 2 0 2 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
2
{@
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2),
Mod: ( 1 0 -1 -1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 2 0 2]
[ 2 -1 2 0]
[ 0 2 -1 2]
[ 2 0 2 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
3
{@
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1)
@}
Intersection Matrix:
[-1 3 1 1]
[ 3 -1 1 1]
[ 1 1 -1 3]
[ 1 1 3 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
4
{@
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1)
@}
Intersection Matrix:
[-1 1 0 0]
[ 1 -1 0 0]
[ 0 0 -1 1]
[ 0 0 1 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
5
{@
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1)
@}
Intersection Matrix:
[-1 0 1 0]
[ 0 -1 0 1]
[ 1 0 -1 0]
[ 0 1 0 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
6
{@
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 1 2 1 2]
[ 1 -1 2 2 1]
[ 2 2 -1 1 1]
[ 1 2 1 -1 2]
[ 2 1 1 2 -1]
Stabilizer Group Name:
C4
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 8 3 2 2 2 1 4 3 4]
[-4 -1 -1 -1 -1 -1 -2 -2 -2]
[-1 0 0 0 0 0 -1 0 -1]
[-2 -1 0 -1 0 0 -1 -1 -1]
[-2 -1 0 0 -1 0 -1 -1 -1]
[-2 -1 -1 0 0 0 -1 -1 -1]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-3 -1 -1 -1 -1 0 -2 -1 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
7
{@
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 2 1 2 1]
[ 2 -1 2 1 1]
[ 1 2 -1 1 2]
[ 2 1 1 -1 2]
[ 1 1 2 2 -1]
Stabilizer Group Name:
C4
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 8 3 2 2 2 1 4 3 4]
[-4 -1 -1 -1 -1 -1 -2 -2 -2]
[-1 0 0 0 0 0 -1 0 -1]
[-2 -1 0 -1 0 0 -1 -1 -1]
[-2 -1 0 0 -1 0 -1 -1 -1]
[-2 -1 -1 0 0 0 -1 -1 -1]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-3 -1 -1 -1 -1 0 -2 -1 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
8
{@
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 -1 0)
@}
Intersection Matrix:
[-1 2 2 1 1]
[ 2 -1 1 2 1]
[ 2 1 -1 1 2]
[ 1 2 1 -1 2]
[ 1 1 2 2 -1]
Stabilizer Group Name:
C4
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[14 5 5 5 6 4 6 4 4]
[-6 -2 -2 -2 -2 -2 -3 -2 -2]
[-4 -1 -1 -2 -2 -1 -2 -1 -1]
[-5 -2 -2 -2 -2 -2 -2 -1 -1]
[-6 -2 -2 -2 -3 -2 -2 -2 -2]
[-5 -2 -2 -2 -2 -1 -2 -2 -1]
[-5 -2 -2 -2 -2 -1 -2 -1 -2]
[-4 -1 -2 -1 -2 -1 -2 -1 -1]
[-4 -2 -1 -1 -2 -1 -2 -1 -1]
9
{@
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1),
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2),
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 1 2 1 2]
[ 1 -1 2 2 1]
[ 2 2 -1 1 1]
[ 1 2 1 -1 2]
[ 2 1 1 2 -1]
Stabilizer Group Name:
C4
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[11 4 2 4 5 3 3 5 4]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -2 -1]
[-4 -1 -1 -2 -2 -1 -1 -2 -1]
[-5 -2 -1 -2 -2 -1 -2 -2 -2]
[-2 -1 0 -1 -1 0 0 -1 -1]
[-4 -2 -1 -1 -2 -1 -1 -2 -1]
[-5 -2 -1 -2 -2 -2 -1 -2 -2]
[-4 -1 -1 -1 -2 -1 -1 -2 -2]
10
{@
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2),
Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1 1 2 1 1 1 0 3 2 0]
[ 1 -1 0 3 0 2 2 1 1 1]
[ 2 0 -1 2 1 1 3 0 1 1]
[ 1 3 2 -1 2 0 0 1 1 1]
[ 1 0 1 2 -1 3 1 1 0 2]
[ 1 2 1 0 3 -1 1 1 2 0]
[ 0 2 3 0 1 1 -1 2 1 1]
[ 3 1 0 1 1 1 2 -1 0 2]
[ 2 1 1 1 0 2 1 0 -1 3]
[ 0 1 1 1 2 0 1 2 3 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
11
{@
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2)
@}
Intersection Matrix:
[-1 2 1 3 0 1 2 1 1 0]
[ 2 -1 1 0 3 2 1 1 0 1]
[ 1 1 -1 1 1 2 0 3 0 2]
[ 3 0 1 -1 2 1 0 1 1 2]
[ 0 3 1 2 -1 0 1 1 2 1]
[ 1 2 2 1 0 -1 1 0 3 1]
[ 2 1 0 0 1 1 -1 2 1 3]
[ 1 1 3 1 1 0 2 -1 2 0]
[ 1 0 0 1 2 3 1 2 -1 1]
[ 0 1 2 2 1 1 3 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
12
{@
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 0 0 0 0 0 0 0 0]
[ 1 -1 0 0 0 0 0 0 0 0]
[ 0 0 -1 0 0 0 1 0 0 0]
[ 0 0 0 -1 0 0 0 0 0 1]
[ 0 0 0 0 -1 0 0 1 0 0]
[ 0 0 0 0 0 -1 0 0 1 0]
[ 0 0 1 0 0 0 -1 0 0 0]
[ 0 0 0 0 1 0 0 -1 0 0]
[ 0 0 0 0 0 1 0 0 -1 0]
[ 0 0 0 1 0 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
13
{@
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0]
[ 0 -1 0 0 0 0 0 0 0 1]
[ 0 0 -1 0 0 1 0 0 0 0]
[ 0 0 0 -1 0 0 1 0 0 0]
[ 1 0 0 0 -1 0 0 0 0 0]
[ 0 0 1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 -1 1 0]
[ 0 0 0 0 0 0 0 1 -1 0]
[ 0 1 0 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
14
{@
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2)
@}
Intersection Matrix:
[-1 1 0 2 1 1 1 0 2 0 1 2 0 1 0 2 1 0 0 1]
[ 1 -1 2 1 1 0 0 1 0 1 1 0 2 0 0 0 1 2 1 2]
[ 0 2 -1 1 1 2 1 1 2 0 0 1 0 1 1 2 1 0 0 0]
[ 2 1 1 -1 1 1 0 2 0 2 0 0 1 1 2 0 0 1 1 0]
[ 1 1 1 1 -1 0 2 0 1 0 2 1 1 0 0 0 2 0 2 1]
[ 1 0 2 1 0 -1 1 0 0 1 2 1 1 0 0 0 1 1 2 2]
[ 1 0 1 0 2 1 -1 2 0 2 0 0 1 1 1 1 0 2 0 1]
[ 0 1 1 2 0 0 2 -1 1 0 2 2 0 1 0 1 1 0 1 1]
[ 2 0 2 0 1 0 0 1 -1 2 1 0 1 1 1 0 0 2 1 1]
[ 0 1 0 2 0 1 2 0 2 -1 1 1 1 0 0 1 2 0 1 1]
[ 1 1 0 0 2 2 0 2 1 1 -1 0 1 1 2 1 0 1 0 0]
[ 2 0 1 0 1 1 0 2 0 1 0 -1 2 0 1 0 1 2 1 1]
[ 0 2 0 1 1 1 1 0 1 1 1 2 -1 2 1 2 0 0 0 0]
[ 1 0 1 1 0 0 1 1 1 0 1 0 2 -1 0 0 2 1 2 2]
[ 0 0 1 2 0 0 1 0 1 0 2 1 1 0 -1 1 2 1 1 2]
[ 2 0 2 0 0 0 1 1 0 1 1 0 2 0 1 -1 1 1 2 1]
[ 1 1 1 0 2 1 0 1 0 2 0 1 0 2 2 1 -1 1 0 0]
[ 0 2 0 1 0 1 2 0 2 0 1 2 0 1 1 1 1 -1 1 0]
[ 0 1 0 1 2 2 0 1 1 1 0 1 0 2 1 2 0 1 -1 0]
[ 1 2 0 0 1 2 1 1 1 1 0 1 0 2 2 1 0 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
15
{@
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 0 2 0 2 1 1 0 0 1 1 0 0 2 2 1 1 1 0 1]
[ 0 -1 2 0 1 0 2 1 0 1 0 0 0 1 2 1 1 1 1 2]
[ 2 2 -1 1 0 1 0 1 1 0 1 2 2 0 0 1 1 0 1 0]
[ 0 0 1 -1 2 1 1 0 0 1 0 1 0 1 2 2 1 0 1 2]
[ 2 1 0 2 -1 0 1 2 1 0 1 1 2 0 0 0 1 1 1 0]
[ 1 0 1 1 0 -1 2 2 1 1 0 0 1 0 1 0 0 2 2 1]
[ 1 2 0 1 1 2 -1 0 1 0 2 2 1 1 0 1 1 0 0 0]
[ 0 1 1 0 2 2 0 -1 0 1 1 1 0 2 1 2 1 0 0 1]
[ 0 0 1 0 1 1 1 0 -1 0 1 1 1 2 2 2 2 0 0 1]
[ 1 1 0 1 0 1 0 1 0 -1 2 2 2 1 1 1 2 0 0 0]
[ 1 0 1 0 1 0 2 1 1 2 -1 0 0 0 1 1 0 1 2 2]
[ 0 0 2 1 1 0 2 1 1 2 0 -1 0 1 1 0 0 2 1 1]
[ 0 0 2 0 2 1 1 0 1 2 0 0 -1 1 1 1 0 1 1 2]
[ 2 1 0 1 0 0 1 2 2 1 0 1 1 -1 0 0 0 1 2 1]
[ 2 2 0 2 0 1 0 1 2 1 1 1 1 0 -1 0 0 1 1 0]
[ 1 1 1 2 0 0 1 2 2 1 1 0 1 0 0 -1 0 2 1 0]
[ 1 1 1 1 1 0 1 1 2 2 0 0 0 0 0 0 -1 2 2 1]
[ 1 1 0 0 1 2 0 0 0 0 1 2 1 1 1 2 2 -1 0 1]
[ 0 1 1 1 1 2 0 0 0 0 2 1 1 2 1 1 2 0 -1 0]
[ 1 2 0 2 0 1 0 1 1 0 2 1 2 1 0 0 1 1 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
16
{@
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2)
@}
Intersection Matrix:
[-1 1 0 1 1 1 0 1 1 0 1 2 2 0 2 2 0 0 1 0]
[ 1 -1 2 2 0 0 1 1 1 0 0 0 0 1 1 0 1 2 1 2]
[ 0 2 -1 0 1 2 1 0 1 1 1 2 2 0 1 1 0 0 1 0]
[ 1 2 0 -1 2 1 0 1 0 2 2 1 1 1 0 1 1 0 0 0]
[ 1 0 1 2 -1 1 2 0 1 0 0 1 0 1 1 0 0 1 2 2]
[ 1 0 2 1 1 -1 0 2 0 1 1 0 0 2 0 1 2 1 0 1]
[ 0 1 1 0 2 0 -1 2 0 1 2 1 1 1 1 2 1 0 0 0]
[ 1 1 0 1 0 2 2 -1 2 0 0 1 1 0 1 0 0 1 2 1]
[ 1 1 1 0 1 0 0 2 -1 2 2 1 0 2 0 1 1 0 0 1]
[ 0 0 1 2 0 1 1 0 2 -1 0 1 1 0 2 1 0 1 2 1]
[ 1 0 1 2 0 1 2 0 2 0 -1 0 1 0 1 0 1 2 1 1]
[ 2 0 2 1 1 0 1 1 1 1 0 -1 0 1 0 0 2 2 0 1]
[ 2 0 2 1 0 0 1 1 0 1 1 0 -1 2 0 0 1 1 1 2]
[ 0 1 0 1 1 2 1 0 2 0 0 1 2 -1 2 1 0 1 1 0]
[ 2 1 1 0 1 0 1 1 0 2 1 0 0 2 -1 0 2 1 0 1]
[ 2 0 1 1 0 1 2 0 1 1 0 0 0 1 0 -1 1 2 1 2]
[ 0 1 0 1 0 2 1 0 1 0 1 2 1 0 2 1 -1 0 2 1]
[ 0 2 0 0 1 1 0 1 0 1 2 2 1 1 1 2 0 -1 1 0]
[ 1 1 1 0 2 0 0 2 0 2 1 0 1 1 0 1 2 1 -1 0]
[ 0 2 0 0 2 1 0 1 1 1 1 1 2 0 1 2 1 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
17
{@
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1)
@}
Intersection Matrix:
[-1 0 1 2 1 0 0 1 0 0 2 0 1 2 1 0 1 2 1 1]
[ 0 -1 2 1 1 0 1 2 1 0 2 0 1 2 1 0 0 1 0 1]
[ 1 2 -1 0 0 2 1 0 0 1 0 2 1 0 0 1 1 1 2 1]
[ 2 1 0 -1 0 2 2 1 1 1 0 2 1 0 0 1 0 0 1 1]
[ 1 1 0 0 -1 1 2 1 0 0 1 2 1 0 0 1 0 1 2 2]
[ 0 0 2 2 1 -1 0 1 1 0 2 0 0 1 2 1 1 1 0 1]
[ 0 1 1 2 2 0 -1 0 1 1 1 0 0 1 2 1 2 1 0 0]
[ 1 2 0 1 1 1 0 -1 1 2 0 1 0 0 1 2 2 0 1 0]
[ 0 1 0 1 0 1 1 1 -1 0 1 1 2 1 0 0 0 2 2 2]
[ 0 0 1 1 0 0 1 2 0 -1 2 1 1 1 1 0 0 2 1 2]
[ 2 2 0 0 1 2 1 0 1 2 -1 1 1 0 0 1 1 0 1 0]
[ 0 0 2 2 2 0 0 1 1 1 1 -1 1 2 1 0 1 1 0 0]
[ 1 1 1 1 1 0 0 0 2 1 1 1 -1 0 2 2 2 0 0 0]
[ 2 2 0 0 0 1 1 0 1 1 0 2 0 -1 1 2 1 0 1 1]
[ 1 1 0 0 0 2 2 1 0 1 0 1 2 1 -1 0 0 1 2 1]
[ 0 0 1 1 1 1 1 2 0 0 1 0 2 2 0 -1 0 2 1 1]
[ 1 0 1 0 0 1 2 2 0 0 1 1 2 1 0 0 -1 1 1 2]
[ 2 1 1 0 1 1 1 0 2 2 0 1 0 0 1 2 1 -1 0 0]
[ 1 0 2 1 2 0 0 1 2 1 1 0 0 1 2 1 1 0 -1 0]
[ 1 1 1 1 2 1 0 0 2 2 0 0 0 1 1 1 2 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
18
{@
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 1 0 1 1 1 2 0 1 1 1 2 1 0 0 1 1 0 1 1]
[ 1 -1 1 2 0 0 1 1 1 1 1 0 0 2 1 1 1 1 1 0]
[ 0 1 -1 0 1 1 2 1 0 1 1 2 1 1 1 0 1 1 0 1]
[ 1 2 0 -1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 2]
[ 1 0 1 1 -1 0 1 2 2 1 0 0 0 1 1 1 1 1 1 1]
[ 1 0 1 1 0 -1 1 1 1 1 1 0 0 1 1 2 0 2 1 1]
[ 2 1 2 1 1 1 -1 1 1 0 0 0 1 1 1 1 0 1 1 0]
[ 0 1 1 1 2 1 1 -1 0 1 2 1 1 0 0 1 1 0 1 1]
[ 1 1 0 0 2 1 1 0 -1 1 2 1 1 1 1 0 1 1 0 1]
[ 1 1 1 1 1 1 0 1 1 -1 0 1 0 1 2 1 0 1 2 0]
[ 1 1 1 1 0 1 0 2 2 0 -1 1 1 1 1 1 0 1 1 0]
[ 2 0 2 1 0 0 0 1 1 1 1 -1 0 1 1 1 1 1 1 1]
[ 1 0 1 1 0 0 1 1 1 0 1 0 -1 1 2 1 1 1 2 1]
[ 0 2 1 0 1 1 1 0 1 1 1 1 1 -1 0 1 1 0 1 2]
[ 0 1 1 1 1 1 1 0 1 2 1 1 2 0 -1 1 1 0 0 1]
[ 1 1 0 0 1 2 1 1 0 1 1 1 1 1 1 -1 2 0 0 1]
[ 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 2 -1 2 1 0]
[ 0 1 1 1 1 2 1 0 1 1 1 1 1 0 0 0 2 -1 1 1]
[ 1 1 0 0 1 1 1 1 0 2 1 1 2 1 0 0 1 1 -1 1]
[ 1 0 1 2 1 1 0 1 1 0 0 1 1 2 1 1 0 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
19
{@
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2),
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2),
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 2 1 1 1 1 0 0 1 1 1 0 1 2 0 1 1 1 1]
[ 0 -1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 2 1 2 0]
[ 2 1 -1 0 1 0 0 1 1 1 1 1 1 1 0 2 0 1 1 1]
[ 1 1 0 -1 1 0 0 1 2 1 1 1 1 0 1 1 0 2 1 1]
[ 1 1 1 1 -1 2 1 0 1 2 1 0 1 1 1 0 1 0 1 0]
[ 1 1 0 0 2 -1 0 2 1 0 1 1 1 1 1 1 0 1 1 1]
[ 1 1 0 0 1 0 -1 1 1 1 0 2 2 1 1 1 0 1 1 1]
[ 0 0 1 1 0 2 1 -1 0 2 1 1 0 1 1 1 1 1 1 1]
[ 0 0 1 2 1 1 1 0 -1 1 1 1 0 2 1 1 1 0 1 1]
[ 1 1 1 1 2 0 1 2 1 -1 0 1 1 0 0 1 1 1 0 1]
[ 1 1 1 1 1 1 0 1 1 0 -1 2 2 0 0 1 1 1 0 1]
[ 1 1 1 1 0 1 2 1 1 1 2 -1 0 1 1 0 1 0 1 0]
[ 0 0 1 1 1 1 2 0 0 1 2 0 -1 1 1 1 1 1 1 1]
[ 1 1 1 0 1 1 1 1 2 0 0 1 1 -1 0 1 1 2 0 1]
[ 2 1 0 1 1 1 1 1 1 0 0 1 1 0 -1 2 1 1 0 1]
[ 0 1 2 1 0 1 1 1 1 1 1 0 1 1 2 -1 1 0 1 0]
[ 1 2 0 0 1 0 0 1 1 1 1 1 1 1 1 1 -1 1 0 2]
[ 1 1 1 2 0 1 1 1 0 1 1 0 1 2 1 0 1 -1 1 0]
[ 1 2 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 -1 2]
[ 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 2 0 2 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
20
{@
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 1 1 2 1 1 2 0 1 1 1 0 2 0 1 1 2 2 0 2]
[ 1 -1 0 1 0 2 1 1 2 2 0 1 1 1 1 1 2 2 2 0]
[ 1 0 -1 1 0 1 2 2 2 2 0 1 1 1 1 2 1 2 1 0]
[ 2 1 1 -1 2 1 0 2 1 2 1 1 0 2 0 1 0 1 2 1]
[ 1 0 0 2 -1 2 1 1 2 1 0 2 1 1 1 2 1 2 1 0]
[ 1 2 1 1 2 -1 2 2 0 0 2 1 1 1 1 0 1 0 1 2]
[ 2 1 2 0 1 2 -1 1 1 1 1 2 0 2 0 1 0 1 2 1]
[ 0 1 2 2 1 2 1 -1 1 1 1 0 2 0 2 1 2 1 0 1]
[ 1 2 2 1 2 0 1 1 -1 0 1 1 2 2 1 0 1 0 1 2]
[ 1 2 2 2 1 0 1 1 0 -1 2 2 1 1 1 0 1 0 1 2]
[ 1 0 0 1 0 2 1 1 1 2 -1 1 2 2 1 2 1 2 1 0]
[ 0 1 1 1 2 1 2 0 1 2 1 -1 2 0 2 1 2 1 0 1]
[ 2 1 1 0 1 1 0 2 2 1 2 2 -1 1 0 1 0 1 2 1]
[ 0 1 1 2 1 1 2 0 2 1 2 0 1 -1 2 1 2 1 0 1]
[ 1 1 1 0 1 1 0 2 1 1 1 2 0 2 -1 1 0 2 2 2]
[ 1 1 2 1 2 0 1 1 0 0 2 1 1 1 1 -1 2 0 2 2]
[ 2 2 1 0 1 1 0 2 1 1 1 2 0 2 0 2 -1 1 1 1]
[ 2 2 2 1 2 0 1 1 0 0 2 1 1 1 2 0 1 -1 1 1]
[ 0 2 1 2 1 1 2 0 1 1 1 0 2 0 2 2 1 1 -1 1]
[ 2 0 0 1 0 2 1 1 2 2 0 1 1 1 2 2 1 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
21
{@
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2),
Mod: ( 1 0 0 -1 0 0 0 0 -1),
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1)
@}
Intersection Matrix:
[-1 0 0 0 1 0 1 2 1 2 1 2 1 1 1 2 2 2 1 1]
[ 0 -1 0 0 1 0 1 2 2 2 1 2 1 2 1 1 1 1 2 1]
[ 0 0 -1 0 2 0 1 2 2 1 1 2 2 1 1 1 2 1 1 1]
[ 0 0 0 -1 1 0 2 2 2 2 2 1 1 1 1 1 2 1 1 1]
[ 1 1 2 1 -1 1 2 1 1 2 0 1 1 2 0 0 1 2 0 2]
[ 0 0 0 0 1 -1 1 1 2 2 1 2 1 1 2 1 2 1 1 2]
[ 1 1 1 2 2 1 -1 1 1 1 1 2 0 0 2 2 1 0 2 0]
[ 2 2 2 2 1 1 1 -1 0 0 1 0 1 1 2 1 0 1 1 2]
[ 1 2 2 2 1 2 1 0 -1 0 1 0 1 1 1 2 0 2 1 1]
[ 2 2 1 2 2 2 1 0 0 -1 1 0 2 1 1 1 0 1 1 1]
[ 1 1 1 2 0 1 1 1 1 1 -1 2 2 2 0 0 1 2 0 2]
[ 2 2 2 1 1 2 2 0 0 0 2 -1 1 1 1 1 0 1 1 1]
[ 1 1 2 1 1 1 0 1 1 2 2 1 -1 0 2 2 1 0 2 0]
[ 1 2 1 1 2 1 0 1 1 1 2 1 0 -1 2 2 2 0 1 0]
[ 1 1 1 1 0 2 2 2 1 1 0 1 2 2 -1 0 1 2 0 1]
[ 2 1 1 1 0 1 2 1 2 1 0 1 2 2 0 -1 1 1 0 2]
[ 2 1 2 2 1 2 1 0 0 0 1 0 1 2 1 1 -1 1 2 1]
[ 2 1 1 1 2 1 0 1 2 1 2 1 0 0 2 1 1 -1 2 0]
[ 1 2 1 1 0 1 2 1 1 1 0 1 2 1 0 0 2 2 -1 2]
[ 1 1 1 1 2 2 0 2 1 1 2 1 0 0 1 2 1 0 2 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D7(5):F5
order := 20,
length := 4354560,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 5
Generators:
[ 4 0 1 2 1 2 1 2 0]
[-1 0 0 -1 0 -1 0 0 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-2 0 0 -1 -1 -1 -1 -1 0]
[-1 0 0 -1 0 0 0 -1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[-2 0 -1 -1 -1 -1 0 -1 0]
[ 7 1 3 4 2 3 1 2 2]
[-1 0 -1 -1 0 0 0 0 0]
[-3 -1 -1 -2 -1 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-1 0 0 -1 0 -1 0 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]>
Orbit type:{4,4,4,4,4,10,10,10,10,20,20,20,20,20,20,20,20,20}
Orbit:
1
{@
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 0 2 2]
[ 0 -1 2 2]
[ 2 2 -1 0]
[ 2 2 0 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
2
{@
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 2 2 0]
[ 2 -1 0 2]
[ 2 0 -1 2]
[ 0 2 2 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
3
{@
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 3]
[ 1 -1 3 1]
[ 1 3 -1 1]
[ 3 1 1 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
4
{@
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1)
@}
Intersection Matrix:
[-1 1 0 0]
[ 1 -1 0 0]
[ 0 0 -1 1]
[ 0 0 1 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
5
{@
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 0 0]
[ 1 -1 0 0]
[ 0 0 -1 1]
[ 0 0 1 -1]
Stabilizer Group Name:
C5
MatrixGroup(9, Integer Ring)
Generators:
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
6
{@
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 2 1 2 2 1 1 0 2 0]
[ 2 -1 1 1 0 2 0 2 1 2]
[ 1 1 -1 2 2 0 2 1 2 0]
[ 2 1 2 -1 0 2 1 2 0 1]
[ 2 0 2 0 -1 2 1 1 1 2]
[ 1 2 0 2 2 -1 2 0 1 1]
[ 1 0 2 1 1 2 -1 2 0 2]
[ 0 2 1 2 1 0 2 -1 2 1]
[ 2 1 2 0 1 1 0 2 -1 2]
[ 0 2 0 1 2 1 2 1 2 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 7 1 3 4 2 3 1 2 2]
[-1 0 -1 -1 0 0 0 0 0]
[-3 -1 -1 -2 -1 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-1 0 0 -1 0 -1 0 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
7
{@
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2)
@}
Intersection Matrix:
[-1 2 1 1 2 2 1 2 0 0]
[ 2 -1 2 1 0 1 2 0 1 2]
[ 1 2 -1 2 2 2 0 1 1 0]
[ 1 1 2 -1 1 0 2 0 2 2]
[ 2 0 2 1 -1 0 2 1 2 1]
[ 2 1 2 0 0 -1 1 1 2 2]
[ 1 2 0 2 2 1 -1 2 0 1]
[ 2 0 1 0 1 1 2 -1 2 2]
[ 0 1 1 2 2 2 0 2 -1 1]
[ 0 2 0 2 1 2 1 2 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[12 4 4 5 3 4 4 3 6]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-4 -2 -1 -2 -1 -1 -1 -1 -2]
[-5 -2 -2 -2 -1 -2 -2 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -1 -1 -2 -1 -2 -1 -1 -2]
[-4 -1 -1 -2 -1 -1 -2 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
8
{@
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 0 0 -1 0 0 0 0 -1)
@}
Intersection Matrix:
[-1 0 1 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 1 0 0 0 0]
[ 1 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 -1 1 0 0 0 0 0]
[ 0 0 0 1 -1 0 0 0 0 0]
[ 0 1 0 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 1]
[ 0 0 0 0 0 0 0 -1 1 0]
[ 0 0 0 0 0 0 0 1 -1 0]
[ 0 0 0 0 0 0 1 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 8 2 3 4 2 1 4 3 2]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-3 -1 -1 -2 -1 0 -1 -1 -1]
[-4 -1 -2 -2 -1 -1 -2 -1 -1]
[-2 0 -1 -1 0 0 -1 -1 -1]
[-1 0 0 -1 0 0 -1 0 0]
[-4 -1 -1 -2 -1 -1 -2 -2 -1]
[-3 -1 -1 -1 -1 0 -2 -1 -1]
[-2 0 -1 -1 -1 0 -1 -1 0]
9
{@
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 0 0 0 1 0 0 0]
[ 0 0 -1 0 0 0 0 0 0 1]
[ 0 0 0 -1 0 0 0 1 0 0]
[ 0 0 0 0 -1 1 0 0 0 0]
[ 0 0 0 0 1 -1 0 0 0 0]
[ 0 1 0 0 0 0 -1 0 0 0]
[ 0 0 0 1 0 0 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 3 1 2 0 2 2 1 1]
[-3 -2 -1 -1 0 -1 -1 -1 -1]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 0 -1]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
10
{@
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3),
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2),
Mod: ( 1 -1 0 0 0 0 -1 0 0)
@}
Intersection Matrix:
[-1 0 2 1 1 0 0 1 0 2 2 3 1 2 1 1 2 0 2 0]
[ 0 -1 2 1 0 0 2 1 1 1 0 2 2 2 0 2 3 1 1 0]
[ 2 2 -1 2 0 2 1 0 0 1 1 0 2 0 1 1 0 1 2 3]
[ 1 1 2 -1 2 2 1 3 2 2 1 1 0 0 0 2 1 0 0 0]
[ 1 0 0 2 -1 1 2 0 0 1 0 1 3 1 0 2 2 1 2 2]
[ 0 0 2 2 1 -1 1 0 1 0 1 2 1 3 2 0 2 2 1 0]
[ 0 2 1 1 2 1 -1 1 0 2 3 2 0 1 2 0 0 0 2 1]
[ 1 1 0 3 0 0 1 -1 0 0 1 1 2 2 2 0 1 2 2 2]
[ 0 1 0 2 0 1 0 0 -1 2 2 2 2 1 1 1 1 0 3 2]
[ 2 1 1 2 1 0 2 0 2 -1 0 0 1 2 2 0 1 3 0 1]
[ 2 0 1 1 0 1 3 1 2 0 -1 0 2 1 0 2 2 2 0 1]
[ 3 2 0 1 1 2 2 1 2 0 0 -1 1 0 1 1 0 2 0 2]
[ 1 2 2 0 3 1 0 2 2 1 2 1 -1 1 2 0 0 1 0 0]
[ 2 2 0 0 1 3 1 2 1 2 1 0 1 -1 0 2 0 0 1 2]
[ 1 0 1 0 0 2 2 2 1 2 0 1 2 0 -1 3 2 0 1 1]
[ 1 2 1 2 2 0 0 0 1 0 2 1 0 2 3 -1 0 2 1 1]
[ 2 3 0 1 2 2 0 1 1 1 2 0 0 0 2 0 -1 1 1 2]
[ 0 1 1 0 1 2 0 2 0 3 2 2 1 0 0 2 1 -1 2 1]
[ 2 1 2 0 2 1 2 2 3 0 0 0 0 1 1 1 1 2 -1 0]
[ 0 0 3 0 2 0 1 2 2 1 1 2 0 2 1 1 2 1 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
11
{@
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2)
@}
Intersection Matrix:
[-1 1 0 1 1 1 1 1 1 1 0 1 1 0 2 1 2 1 0 0]
[ 1 -1 1 1 0 0 1 0 1 1 1 1 0 2 0 2 1 1 1 1]
[ 0 1 -1 1 1 1 0 2 1 1 0 1 1 0 1 1 1 2 1 0]
[ 1 1 1 -1 1 0 1 1 1 2 2 0 0 1 1 1 0 0 1 1]
[ 1 0 1 1 -1 0 1 0 2 1 1 0 1 1 0 1 1 1 1 2]
[ 1 0 1 0 0 -1 1 0 1 2 2 1 1 1 0 1 1 1 1 1]
[ 1 1 0 1 1 1 -1 2 0 0 1 1 1 1 1 0 1 2 0 1]
[ 1 0 2 1 0 0 2 -1 1 1 1 1 1 1 0 1 1 0 1 1]
[ 1 1 1 1 2 1 0 1 -1 0 1 2 1 1 1 0 1 1 0 0]
[ 1 1 1 2 1 2 0 1 0 -1 0 1 1 1 1 0 1 1 0 1]
[ 0 1 0 2 1 2 1 1 1 0 -1 1 1 0 1 1 1 1 1 0]
[ 1 1 1 0 0 1 1 1 2 1 1 -1 0 1 1 1 0 0 1 2]
[ 1 0 1 0 1 1 1 1 1 1 1 0 -1 2 1 2 0 0 1 1]
[ 0 2 0 1 1 1 1 1 1 1 0 1 2 -1 1 0 1 1 1 0]
[ 2 0 1 1 0 0 1 0 1 1 1 1 1 1 -1 1 0 1 2 1]
[ 1 2 1 1 1 1 0 1 0 0 1 1 2 0 1 -1 1 1 0 1]
[ 2 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 -1 0 2 1]
[ 1 1 2 0 1 1 2 0 1 1 1 0 0 1 1 1 0 -1 1 1]
[ 0 1 1 1 1 1 0 1 0 0 1 1 1 1 2 0 2 1 -1 1]
[ 0 1 0 1 2 1 1 1 0 1 0 2 1 0 1 1 1 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
12
{@
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 1 0 2 0 1 1 0 1 1 1 0 1 1 0 1 1 2 1 1]
[ 1 -1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 2 2]
[ 0 0 -1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 2 2]
[ 2 1 1 -1 1 1 0 2 1 0 1 1 1 1 1 1 0 0 0 1]
[ 0 1 0 1 -1 2 1 1 1 2 1 0 1 0 0 1 1 1 1 1]
[ 1 1 1 1 2 -1 1 1 1 0 1 1 0 2 1 0 1 0 1 0]
[ 1 1 1 0 1 1 -1 1 1 0 2 2 1 1 1 0 0 1 0 1]
[ 0 0 1 2 1 1 1 -1 0 1 0 1 1 0 1 1 1 2 1 1]
[ 1 0 1 1 1 1 1 0 -1 1 0 1 2 0 0 1 2 1 1 1]
[ 1 1 1 0 2 0 0 1 1 -1 1 1 1 2 1 1 0 1 0 1]
[ 1 0 1 1 1 1 2 0 0 1 -1 0 1 0 1 2 1 1 1 1]
[ 0 1 0 1 0 1 2 1 1 1 0 -1 1 1 0 2 1 1 1 1]
[ 1 1 1 1 1 0 1 1 2 1 1 1 -1 1 2 0 0 0 1 0]
[ 1 0 1 1 0 2 1 0 0 2 0 1 1 -1 1 1 1 1 1 1]
[ 0 1 0 1 0 1 1 1 0 1 1 0 2 1 -1 1 2 1 1 1]
[ 1 1 1 1 1 0 0 1 1 1 2 2 0 1 1 -1 1 0 1 0]
[ 1 1 1 0 1 1 0 1 2 0 1 1 0 1 2 1 -1 1 0 1]
[ 2 1 1 0 1 0 1 2 1 1 1 1 0 1 1 0 1 -1 1 0]
[ 1 2 2 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 -1 0]
[ 1 2 2 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
13
{@
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2)
@}
Intersection Matrix:
[-1 1 1 2 1 1 1 1 1 0 0 0 0 2 1 1 1 1 1 0]
[ 1 -1 1 1 0 2 0 1 0 1 1 1 2 0 1 1 1 1 1 0]
[ 1 1 -1 1 1 0 0 2 1 1 2 0 1 1 1 0 1 1 0 1]
[ 2 1 1 -1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 2]
[ 1 0 1 1 -1 1 0 1 1 1 0 1 1 0 2 2 1 1 0 1]
[ 1 2 0 0 1 -1 1 1 1 1 1 0 0 1 1 1 1 1 0 2]
[ 1 0 0 1 0 1 -1 2 1 0 1 1 1 0 1 1 2 1 1 1]
[ 1 1 2 0 1 1 2 -1 0 1 0 1 1 1 0 1 0 1 1 1]
[ 1 0 1 0 1 1 1 0 -1 1 1 0 2 1 0 1 1 2 1 1]
[ 0 1 1 1 1 1 0 1 1 -1 0 1 0 1 0 1 2 1 2 1]
[ 0 1 2 1 0 1 1 0 1 0 -1 1 0 1 1 2 1 1 1 1]
[ 0 1 0 1 1 0 1 1 0 1 1 -1 1 2 1 1 1 2 0 1]
[ 0 2 1 1 1 0 1 1 2 0 0 1 -1 1 1 1 1 0 1 1]
[ 2 0 1 0 0 1 0 1 1 1 1 2 1 -1 1 1 1 0 1 1]
[ 1 1 1 0 2 1 1 0 0 0 1 1 1 1 -1 0 1 1 2 1]
[ 1 1 0 1 2 1 1 1 1 1 2 1 1 1 0 -1 0 0 1 0]
[ 1 1 1 1 1 1 2 0 1 2 1 1 1 1 1 0 -1 0 0 0]
[ 1 1 1 1 1 1 1 1 2 1 1 2 0 0 1 0 0 -1 1 0]
[ 1 1 0 1 0 0 1 1 1 2 1 0 1 1 2 1 0 1 -1 1]
[ 0 0 1 2 1 2 1 1 1 1 1 1 1 1 1 0 0 0 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
14
{@
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 1 1 0 2 1 1 0 0 1 0 2 1 0 1 1 1 1]
[ 1 -1 0 1 1 2 1 1 0 1 0 1 1 1 0 1 1 2 1 0]
[ 1 0 -1 1 1 1 1 1 0 2 0 1 0 0 1 1 2 1 1 1]
[ 1 1 1 -1 2 1 1 0 1 1 0 1 2 0 1 1 0 0 1 1]
[ 1 1 1 2 -1 1 0 1 1 0 2 1 0 1 0 1 1 1 0 1]
[ 0 2 1 1 1 -1 1 1 1 1 1 0 0 1 2 0 1 0 1 1]
[ 2 1 1 1 0 1 -1 1 1 1 2 0 1 0 1 1 0 1 1 0]
[ 1 1 1 0 1 1 1 -1 2 1 1 2 1 0 0 0 1 0 1 1]
[ 1 0 0 1 1 1 1 2 -1 1 0 0 1 1 1 2 1 1 0 1]
[ 0 1 2 1 0 1 1 1 1 -1 1 1 1 2 0 1 0 1 0 1]
[ 0 0 0 0 2 1 2 1 0 1 -1 1 1 1 1 1 1 1 1 1]
[ 1 1 1 1 1 0 0 2 0 1 1 -1 1 1 2 1 0 1 1 0]
[ 0 1 0 2 0 0 1 1 1 1 1 1 -1 1 1 0 2 1 1 1]
[ 2 1 0 0 1 1 0 0 1 2 1 1 1 -1 1 1 1 0 1 1]
[ 1 0 1 1 0 2 1 0 1 0 1 2 1 1 -1 1 1 1 0 1]
[ 0 1 1 1 1 0 1 0 2 1 1 1 0 1 1 -1 1 1 2 0]
[ 1 1 2 0 1 1 0 1 1 0 1 0 2 1 1 1 -1 1 1 0]
[ 1 2 1 0 1 0 1 0 1 1 1 1 1 0 1 1 1 -1 0 2]
[ 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 2 1 0 -1 2]
[ 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 2 2 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
15
{@
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2),
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2)
@}
Intersection Matrix:
[-1 0 1 1 0 1 1 0 1 2 1 0 1 1 2 1 1 0 1 1]
[ 0 -1 1 1 1 1 1 1 0 1 2 0 1 0 1 2 1 0 1 1]
[ 1 1 -1 0 1 1 2 0 0 1 0 1 1 1 1 1 0 2 1 1]
[ 1 1 0 -1 0 1 1 1 1 1 1 1 1 0 1 0 1 2 0 2]
[ 0 1 1 0 -1 1 1 1 1 1 1 1 0 1 2 0 2 1 0 1]
[ 1 1 1 1 1 -1 0 0 1 1 1 2 0 0 0 1 1 1 2 1]
[ 1 1 2 1 1 0 -1 1 2 1 1 1 1 0 0 0 1 0 1 1]
[ 0 1 0 1 1 0 1 -1 1 2 0 1 1 1 1 1 0 1 2 1]
[ 1 0 0 1 1 1 2 1 -1 0 1 1 0 1 1 2 1 1 1 0]
[ 2 1 1 1 1 1 1 2 0 -1 1 1 0 1 0 1 1 1 0 0]
[ 1 2 0 1 1 1 1 0 1 1 -1 1 1 2 1 0 0 1 1 0]
[ 0 0 1 1 1 2 1 1 1 1 1 -1 2 1 1 1 0 0 0 1]
[ 1 1 1 1 0 0 1 1 0 0 1 2 -1 1 1 1 2 1 1 0]
[ 1 0 1 0 1 0 0 1 1 1 2 1 1 -1 0 1 1 1 1 2]
[ 2 1 1 1 2 0 0 1 1 0 1 1 1 0 -1 1 0 1 1 1]
[ 1 2 1 0 0 1 0 1 2 1 0 1 1 1 1 -1 1 1 0 1]
[ 1 1 0 1 2 1 1 0 1 1 0 0 2 1 0 1 -1 1 1 1]
[ 0 0 2 2 1 1 0 1 1 1 1 0 1 1 1 1 1 -1 1 0]
[ 1 1 1 0 0 2 1 2 1 0 1 0 1 1 1 0 1 1 -1 1]
[ 1 1 1 2 1 1 1 1 0 0 0 1 0 2 1 1 1 0 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
16
{@
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1),
Mod: ( 1 0 -1 0 -1 0 0 0 0)
@}
Intersection Matrix:
[-1 0 1 0 1 1 0 1 1 2 1 1 0 1 1 0 2 1 1 1]
[ 0 -1 1 1 2 1 0 1 1 1 1 0 1 0 2 0 1 1 1 1]
[ 1 1 -1 1 1 1 1 1 1 1 2 0 1 2 0 0 0 1 1 0]
[ 0 1 1 -1 0 1 1 0 1 2 0 1 1 1 1 1 1 1 2 0]
[ 1 2 1 0 -1 1 1 0 0 1 0 2 1 1 0 1 1 1 1 1]
[ 1 1 1 1 1 -1 1 1 2 1 0 0 0 1 0 2 1 1 0 1]
[ 0 0 1 1 1 1 -1 0 1 1 1 1 1 1 1 0 1 2 0 2]
[ 1 1 1 0 0 1 0 -1 1 1 0 1 2 1 1 1 0 2 1 1]
[ 1 1 1 1 0 2 1 1 -1 0 1 2 1 0 1 0 1 0 1 1]
[ 2 1 1 2 1 1 1 1 0 -1 1 1 1 0 1 1 0 0 0 1]
[ 1 1 2 0 0 0 1 0 1 1 -1 1 1 0 1 2 1 1 1 1]
[ 1 0 0 1 2 0 1 1 2 1 1 -1 1 1 1 1 0 1 1 0]
[ 0 1 1 1 1 0 1 2 1 1 1 1 -1 1 0 1 2 0 0 1]
[ 1 0 2 1 1 1 1 1 0 0 0 1 1 -1 2 1 1 0 1 1]
[ 1 2 0 1 0 0 1 1 1 1 1 1 0 2 -1 1 1 1 0 1]
[ 0 0 0 1 1 2 0 1 0 1 2 1 1 1 1 -1 1 1 1 1]
[ 2 1 0 1 1 1 1 0 1 0 1 0 2 1 1 1 -1 1 1 0]
[ 1 1 1 1 1 1 2 2 0 0 1 1 0 0 1 1 1 -1 1 0]
[ 1 1 1 2 1 0 0 1 1 0 1 1 0 1 0 1 1 1 -1 2]
[ 1 1 0 0 1 1 2 1 1 1 1 0 1 1 1 1 0 0 2 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
17
{@
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2),
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1)
@}
Intersection Matrix:
[-1 1 2 2 1 1 1 1 1 2 2 2 0 0 2 0 1 1 0 1]
[ 1 -1 0 2 1 1 1 1 1 2 0 0 2 2 0 2 1 1 2 1]
[ 2 0 -1 1 1 1 2 1 1 1 0 0 2 1 0 2 1 1 2 2]
[ 2 2 1 -1 0 0 2 2 2 1 1 1 1 1 1 1 0 2 1 0]
[ 1 1 1 0 -1 0 2 2 1 2 1 2 2 1 1 1 0 2 1 0]
[ 1 1 1 0 0 -1 2 2 2 2 2 1 1 1 1 1 0 1 2 0]
[ 1 1 2 2 2 2 -1 0 0 0 1 1 1 2 1 1 2 0 1 1]
[ 1 1 1 2 2 2 0 -1 0 0 1 1 1 1 2 2 1 0 1 2]
[ 1 1 1 2 1 2 0 0 -1 0 1 2 2 1 1 1 2 0 1 2]
[ 2 2 1 1 2 2 0 0 0 -1 1 1 1 1 1 1 2 0 1 2]
[ 2 0 0 1 1 2 1 1 1 1 -1 0 2 2 0 2 1 2 1 1]
[ 2 0 0 1 2 1 1 1 2 1 0 -1 1 2 0 2 1 1 2 1]
[ 0 2 2 1 2 1 1 1 2 1 2 1 -1 0 2 0 1 1 0 1]
[ 0 2 1 1 1 1 2 1 1 1 2 2 0 -1 2 0 1 1 0 2]
[ 2 0 0 1 1 1 1 2 1 1 0 0 2 2 -1 1 2 1 2 1]
[ 0 2 2 1 1 1 1 2 1 1 2 2 0 0 1 -1 2 1 0 1]
[ 1 1 1 0 0 0 2 1 2 2 1 1 1 1 2 2 -1 2 1 0]
[ 1 1 1 2 2 1 0 0 0 0 2 1 1 1 1 1 2 -1 2 2]
[ 0 2 2 1 1 2 1 1 1 1 1 2 0 0 2 0 1 2 -1 1]
[ 1 1 2 0 0 0 1 2 2 2 1 1 1 2 1 1 0 2 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
18
{@
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1),
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 0 1 0 1 2 0 2 1 2 2 1 1 1 2 1 2 1 0 1]
[ 0 -1 1 0 1 2 0 2 2 2 1 2 1 1 1 1 1 2 0 1]
[ 1 1 -1 1 2 2 2 1 2 1 2 0 1 0 1 2 0 1 1 0]
[ 0 0 1 -1 2 2 0 1 1 2 1 1 1 2 2 1 1 2 0 1]
[ 1 1 2 2 -1 1 1 2 0 1 0 2 0 1 1 0 2 1 1 2]
[ 2 2 2 2 1 -1 1 0 1 0 1 1 2 1 0 1 1 0 2 1]
[ 0 0 2 0 1 1 -1 2 1 2 1 1 2 1 2 1 1 2 0 1]
[ 2 2 1 1 2 0 2 -1 1 0 1 1 1 2 0 1 1 0 2 1]
[ 1 2 2 1 0 1 1 1 -1 1 0 1 0 2 2 0 2 1 1 2]
[ 2 2 1 2 1 0 2 0 1 -1 1 1 1 1 0 2 1 0 1 2]
[ 2 1 2 1 0 1 1 1 0 1 -1 2 0 2 1 0 1 2 1 2]
[ 1 2 0 1 2 1 1 1 1 1 2 -1 2 0 2 2 0 1 1 0]
[ 1 1 1 1 0 2 2 1 0 1 0 2 -1 2 1 0 2 1 1 2]
[ 1 1 0 2 1 1 1 2 2 1 2 0 2 -1 1 2 0 1 1 0]
[ 2 1 1 2 1 0 2 0 2 0 1 2 1 1 -1 1 1 0 2 1]
[ 1 1 2 1 0 1 1 1 0 2 0 2 0 2 1 -1 2 1 2 1]
[ 2 1 0 1 2 1 1 1 2 1 1 0 2 0 1 2 -1 2 1 0]
[ 1 2 1 2 1 0 2 0 1 0 2 1 1 1 0 1 2 -1 2 1]
[ 0 0 1 0 1 2 0 2 1 1 1 1 1 1 2 2 1 2 -1 2]
[ 1 1 0 1 2 1 1 1 2 2 2 0 2 0 1 1 0 1 2 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D7(6):C5⋊D4
order := 40,
length := 2177280,
subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 5
Generators:
[13 5 4 5 6 4 5 3 4]
[-5 -2 -1 -2 -2 -2 -2 -1 -2]
[-4 -1 -1 -2 -2 -1 -2 -1 -1]
[-5 -2 -2 -2 -2 -2 -2 -1 -1]
[-6 -2 -2 -2 -3 -2 -2 -2 -2]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-5 -2 -2 -2 -2 -1 -2 -1 -2]
[-3 -1 -1 -1 -2 -1 -1 0 -1]
[-4 -2 -1 -1 -2 -1 -2 -1 -1]
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{4,4,4,4,4,5,5,5,5,10,10,10,10,20,20,20,20,20,20,40}
Orbit:
1
{@
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2),
Mod: ( 1 0 -1 -1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 2 0 2]
[ 2 -1 2 0]
[ 0 2 -1 2]
[ 2 0 2 -1]
Stabilizer Group Name:
C10
MatrixGroup(9, Integer Ring)
Generators:
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
2
{@
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 2 0 2]
[ 2 -1 2 0]
[ 0 2 -1 2]
[ 2 0 2 -1]
Stabilizer Group Name:
C10
MatrixGroup(9, Integer Ring)
Generators:
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[ 7 2 2 4 1 1 3 3 2]
[-1 0 0 -1 0 0 -1 0 0]
[-4 -1 -1 -2 -1 -1 -2 -2 -1]
[-2 -1 0 -1 0 0 -1 -1 -1]
[-1 0 0 -1 0 0 0 -1 0]
[-3 -1 -1 -2 -1 0 -1 -1 -1]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 0 -1 -1 0 0 -1 -1 -1]
[-3 -1 -1 -2 0 -1 -1 -1 -1]
3
{@
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1)
@}
Intersection Matrix:
[-1 3 1 1]
[ 3 -1 1 1]
[ 1 1 -1 3]
[ 1 1 3 -1]
Stabilizer Group Name:
C10
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 0 0 1 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
4
{@
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1)
@}
Intersection Matrix:
[-1 0 1 0]
[ 0 -1 0 1]
[ 1 0 -1 0]
[ 0 1 0 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[12 4 3 4 5 3 4 6 4]
[-4 -1 -1 -1 -2 -1 -2 -2 -1]
[-3 -1 0 -1 -1 -1 -1 -2 -1]
[-4 -1 -1 -2 -2 -1 -1 -2 -1]
[-5 -2 -1 -2 -2 -1 -2 -2 -2]
[-3 -1 -1 -1 -1 0 -1 -2 -1]
[-4 -2 -1 -1 -2 -1 -1 -2 -1]
[-6 -2 -2 -2 -2 -2 -2 -3 -2]
[-4 -1 -1 -1 -2 -1 -1 -2 -2]
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
5
{@
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1)
@}
Intersection Matrix:
[-1 1 0 0]
[ 1 -1 0 0]
[ 0 0 -1 1]
[ 0 0 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[12 4 3 4 5 3 4 6 4]
[-4 -1 -1 -1 -2 -1 -2 -2 -1]
[-3 -1 0 -1 -1 -1 -1 -2 -1]
[-4 -1 -1 -2 -2 -1 -1 -2 -1]
[-5 -2 -1 -2 -2 -1 -2 -2 -2]
[-3 -1 -1 -1 -1 0 -1 -2 -1]
[-4 -2 -1 -1 -2 -1 -1 -2 -1]
[-6 -2 -2 -2 -2 -2 -2 -3 -2]
[-4 -1 -1 -1 -2 -1 -1 -2 -2]
[ 6 1 3 2 1 3 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-1 0 -1 0 0 -1 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
6
{@
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 2 1 1 2]
[ 2 -1 2 1 1]
[ 1 2 -1 2 1]
[ 1 1 2 -1 2]
[ 2 1 1 2 -1]
Stabilizer Group Name:
D4
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 9 4 2 2 2 2 4 4 4]
[-4 -1 -1 -1 -1 -1 -2 -2 -2]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-2 -1 0 -1 0 0 -1 -1 -1]
[-2 -1 0 0 -1 0 -1 -1 -1]
[-2 -1 -1 0 0 0 -1 -1 -1]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-4 -2 -1 -1 -1 -1 -2 -2 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
7
{@
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 -1 0)
@}
Intersection Matrix:
[-1 2 2 1 1]
[ 2 -1 1 2 1]
[ 2 1 -1 1 2]
[ 1 2 1 -1 2]
[ 1 1 2 2 -1]
Stabilizer Group Name:
D4
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[13 5 4 5 6 4 5 3 4]
[-5 -2 -1 -2 -2 -2 -2 -1 -2]
[-4 -1 -1 -2 -2 -1 -2 -1 -1]
[-5 -2 -2 -2 -2 -2 -2 -1 -1]
[-6 -2 -2 -2 -3 -2 -2 -2 -2]
[-4 -2 -1 -2 -2 -1 -1 -1 -1]
[-5 -2 -2 -2 -2 -1 -2 -1 -2]
[-3 -1 -1 -1 -2 -1 -1 0 -1]
[-4 -2 -1 -1 -2 -1 -2 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
8
{@
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 2 1 2 1]
[ 2 -1 2 1 1]
[ 1 2 -1 1 2]
[ 2 1 1 -1 2]
[ 1 1 2 2 -1]
Stabilizer Group Name:
D4
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 7 3 1 2 2 1 3 2 4]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-1 0 0 0 0 0 -1 0 -1]
[-2 -1 0 -1 0 0 -1 -1 -1]
[-2 -1 0 0 -1 0 -1 -1 -1]
[-1 -1 0 0 0 0 0 0 -1]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-2 -1 0 -1 -1 0 -1 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
9
{@
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1),
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2),
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0)
@}
Intersection Matrix:
[-1 1 2 1 2]
[ 1 -1 2 2 1]
[ 2 2 -1 1 1]
[ 1 2 1 -1 2]
[ 2 1 1 2 -1]
Stabilizer Group Name:
D4
MatrixGroup(9, Integer Ring)
Generators:
[10 3 2 4 5 2 3 4 4]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-2 0 0 -1 -1 0 -1 -1 -1]
[-4 -1 -1 -2 -2 -1 -1 -2 -1]
[-5 -2 -1 -2 -2 -1 -2 -2 -2]
[-2 -1 0 -1 -1 0 0 -1 -1]
[-3 -1 -1 -1 -2 0 -1 -1 -1]
[-4 -1 -1 -2 -2 -1 -1 -1 -2]
[-4 -1 -1 -1 -2 -1 -1 -2 -2]
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
10
{@
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3),
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2)
@}
Intersection Matrix:
[-1 1 2 3 0 1 2 1 1 0]
[ 1 -1 1 1 1 2 0 3 0 2]
[ 2 1 -1 0 3 2 1 1 0 1]
[ 3 1 0 -1 2 1 0 1 1 2]
[ 0 1 3 2 -1 0 1 1 2 1]
[ 1 2 2 1 0 -1 1 0 3 1]
[ 2 0 1 0 1 1 -1 2 1 3]
[ 1 3 1 1 1 0 2 -1 2 0]
[ 1 0 0 1 2 3 1 2 -1 1]
[ 0 2 1 2 1 1 3 0 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
11
{@
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2),
Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1 1 2 1 1 1 0 3 2 0]
[ 1 -1 0 3 0 2 2 1 1 1]
[ 2 0 -1 2 1 1 3 0 1 1]
[ 1 3 2 -1 2 0 0 1 1 1]
[ 1 0 1 2 -1 3 1 1 0 2]
[ 1 2 1 0 3 -1 1 1 2 0]
[ 0 2 3 0 1 1 -1 2 1 1]
[ 3 1 0 1 1 1 2 -1 0 2]
[ 2 1 1 1 0 2 1 0 -1 3]
[ 0 1 1 1 2 0 1 2 3 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
12
{@
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0]
[ 0 -1 0 0 0 0 0 0 0 1]
[ 0 0 -1 0 0 1 0 0 0 0]
[ 0 0 0 -1 0 0 1 0 0 0]
[ 1 0 0 0 -1 0 0 0 0 0]
[ 0 0 1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 -1 1 0]
[ 0 0 0 0 0 0 0 1 -1 0]
[ 0 1 0 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
13
{@
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 0 0 0 0 0 0 0 0]
[ 1 -1 0 0 0 0 0 0 0 0]
[ 0 0 -1 0 0 1 0 0 0 0]
[ 0 0 0 -1 0 0 0 0 0 1]
[ 0 0 0 0 -1 0 0 1 0 0]
[ 0 0 1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 1 0]
[ 0 0 0 0 1 0 0 -1 0 0]
[ 0 0 0 0 0 0 1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
14
{@
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2)
@}
Intersection Matrix:
[-1 1 0 2 1 1 1 0 2 0 1 2 0 1 0 2 1 0 0 1]
[ 1 -1 2 1 1 0 0 1 0 1 1 0 2 0 0 0 1 2 1 2]
[ 0 2 -1 1 1 2 1 1 2 0 0 1 0 1 1 2 1 0 0 0]
[ 2 1 1 -1 1 1 0 2 0 2 0 0 1 1 2 0 0 1 1 0]
[ 1 1 1 1 -1 0 2 0 1 0 2 1 1 0 0 0 2 0 2 1]
[ 1 0 2 1 0 -1 1 0 0 1 2 1 1 0 0 0 1 1 2 2]
[ 1 0 1 0 2 1 -1 2 0 2 0 0 1 1 1 1 0 2 0 1]
[ 0 1 1 2 0 0 2 -1 1 0 2 2 0 1 0 1 1 0 1 1]
[ 2 0 2 0 1 0 0 1 -1 2 1 0 1 1 1 0 0 2 1 1]
[ 0 1 0 2 0 1 2 0 2 -1 1 1 1 0 0 1 2 0 1 1]
[ 1 1 0 0 2 2 0 2 1 1 -1 0 1 1 2 1 0 1 0 0]
[ 2 0 1 0 1 1 0 2 0 1 0 -1 2 0 1 0 1 2 1 1]
[ 0 2 0 1 1 1 1 0 1 1 1 2 -1 2 1 2 0 0 0 0]
[ 1 0 1 1 0 0 1 1 1 0 1 0 2 -1 0 0 2 1 2 2]
[ 0 0 1 2 0 0 1 0 1 0 2 1 1 0 -1 1 2 1 1 2]
[ 2 0 2 0 0 0 1 1 0 1 1 0 2 0 1 -1 1 1 2 1]
[ 1 1 1 0 2 1 0 1 0 2 0 1 0 2 2 1 -1 1 0 0]
[ 0 2 0 1 0 1 2 0 2 0 1 2 0 1 1 1 1 -1 1 0]
[ 0 1 0 1 2 2 0 1 1 1 0 1 0 2 1 2 0 1 -1 0]
[ 1 2 0 0 1 2 1 1 1 1 0 1 0 2 2 1 0 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 0 0 1 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
15
{@
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 0 2 0 2 1 1 0 0 1 1 0 0 2 1 2 1 1 0 1]
[ 0 -1 2 0 1 0 2 1 0 1 0 0 0 1 1 2 1 1 1 2]
[ 2 2 -1 1 0 1 0 1 1 0 1 2 2 0 1 0 1 0 1 0]
[ 0 0 1 -1 2 1 1 0 0 1 0 1 0 1 2 2 1 0 1 2]
[ 2 1 0 2 -1 0 1 2 1 0 1 1 2 0 0 0 1 1 1 0]
[ 1 0 1 1 0 -1 2 2 1 1 0 0 1 0 0 1 0 2 2 1]
[ 1 2 0 1 1 2 -1 0 1 0 2 2 1 1 1 0 1 0 0 0]
[ 0 1 1 0 2 2 0 -1 0 1 1 1 0 2 2 1 1 0 0 1]
[ 0 0 1 0 1 1 1 0 -1 0 1 1 1 2 2 2 2 0 0 1]
[ 1 1 0 1 0 1 0 1 0 -1 2 2 2 1 1 1 2 0 0 0]
[ 1 0 1 0 1 0 2 1 1 2 -1 0 0 0 1 1 0 1 2 2]
[ 0 0 2 1 1 0 2 1 1 2 0 -1 0 1 0 1 0 2 1 1]
[ 0 0 2 0 2 1 1 0 1 2 0 0 -1 1 1 1 0 1 1 2]
[ 2 1 0 1 0 0 1 2 2 1 0 1 1 -1 0 0 0 1 2 1]
[ 1 1 1 2 0 0 1 2 2 1 1 0 1 0 -1 0 0 2 1 0]
[ 2 2 0 2 0 1 0 1 2 1 1 1 1 0 0 -1 0 1 1 0]
[ 1 1 1 1 1 0 1 1 2 2 0 0 0 0 0 0 -1 2 2 1]
[ 1 1 0 0 1 2 0 0 0 0 1 2 1 1 2 1 2 -1 0 1]
[ 0 1 1 1 1 2 0 0 0 0 2 1 1 2 1 1 2 0 -1 0]
[ 1 2 0 2 0 1 0 1 1 0 2 1 2 1 0 0 1 1 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 0 0 1 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
16
{@
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2)
@}
Intersection Matrix:
[-1 1 0 1 1 1 0 1 1 0 1 2 2 0 2 2 0 0 1 0]
[ 1 -1 2 2 0 0 1 1 1 0 0 0 0 1 1 0 1 2 1 2]
[ 0 2 -1 0 1 2 1 0 1 1 1 2 2 0 1 1 0 0 1 0]
[ 1 2 0 -1 2 1 0 1 0 2 2 1 1 1 0 1 1 0 0 0]
[ 1 0 1 2 -1 1 2 0 1 0 0 1 0 1 1 0 0 1 2 2]
[ 1 0 2 1 1 -1 0 2 0 1 1 0 0 2 0 1 2 1 0 1]
[ 0 1 1 0 2 0 -1 2 0 1 2 1 1 1 1 2 1 0 0 0]
[ 1 1 0 1 0 2 2 -1 2 0 0 1 1 0 1 0 0 1 2 1]
[ 1 1 1 0 1 0 0 2 -1 2 2 1 0 2 0 1 1 0 0 1]
[ 0 0 1 2 0 1 1 0 2 -1 0 1 1 0 2 1 0 1 2 1]
[ 1 0 1 2 0 1 2 0 2 0 -1 0 1 0 1 0 1 2 1 1]
[ 2 0 2 1 1 0 1 1 1 1 0 -1 0 1 0 0 2 2 0 1]
[ 2 0 2 1 0 0 1 1 0 1 1 0 -1 2 0 0 1 1 1 2]
[ 0 1 0 1 1 2 1 0 2 0 0 1 2 -1 2 1 0 1 1 0]
[ 2 1 1 0 1 0 1 1 0 2 1 0 0 2 -1 0 2 1 0 1]
[ 2 0 1 1 0 1 2 0 1 1 0 0 0 1 0 -1 1 2 1 2]
[ 0 1 0 1 0 2 1 0 1 0 1 2 1 0 2 1 -1 0 2 1]
[ 0 2 0 0 1 1 0 1 0 1 2 2 1 1 1 2 0 -1 1 0]
[ 1 1 1 0 2 0 0 2 0 2 1 0 1 1 0 1 2 1 -1 0]
[ 0 2 0 0 2 1 0 1 1 1 1 1 2 0 1 2 1 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
17
{@
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1)
@}
Intersection Matrix:
[-1 0 1 2 1 0 0 1 0 0 2 0 1 2 1 0 1 2 1 1]
[ 0 -1 2 1 1 0 1 2 1 0 2 0 1 2 1 0 0 1 0 1]
[ 1 2 -1 0 0 2 1 0 0 1 0 2 1 0 0 1 1 1 2 1]
[ 2 1 0 -1 0 2 2 1 1 1 0 2 1 0 0 1 0 0 1 1]
[ 1 1 0 0 -1 1 2 1 0 0 1 2 1 0 0 1 0 1 2 2]
[ 0 0 2 2 1 -1 0 1 1 0 2 0 0 1 2 1 1 1 0 1]
[ 0 1 1 2 2 0 -1 0 1 1 1 0 0 1 2 1 2 1 0 0]
[ 1 2 0 1 1 1 0 -1 1 2 0 1 0 0 1 2 2 0 1 0]
[ 0 1 0 1 0 1 1 1 -1 0 1 1 2 1 0 0 0 2 2 2]
[ 0 0 1 1 0 0 1 2 0 -1 2 1 1 1 1 0 0 2 1 2]
[ 2 2 0 0 1 2 1 0 1 2 -1 1 1 0 0 1 1 0 1 0]
[ 0 0 2 2 2 0 0 1 1 1 1 -1 1 2 1 0 1 1 0 0]
[ 1 1 1 1 1 0 0 0 2 1 1 1 -1 0 2 2 2 0 0 0]
[ 2 2 0 0 0 1 1 0 1 1 0 2 0 -1 1 2 1 0 1 1]
[ 1 1 0 0 0 2 2 1 0 1 0 1 2 1 -1 0 0 1 2 1]
[ 0 0 1 1 1 1 1 2 0 0 1 0 2 2 0 -1 0 2 1 1]
[ 1 0 1 0 0 1 2 2 0 0 1 1 2 1 0 0 -1 1 1 2]
[ 2 1 1 0 1 1 1 0 2 2 0 1 0 0 1 2 1 -1 0 0]
[ 1 0 2 1 2 0 0 1 2 1 1 0 0 1 2 1 1 0 -1 0]
[ 1 1 1 1 2 1 0 0 2 2 0 0 0 1 1 1 2 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 0 0 1 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
18
{@
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2),
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2),
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 2 1 1 1 1 0 0 1 1 0 1 1 2 0 1 1 1 1]
[ 0 -1 1 1 1 1 1 0 0 1 1 0 1 1 1 1 2 1 2 0]
[ 2 1 -1 0 1 0 0 1 1 1 1 1 1 1 0 2 0 1 1 1]
[ 1 1 0 -1 1 0 0 1 2 1 1 1 1 0 1 1 0 2 1 1]
[ 1 1 1 1 -1 2 1 0 1 2 1 1 0 1 1 0 1 0 1 0]
[ 1 1 0 0 2 -1 0 2 1 0 1 1 1 1 1 1 0 1 1 1]
[ 1 1 0 0 1 0 -1 1 1 1 0 2 2 1 1 1 0 1 1 1]
[ 0 0 1 1 0 2 1 -1 0 2 1 0 1 1 1 1 1 1 1 1]
[ 0 0 1 2 1 1 1 0 -1 1 1 0 1 2 1 1 1 0 1 1]
[ 1 1 1 1 2 0 1 2 1 -1 0 1 1 0 0 1 1 1 0 1]
[ 1 1 1 1 1 1 0 1 1 0 -1 2 2 0 0 1 1 1 0 1]
[ 0 0 1 1 1 1 2 0 0 1 2 -1 0 1 1 1 1 1 1 1]
[ 1 1 1 1 0 1 2 1 1 1 2 0 -1 1 1 0 1 0 1 0]
[ 1 1 1 0 1 1 1 1 2 0 0 1 1 -1 0 1 1 2 0 1]
[ 2 1 0 1 1 1 1 1 1 0 0 1 1 0 -1 2 1 1 0 1]
[ 0 1 2 1 0 1 1 1 1 1 1 1 0 1 2 -1 1 0 1 0]
[ 1 2 0 0 1 0 0 1 1 1 1 1 1 1 1 1 -1 1 0 2]
[ 1 1 1 2 0 1 1 1 0 1 1 1 0 2 1 0 1 -1 1 0]
[ 1 2 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 -1 2]
[ 1 0 1 1 0 1 1 1 1 1 1 1 0 1 1 0 2 0 2 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 0 0 1 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
19
{@
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 1 0 1 1 1 0 2 1 1 1 2 1 0 0 1 1 0 1 1]
[ 1 -1 1 2 0 0 1 1 1 1 1 0 0 2 1 1 1 1 1 0]
[ 0 1 -1 0 1 1 1 2 0 1 1 2 1 1 1 0 1 1 0 1]
[ 1 2 0 -1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 2]
[ 1 0 1 1 -1 0 2 1 2 1 0 0 0 1 1 1 1 1 1 1]
[ 1 0 1 1 0 -1 1 1 1 1 1 0 0 1 1 2 0 2 1 1]
[ 0 1 1 1 2 1 -1 1 0 1 2 1 1 0 0 1 1 0 1 1]
[ 2 1 2 1 1 1 1 -1 1 0 0 0 1 1 1 1 0 1 1 0]
[ 1 1 0 0 2 1 0 1 -1 1 2 1 1 1 1 0 1 1 0 1]
[ 1 1 1 1 1 1 1 0 1 -1 0 1 0 1 2 1 0 1 2 0]
[ 1 1 1 1 0 1 2 0 2 0 -1 1 1 1 1 1 0 1 1 0]
[ 2 0 2 1 0 0 1 0 1 1 1 -1 0 1 1 1 1 1 1 1]
[ 1 0 1 1 0 0 1 1 1 0 1 0 -1 1 2 1 1 1 2 1]
[ 0 2 1 0 1 1 0 1 1 1 1 1 1 -1 0 1 1 0 1 2]
[ 0 1 1 1 1 1 0 1 1 2 1 1 2 0 -1 1 1 0 0 1]
[ 1 1 0 0 1 2 1 1 0 1 1 1 1 1 1 -1 2 0 0 1]
[ 1 1 1 1 1 0 1 0 1 0 0 1 1 1 1 2 -1 2 1 0]
[ 0 1 1 1 1 2 0 1 1 1 1 1 1 0 0 0 2 -1 1 1]
[ 1 1 0 0 1 1 1 1 0 2 1 1 2 1 0 0 1 1 -1 1]
[ 1 0 1 2 1 1 1 0 1 0 0 1 1 2 1 1 0 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 0 0 1 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
20
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 1 0 0 -1 0 0 0 0 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2),
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2)
@}
Intersection Matrix:
[-1 1 0 1 1 0 0 0 3 0 1 1 1 0 2 1 2 2 2 1 1 0 2 2 1 0 1 1 1 2 1 2 1 0 2 2 1 1 1 0]
[ 1 -1 1 2 2 1 0 1 1 1 2 0 1 1 0 1 2 0 1 3 1 2 1 2 1 2 0 0 0 1 0 1 0 0 1 1 2 2 2 1]
[ 0 1 -1 2 1 0 1 0 2 1 1 1 1 0 1 1 1 2 3 1 2 0 2 2 0 1 1 2 1 2 0 2 1 0 1 2 1 0 1 0]
[ 1 2 2 -1 0 1 2 1 1 0 0 2 2 1 2 0 0 1 0 0 1 1 1 1 1 0 2 1 2 1 3 1 2 1 2 1 0 1 0 1]
[ 1 2 1 0 -1 2 2 0 1 1 0 2 2 1 2 0 0 1 1 0 1 1 0 1 1 0 3 2 1 1 2 1 2 1 1 2 0 0 1 1]
[ 0 1 0 1 2 -1 1 1 2 0 1 1 1 0 1 1 1 2 2 1 2 0 3 2 0 1 0 1 2 2 1 2 1 0 2 1 1 1 0 0]
[ 0 0 1 2 2 1 -1 1 2 1 2 0 0 1 1 2 3 1 1 2 0 1 1 1 2 1 0 0 0 1 0 1 0 1 1 1 2 2 2 1]
[ 0 1 0 1 0 1 1 -1 2 0 1 1 1 0 1 1 1 2 2 1 2 0 1 2 0 1 2 1 0 2 1 2 1 0 2 3 1 1 2 0]
[ 3 1 2 1 1 2 2 2 -1 2 1 1 1 2 0 1 0 0 0 1 1 2 0 0 1 2 1 1 1 0 1 0 1 2 0 0 1 1 1 2]
[ 0 1 1 0 1 0 1 0 2 -1 1 1 1 0 1 1 1 2 1 1 2 0 2 2 0 1 1 0 1 2 2 2 1 0 3 2 1 2 1 0]
[ 1 2 1 0 0 1 2 1 1 1 -1 1 2 0 2 0 0 1 1 0 1 1 1 1 1 0 2 2 2 0 2 2 3 1 1 1 1 0 0 2]
[ 1 0 1 2 2 1 0 1 1 1 1 -1 0 0 0 2 2 1 1 2 1 1 1 1 1 2 0 0 0 0 0 2 1 1 1 1 3 2 2 2]
[ 1 1 1 2 2 1 0 1 1 1 2 0 -1 1 0 3 2 2 1 1 1 0 1 0 1 2 0 0 0 1 0 1 0 2 1 1 2 2 2 1]
[ 0 1 0 1 1 0 1 0 2 0 0 0 1 -1 1 1 1 2 2 1 2 0 2 2 0 1 1 1 1 1 1 3 2 0 2 2 2 1 1 1]
[ 2 0 1 2 2 1 1 1 0 1 2 0 0 1 -1 2 1 1 1 2 2 1 1 1 0 3 0 0 0 1 0 1 0 1 1 1 2 2 2 1]
[ 1 1 1 0 0 1 2 1 1 1 0 2 3 1 2 -1 0 0 1 1 1 2 1 2 1 0 2 2 2 1 2 1 2 0 1 1 0 0 0 1]
[ 2 2 1 0 0 1 3 1 0 1 0 2 2 1 1 0 -1 1 1 0 2 1 1 1 0 1 2 2 2 1 2 1 2 1 1 1 0 0 0 1]
[ 2 0 2 1 1 2 1 2 0 2 1 1 2 2 1 0 1 -1 0 2 0 3 0 1 2 1 1 1 1 0 1 0 1 1 0 0 1 1 1 2]
[ 2 1 3 0 1 2 1 2 0 1 1 1 1 2 1 1 1 0 -1 1 0 2 0 0 2 1 1 0 1 0 2 0 1 2 1 0 1 2 1 2]
[ 1 3 1 0 0 1 2 1 1 1 0 2 1 1 2 1 0 2 1 -1 1 0 1 0 1 0 2 2 2 1 2 1 2 2 1 1 0 0 0 1]
[ 1 1 2 1 1 2 0 2 1 2 1 1 1 2 2 1 2 0 0 1 -1 2 0 0 3 0 1 1 1 0 1 0 1 2 0 0 1 1 1 2]
[ 0 2 0 1 1 0 1 0 2 0 1 1 0 0 1 2 1 3 2 0 2 -1 2 1 0 1 1 1 1 2 1 2 1 1 2 2 1 1 1 0]
[ 2 1 2 1 0 3 1 1 0 2 1 1 1 2 1 1 1 0 0 1 0 2 -1 0 2 1 2 1 0 0 1 0 1 2 0 1 1 1 2 2]
[ 2 2 2 1 1 2 1 2 0 2 1 1 0 2 1 2 1 1 0 0 0 1 0 -1 2 1 1 1 1 0 1 0 1 3 0 0 1 1 1 2]
[ 1 1 0 1 1 0 2 0 1 0 1 1 1 0 0 1 0 2 2 1 3 0 2 2 -1 2 1 1 1 2 1 2 1 0 2 2 1 1 1 0]
[ 0 2 1 0 0 1 1 1 2 1 0 2 2 1 3 0 1 1 1 0 0 1 1 1 2 -1 2 2 2 1 2 1 2 1 1 1 0 0 0 1]
[ 1 0 1 2 3 0 0 2 1 1 2 0 0 1 0 2 2 1 1 2 1 1 2 1 1 2 -1 0 1 1 0 1 0 1 1 0 2 2 1 1]
[ 1 0 2 1 2 1 0 1 1 0 2 0 0 1 0 2 2 1 0 2 1 1 1 1 1 2 0 -1 0 1 1 1 0 1 2 1 2 3 2 1]
[ 1 0 1 2 1 2 0 0 1 1 2 0 0 1 0 2 2 1 1 2 1 1 0 1 1 2 1 0 -1 1 0 1 0 1 1 2 2 2 3 1]
[ 2 1 2 1 1 2 1 2 0 2 0 0 1 1 1 1 1 0 0 1 0 2 0 0 2 1 1 1 1 -1 1 1 2 2 0 0 2 1 1 3]
[ 1 0 0 3 2 1 0 1 1 2 2 0 0 1 0 2 2 1 2 2 1 1 1 1 1 2 0 1 0 1 -1 1 0 1 0 1 2 1 2 1]
[ 2 1 2 1 1 2 1 2 0 2 2 2 1 3 1 1 1 0 0 1 0 2 0 0 2 1 1 1 1 1 1 -1 0 2 0 0 0 1 1 1]
[ 1 0 1 2 2 1 0 1 1 1 3 1 0 2 0 2 2 1 1 2 1 1 1 1 1 2 0 0 0 2 0 0 -1 1 1 1 1 2 2 0]
[ 0 0 0 1 1 0 1 0 2 0 1 1 2 0 1 0 1 1 2 2 2 1 2 3 0 1 1 1 1 2 1 2 1 -1 2 2 1 1 1 0]
[ 2 1 1 2 1 2 1 2 0 3 1 1 1 2 1 1 1 0 1 1 0 2 0 0 2 1 1 2 1 0 0 0 1 2 -1 0 1 0 1 2]
[ 2 1 2 1 2 1 1 3 0 2 1 1 1 2 1 1 1 0 0 1 0 2 1 0 2 1 0 1 2 0 1 0 1 2 0 -1 1 1 0 2]
[ 1 2 1 0 0 1 2 1 1 1 1 3 2 2 2 0 0 1 1 0 1 1 1 1 1 0 2 2 2 2 2 0 1 1 1 1 -1 0 0 0]
[ 1 2 0 1 0 1 2 1 1 2 0 2 2 1 2 0 0 1 2 0 1 1 1 1 1 0 2 3 2 1 1 1 2 1 0 1 0 -1 0 1]
[ 1 2 1 0 1 0 2 2 1 1 0 2 2 1 2 0 0 1 1 0 1 1 2 1 1 0 1 2 3 1 2 1 2 1 1 0 0 0 -1 1]
[ 0 1 0 1 1 0 1 0 2 0 2 2 1 1 1 1 1 2 2 1 2 0 2 2 0 1 1 1 1 3 1 1 0 0 2 2 0 1 1 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D7(7):C2*F5
order := 40,
length := 2177280,
subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 5
Generators:
[ 4 1 2 2 1 1 0 2 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 -1 -1 0 0 -1 0]
[-1 0 0 -1 0 0 0 -1 0]
[-2 -1 -1 -1 0 -1 0 -1 0]
[-1 0 -1 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[-2 0 -1 -1 -1 -1 0 -1 0]
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{4,4,4,4,4,10,10,10,10,20,20,20,20,20,20,20,20,20}
Orbit:
1
{@
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 0 2 2]
[ 0 -1 2 2]
[ 2 2 -1 0]
[ 2 2 0 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
2
{@
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 2 2 0]
[ 2 -1 0 2]
[ 2 0 -1 2]
[ 0 2 2 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
3
{@
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 3]
[ 1 -1 3 1]
[ 1 3 -1 1]
[ 3 1 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
4
{@
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1)
@}
Intersection Matrix:
[-1 1 0 0]
[ 1 -1 0 0]
[ 0 0 -1 1]
[ 0 0 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
5
{@
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 0 0]
[ 1 -1 0 0]
[ 0 0 -1 1]
[ 0 0 1 -1]
Stabilizer Group Name:
D5
MatrixGroup(9, Integer Ring)
Generators:
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[ 9 4 2 2 2 3 3 3 5]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -2 -1 -1 -1 -1 -1 -2 -2]
[-1 -1 0 0 0 0 0 0 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -1 -1 -2 -1 -1 -2]
6
{@
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 2 1 2 2 1 1 0 2 0]
[ 2 -1 1 1 0 0 2 2 1 2]
[ 1 1 -1 2 2 2 0 1 2 0]
[ 2 1 2 -1 0 1 2 2 0 1]
[ 2 0 2 0 -1 1 2 1 1 2]
[ 1 0 2 1 1 -1 2 2 0 2]
[ 1 2 0 2 2 2 -1 0 1 1]
[ 0 2 1 2 1 2 0 -1 2 1]
[ 2 1 2 0 1 0 1 2 -1 2]
[ 0 2 0 1 2 2 1 1 2 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
7
{@
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2)
@}
Intersection Matrix:
[-1 2 1 1 2 2 1 2 0 0]
[ 2 -1 2 1 0 1 2 0 1 2]
[ 1 2 -1 2 2 2 0 1 1 0]
[ 1 1 2 -1 1 0 2 0 2 2]
[ 2 0 2 1 -1 0 2 1 2 1]
[ 2 1 2 0 0 -1 1 1 2 2]
[ 1 2 0 2 2 1 -1 2 0 1]
[ 2 0 1 0 1 1 2 -1 2 2]
[ 0 1 1 2 2 2 0 2 -1 1]
[ 0 2 0 2 1 2 1 2 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[12 4 4 5 3 4 4 3 6]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-4 -2 -1 -2 -1 -1 -1 -1 -2]
[-5 -2 -2 -2 -1 -2 -2 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-4 -1 -1 -2 -1 -2 -1 -1 -2]
[-4 -1 -1 -2 -1 -1 -2 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
8
{@
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 1 0 0 -1 0 0 0 0 -1)
@}
Intersection Matrix:
[-1 0 1 0 0 0 0 0 0 0]
[ 0 -1 0 0 0 1 0 0 0 0]
[ 1 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 -1 1 0 0 0 0 0]
[ 0 0 0 1 -1 0 0 0 0 0]
[ 0 1 0 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 0 1]
[ 0 0 0 0 0 0 0 -1 1 0]
[ 0 0 0 0 0 0 0 1 -1 0]
[ 0 0 0 0 0 0 1 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 8 2 3 4 2 1 4 3 2]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-3 -1 -1 -2 -1 0 -1 -1 -1]
[-4 -1 -2 -2 -1 -1 -2 -1 -1]
[-2 0 -1 -1 0 0 -1 -1 -1]
[-1 0 0 -1 0 0 -1 0 0]
[-4 -1 -1 -2 -1 -1 -2 -2 -1]
[-3 -1 -1 -1 -1 0 -2 -1 -1]
[-2 0 -1 -1 -1 0 -1 -1 0]
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
9
{@
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 1 0]
[ 0 -1 0 0 0 0 1 0 0 0]
[ 0 0 -1 0 0 0 0 0 0 1]
[ 0 0 0 -1 0 0 0 1 0 0]
[ 0 0 0 0 -1 1 0 0 0 0]
[ 0 0 0 0 1 -1 0 0 0 0]
[ 0 1 0 0 0 0 -1 0 0 0]
[ 0 0 0 1 0 0 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 3 1 2 0 2 2 1 1]
[-3 -2 -1 -1 0 -1 -1 -1 -1]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-2 -1 0 -1 0 -1 -1 0 -1]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
10
{@
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3),
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2),
Mod: ( 1 -1 0 0 0 0 -1 0 0)
@}
Intersection Matrix:
[-1 0 2 1 1 0 0 1 0 2 2 3 1 2 1 1 2 0 2 0]
[ 0 -1 2 1 0 0 2 1 1 1 0 2 2 2 0 2 3 1 1 0]
[ 2 2 -1 2 0 2 1 0 0 1 1 0 2 0 1 1 0 1 2 3]
[ 1 1 2 -1 2 2 1 3 2 2 1 1 0 0 0 2 1 0 0 0]
[ 1 0 0 2 -1 1 2 0 0 1 0 1 3 1 0 2 2 1 2 2]
[ 0 0 2 2 1 -1 1 0 1 0 1 2 1 3 2 0 2 2 1 0]
[ 0 2 1 1 2 1 -1 1 0 2 3 2 0 1 2 0 0 0 2 1]
[ 1 1 0 3 0 0 1 -1 0 0 1 1 2 2 2 0 1 2 2 2]
[ 0 1 0 2 0 1 0 0 -1 2 2 2 2 1 1 1 1 0 3 2]
[ 2 1 1 2 1 0 2 0 2 -1 0 0 1 2 2 0 1 3 0 1]
[ 2 0 1 1 0 1 3 1 2 0 -1 0 2 1 0 2 2 2 0 1]
[ 3 2 0 1 1 2 2 1 2 0 0 -1 1 0 1 1 0 2 0 2]
[ 1 2 2 0 3 1 0 2 2 1 2 1 -1 1 2 0 0 1 0 0]
[ 2 2 0 0 1 3 1 2 1 2 1 0 1 -1 0 2 0 0 1 2]
[ 1 0 1 0 0 2 2 2 1 2 0 1 2 0 -1 3 2 0 1 1]
[ 1 2 1 2 2 0 0 0 1 0 2 1 0 2 3 -1 0 2 1 1]
[ 2 3 0 1 2 2 0 1 1 1 2 0 0 0 2 0 -1 1 1 2]
[ 0 1 1 0 1 2 0 2 0 3 2 2 1 0 0 2 1 -1 2 1]
[ 2 1 2 0 2 1 2 2 3 0 0 0 0 1 1 1 1 2 -1 0]
[ 0 0 3 0 2 0 1 2 2 1 1 2 0 2 1 1 2 1 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 2 0 1 1 0 0]
[-1 0 -1 -1 0 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-2 -1 -1 -1 0 -1 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
11
{@
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2)
@}
Intersection Matrix:
[-1 1 0 1 1 1 1 1 1 1 0 1 1 0 2 1 2 1 0 0]
[ 1 -1 1 1 0 1 0 0 1 1 1 1 0 2 0 2 1 1 1 1]
[ 0 1 -1 1 1 0 1 2 1 1 0 1 1 0 1 1 1 2 1 0]
[ 1 1 1 -1 1 1 0 1 1 2 2 0 0 1 1 1 0 0 1 1]
[ 1 0 1 1 -1 1 0 0 2 1 1 0 1 1 0 1 1 1 1 2]
[ 1 1 0 1 1 -1 1 2 0 0 1 1 1 1 1 0 1 2 0 1]
[ 1 0 1 0 0 1 -1 0 1 2 2 1 1 1 0 1 1 1 1 1]
[ 1 0 2 1 0 2 0 -1 1 1 1 1 1 1 0 1 1 0 1 1]
[ 1 1 1 1 2 0 1 1 -1 0 1 2 1 1 1 0 1 1 0 0]
[ 1 1 1 2 1 0 2 1 0 -1 0 1 1 1 1 0 1 1 0 1]
[ 0 1 0 2 1 1 2 1 1 0 -1 1 1 0 1 1 1 1 1 0]
[ 1 1 1 0 0 1 1 1 2 1 1 -1 0 1 1 1 0 0 1 2]
[ 1 0 1 0 1 1 1 1 1 1 1 0 -1 2 1 2 0 0 1 1]
[ 0 2 0 1 1 1 1 1 1 1 0 1 2 -1 1 0 1 1 1 0]
[ 2 0 1 1 0 1 0 0 1 1 1 1 1 1 -1 1 0 1 2 1]
[ 1 2 1 1 1 0 1 1 0 0 1 1 2 0 1 -1 1 1 0 1]
[ 2 1 1 0 1 1 1 1 1 1 1 0 0 1 0 1 -1 0 2 1]
[ 1 1 2 0 1 2 1 0 1 1 1 0 0 1 1 1 0 -1 1 1]
[ 0 1 1 1 1 0 1 1 0 0 1 1 1 1 2 0 2 1 -1 1]
[ 0 1 0 1 2 1 1 1 0 1 0 2 1 0 1 1 1 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
12
{@
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 0 1 2 0 1 1 0 1 1 1 0 1 1 0 1 1 2 1 1]
[ 0 -1 0 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 2 2]
[ 1 0 -1 1 1 1 1 0 0 1 0 1 1 0 1 1 1 1 2 2]
[ 2 1 1 -1 1 1 0 2 1 0 1 1 1 1 1 1 0 0 0 1]
[ 0 0 1 1 -1 2 1 1 1 2 1 0 1 0 0 1 1 1 1 1]
[ 1 1 1 1 2 -1 1 1 1 0 1 1 0 2 1 0 1 0 1 0]
[ 1 1 1 0 1 1 -1 1 1 0 2 2 1 1 1 0 0 1 0 1]
[ 0 1 0 2 1 1 1 -1 0 1 0 1 1 0 1 1 1 2 1 1]
[ 1 1 0 1 1 1 1 0 -1 1 0 1 2 0 0 1 2 1 1 1]
[ 1 1 1 0 2 0 0 1 1 -1 1 1 1 2 1 1 0 1 0 1]
[ 1 1 0 1 1 1 2 0 0 1 -1 0 1 0 1 2 1 1 1 1]
[ 0 0 1 1 0 1 2 1 1 1 0 -1 1 1 0 2 1 1 1 1]
[ 1 1 1 1 1 0 1 1 2 1 1 1 -1 1 2 0 0 0 1 0]
[ 1 1 0 1 0 2 1 0 0 2 0 1 1 -1 1 1 1 1 1 1]
[ 0 0 1 1 0 1 1 1 0 1 1 0 2 1 -1 1 2 1 1 1]
[ 1 1 1 1 1 0 0 1 1 1 2 2 0 1 1 -1 1 0 1 0]
[ 1 1 1 0 1 1 0 1 2 0 1 1 0 1 2 1 -1 1 0 1]
[ 2 1 1 0 1 0 1 2 1 1 1 1 0 1 1 0 1 -1 1 0]
[ 1 2 2 0 1 1 0 1 1 0 1 1 1 1 1 1 0 1 -1 0]
[ 1 2 2 1 1 0 1 1 1 1 1 1 0 1 1 0 1 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
13
{@
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2)
@}
Intersection Matrix:
[-1 1 1 2 1 1 1 1 1 0 0 0 0 2 1 1 1 1 1 0]
[ 1 -1 1 1 0 2 0 1 0 1 1 1 2 0 1 1 1 1 1 0]
[ 1 1 -1 1 1 0 0 2 1 1 2 0 1 1 1 0 1 1 0 1]
[ 2 1 1 -1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 1 2]
[ 1 0 1 1 -1 1 0 1 1 1 0 1 1 0 2 2 1 1 0 1]
[ 1 2 0 0 1 -1 1 1 1 1 1 0 0 1 1 1 1 1 0 2]
[ 1 0 0 1 0 1 -1 2 1 0 1 1 1 0 1 1 1 2 1 1]
[ 1 1 2 0 1 1 2 -1 0 1 0 1 1 1 0 1 1 0 1 1]
[ 1 0 1 0 1 1 1 0 -1 1 1 0 2 1 0 1 2 1 1 1]
[ 0 1 1 1 1 1 0 1 1 -1 0 1 0 1 0 1 1 2 2 1]
[ 0 1 2 1 0 1 1 0 1 0 -1 1 0 1 1 2 1 1 1 1]
[ 0 1 0 1 1 0 1 1 0 1 1 -1 1 2 1 1 2 1 0 1]
[ 0 2 1 1 1 0 1 1 2 0 0 1 -1 1 1 1 0 1 1 1]
[ 2 0 1 0 0 1 0 1 1 1 1 2 1 -1 1 1 0 1 1 1]
[ 1 1 1 0 2 1 1 0 0 0 1 1 1 1 -1 0 1 1 2 1]
[ 1 1 0 1 2 1 1 1 1 1 2 1 1 1 0 -1 0 0 1 0]
[ 1 1 1 1 1 1 1 1 2 1 1 2 0 0 1 0 -1 0 1 0]
[ 1 1 1 1 1 1 2 0 1 2 1 1 1 1 1 0 0 -1 0 0]
[ 1 1 0 1 0 0 1 1 1 2 1 0 1 1 2 1 1 0 -1 1]
[ 0 0 1 2 1 2 1 1 1 1 1 1 1 1 1 0 0 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[10 3 3 3 3 3 3 3 6]
[-3 0 -1 -1 -1 -1 -1 -1 -2]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 0 -1 -2]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
14
{@
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2),
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 1 1 0 2 1 1 0 0 1 2 0 1 0 1 1 1 1]
[ 1 -1 1 0 1 2 1 1 0 1 0 1 1 1 0 1 1 2 1 0]
[ 1 1 -1 1 2 1 1 0 1 1 0 1 0 2 1 1 0 0 1 1]
[ 1 0 1 -1 1 1 1 1 0 2 0 1 0 0 1 1 2 1 1 1]
[ 1 1 2 1 -1 1 0 1 1 0 2 1 1 0 0 1 1 1 0 1]
[ 0 2 1 1 1 -1 1 1 1 1 1 0 1 0 2 0 1 0 1 1]
[ 2 1 1 1 0 1 -1 1 1 1 2 0 0 1 1 1 0 1 1 0]
[ 1 1 0 1 1 1 1 -1 2 1 1 2 0 1 0 0 1 0 1 1]
[ 1 0 1 0 1 1 1 2 -1 1 0 0 1 1 1 2 1 1 0 1]
[ 0 1 1 2 0 1 1 1 1 -1 1 1 2 1 0 1 0 1 0 1]
[ 0 0 0 0 2 1 2 1 0 1 -1 1 1 1 1 1 1 1 1 1]
[ 1 1 1 1 1 0 0 2 0 1 1 -1 1 1 2 1 0 1 1 0]
[ 2 1 0 0 1 1 0 0 1 2 1 1 -1 1 1 1 1 0 1 1]
[ 0 1 2 0 0 0 1 1 1 1 1 1 1 -1 1 0 2 1 1 1]
[ 1 0 1 1 0 2 1 0 1 0 1 2 1 1 -1 1 1 1 0 1]
[ 0 1 1 1 1 0 1 0 2 1 1 1 1 0 1 -1 1 1 2 0]
[ 1 1 0 2 1 1 0 1 1 0 1 0 1 2 1 1 -1 1 1 0]
[ 1 2 0 1 1 0 1 0 1 1 1 1 0 1 1 1 1 -1 0 2]
[ 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 2 1 0 -1 2]
[ 1 0 1 1 1 1 0 1 1 1 1 0 1 1 1 0 0 2 2 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 2 0 0 0 1 1 1 1]
[-2 -1 0 0 0 -1 -1 -1 -1]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 -1 0 0 0 0 0 0 -1]
[-1 -1 0 0 0 -1 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
15
{@
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2),
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2)
@}
Intersection Matrix:
[-1 0 1 1 0 1 1 0 1 2 0 1 1 1 2 1 1 0 1 1]
[ 0 -1 1 1 1 1 1 1 0 1 0 2 1 0 1 1 2 0 1 1]
[ 1 1 -1 0 1 1 2 0 0 1 1 0 1 1 1 0 1 2 1 1]
[ 1 1 0 -1 0 1 1 1 1 1 1 1 1 0 1 1 0 2 0 2]
[ 0 1 1 0 -1 1 1 1 1 1 1 1 0 1 2 2 0 1 0 1]
[ 1 1 1 1 1 -1 0 0 1 1 2 1 0 0 0 1 1 1 2 1]
[ 1 1 2 1 1 0 -1 1 2 1 1 1 1 0 0 1 0 0 1 1]
[ 0 1 0 1 1 0 1 -1 1 2 1 0 1 1 1 0 1 1 2 1]
[ 1 0 0 1 1 1 2 1 -1 0 1 1 0 1 1 1 2 1 1 0]
[ 2 1 1 1 1 1 1 2 0 -1 1 1 0 1 0 1 1 1 0 0]
[ 0 0 1 1 1 2 1 1 1 1 -1 1 2 1 1 0 1 0 0 1]
[ 1 2 0 1 1 1 1 0 1 1 1 -1 1 2 1 0 0 1 1 0]
[ 1 1 1 1 0 0 1 1 0 0 2 1 -1 1 1 2 1 1 1 0]
[ 1 0 1 0 1 0 0 1 1 1 1 2 1 -1 0 1 1 1 1 2]
[ 2 1 1 1 2 0 0 1 1 0 1 1 1 0 -1 0 1 1 1 1]
[ 1 1 0 1 2 1 1 0 1 1 0 0 2 1 0 -1 1 1 1 1]
[ 1 2 1 0 0 1 0 1 2 1 1 0 1 1 1 1 -1 1 0 1]
[ 0 0 2 2 1 1 0 1 1 1 0 1 1 1 1 1 1 -1 1 0]
[ 1 1 1 0 0 2 1 2 1 0 0 1 1 1 1 1 0 1 -1 1]
[ 1 1 1 2 1 1 1 1 0 0 1 0 0 2 1 1 1 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[10 3 3 3 3 3 3 3 6]
[-3 0 -1 -1 -1 -1 -1 -1 -2]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 0 -1 -2]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
16
{@
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1),
Mod: ( 1 0 -1 0 -1 0 0 0 0)
@}
Intersection Matrix:
[-1 0 1 0 1 1 0 1 1 2 1 1 0 1 1 0 2 1 1 1]
[ 0 -1 1 1 2 1 0 1 1 1 1 0 1 0 2 0 1 1 1 1]
[ 1 1 -1 1 1 1 1 1 1 1 2 0 1 2 0 0 0 1 1 0]
[ 0 1 1 -1 0 1 1 0 1 2 0 1 1 1 1 1 1 1 2 0]
[ 1 2 1 0 -1 1 1 0 0 1 0 2 1 1 0 1 1 1 1 1]
[ 1 1 1 1 1 -1 1 1 2 1 0 0 0 1 0 2 1 1 0 1]
[ 0 0 1 1 1 1 -1 0 1 1 1 1 1 1 1 0 1 2 0 2]
[ 1 1 1 0 0 1 0 -1 1 1 0 1 2 1 1 1 0 2 1 1]
[ 1 1 1 1 0 2 1 1 -1 0 1 2 1 0 1 0 1 0 1 1]
[ 2 1 1 2 1 1 1 1 0 -1 1 1 1 0 1 1 0 0 0 1]
[ 1 1 2 0 0 0 1 0 1 1 -1 1 1 0 1 2 1 1 1 1]
[ 1 0 0 1 2 0 1 1 2 1 1 -1 1 1 1 1 0 1 1 0]
[ 0 1 1 1 1 0 1 2 1 1 1 1 -1 1 0 1 2 0 0 1]
[ 1 0 2 1 1 1 1 1 0 0 0 1 1 -1 2 1 1 0 1 1]
[ 1 2 0 1 0 0 1 1 1 1 1 1 0 2 -1 1 1 1 0 1]
[ 0 0 0 1 1 2 0 1 0 1 2 1 1 1 1 -1 1 1 1 1]
[ 2 1 0 1 1 1 1 0 1 0 1 0 2 1 1 1 -1 1 1 0]
[ 1 1 1 1 1 1 2 2 0 0 1 1 0 0 1 1 1 -1 1 0]
[ 1 1 1 2 1 0 0 1 1 0 1 1 0 1 0 1 1 1 -1 2]
[ 1 1 0 0 1 1 2 1 1 1 1 0 1 1 1 1 0 0 2 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 6 1 2 2 2 0 3 3 2]
[-1 0 0 0 0 0 -1 -1 0]
[-2 0 0 -1 -1 0 -1 -1 -1]
[-2 0 -1 0 -1 0 -1 -1 -1]
[-2 0 -1 -1 0 0 -1 -1 -1]
[ 0 0 0 0 0 1 0 0 0]
[-3 -1 -1 -1 -1 0 -1 -2 -1]
[-3 -1 -1 -1 -1 0 -2 -1 -1]
[-2 0 -1 -1 -1 0 -1 -1 0]
17
{@
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2),
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1)
@}
Intersection Matrix:
[-1 1 2 2 1 1 1 1 1 2 2 2 0 0 0 2 1 1 0 1]
[ 1 -1 0 2 1 1 1 1 1 2 0 0 2 2 2 0 1 1 2 1]
[ 2 0 -1 1 1 1 2 1 1 1 0 0 2 1 2 0 1 1 2 2]
[ 2 2 1 -1 0 0 2 2 2 1 1 1 1 1 1 1 0 2 1 0]
[ 1 1 1 0 -1 0 2 2 1 2 1 2 2 1 1 1 0 2 1 0]
[ 1 1 1 0 0 -1 2 2 2 2 2 1 1 1 1 1 0 1 2 0]
[ 1 1 2 2 2 2 -1 0 0 0 1 1 1 2 1 1 2 0 1 1]
[ 1 1 1 2 2 2 0 -1 0 0 1 1 1 1 2 2 1 0 1 2]
[ 1 1 1 2 1 2 0 0 -1 0 1 2 2 1 1 1 2 0 1 2]
[ 2 2 1 1 2 2 0 0 0 -1 1 1 1 1 1 1 2 0 1 2]
[ 2 0 0 1 1 2 1 1 1 1 -1 0 2 2 2 0 1 2 1 1]
[ 2 0 0 1 2 1 1 1 2 1 0 -1 1 2 2 0 1 1 2 1]
[ 0 2 2 1 2 1 1 1 2 1 2 1 -1 0 0 2 1 1 0 1]
[ 0 2 1 1 1 1 2 1 1 1 2 2 0 -1 0 2 1 1 0 2]
[ 0 2 2 1 1 1 1 2 1 1 2 2 0 0 -1 1 2 1 0 1]
[ 2 0 0 1 1 1 1 2 1 1 0 0 2 2 1 -1 2 1 2 1]
[ 1 1 1 0 0 0 2 1 2 2 1 1 1 1 2 2 -1 2 1 0]
[ 1 1 1 2 2 1 0 0 0 0 2 1 1 1 1 1 2 -1 2 2]
[ 0 2 2 1 1 2 1 1 1 1 1 2 0 0 0 2 1 2 -1 1]
[ 1 1 2 0 0 0 1 2 2 2 1 1 1 2 1 1 0 2 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[10 3 3 3 3 3 3 3 6]
[-3 0 -1 -1 -1 -1 -1 -1 -2]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 0 -1 -2]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
18
{@
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 0 1 0 1 0 2 2 1 2 2 1 1 2 1 1 2 1 0 1]
[ 0 -1 1 0 1 0 2 2 2 1 2 2 1 1 1 1 1 2 0 1]
[ 1 1 -1 1 2 2 2 1 2 2 1 0 1 1 0 2 0 1 1 0]
[ 0 0 1 -1 2 0 2 1 1 1 2 1 1 2 2 1 1 2 0 1]
[ 1 1 2 2 -1 1 1 2 0 0 1 2 0 1 1 0 2 1 1 2]
[ 0 0 2 0 1 -1 1 2 1 1 2 1 2 2 1 1 1 2 0 1]
[ 2 2 2 2 1 1 -1 0 1 1 0 1 2 0 1 1 1 0 2 1]
[ 2 2 1 1 2 2 0 -1 1 1 0 1 1 0 2 1 1 0 2 1]
[ 1 2 2 1 0 1 1 1 -1 0 1 1 0 2 2 0 2 1 1 2]
[ 2 1 2 1 0 1 1 1 0 -1 1 2 0 1 2 0 1 2 1 2]
[ 2 2 1 2 1 2 0 0 1 1 -1 1 1 0 1 2 1 0 1 2]
[ 1 2 0 1 2 1 1 1 1 2 1 -1 2 2 0 2 0 1 1 0]
[ 1 1 1 1 0 2 2 1 0 0 1 2 -1 1 2 0 2 1 1 2]
[ 2 1 1 2 1 2 0 0 2 1 0 2 1 -1 1 1 1 0 2 1]
[ 1 1 0 2 1 1 1 2 2 2 1 0 2 1 -1 2 0 1 1 0]
[ 1 1 2 1 0 1 1 1 0 0 2 2 0 1 2 -1 2 1 2 1]
[ 2 1 0 1 2 1 1 1 2 1 1 0 2 1 0 2 -1 2 1 0]
[ 1 2 1 2 1 2 0 0 1 2 0 1 1 0 1 1 2 -1 2 1]
[ 0 0 1 0 1 0 2 2 1 1 1 1 1 2 1 2 1 2 -1 2]
[ 1 1 0 1 2 1 1 1 2 2 2 0 2 1 0 1 0 1 2 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 5 0 2 2 2 2 0 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 0 -1 -1 -1 0 -1 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 -1 0 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 0 -1 -1 -1 -1 0 -1 0]
[-2 0 -1 -1 -1 -1 0 0 -1]
D7(8):C2^2⋊F5
order := 80,
length := 2177280,
subgroup := MatrixGroup(9, Integer Ring) of order 2^4 * 5
Generators:
[11 3 3 4 5 2 4 5 4]
[-4 -1 -1 -1 -2 -1 -2 -2 -1]
[-2 0 0 -1 -1 0 -1 -1 -1]
[-4 -1 -1 -2 -2 -1 -1 -2 -1]
[-4 -1 -1 -1 -2 -1 -1 -2 -2]
[-3 -1 -1 -1 -1 0 -1 -2 -1]
[-3 -1 -1 -1 -2 0 -1 -1 -1]
[-5 -1 -2 -2 -2 -1 -2 -2 -2]
[-5 -2 -1 -2 -2 -1 -2 -2 -2]
[ 4 2 1 1 0 1 2 2 0]
[-2 -1 0 -1 0 -1 -1 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[-1 -1 0 0 0 0 0 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 1 0 0 0 0]
[ 7 2 3 2 0 3 2 3 3]
[-3 -1 -1 -1 0 -2 -1 -1 -1]
[-2 0 -1 0 0 -1 -1 -1 -1]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-2 -1 -1 0 0 -1 0 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -1 -1 0 -1 -1 -2 -1]
[ 0 0 0 0 1 0 0 0 0]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]>
Orbit type:{4,4,4,4,4,10,10,10,10,20,20,20,20,20,20,20,40}
Orbit:
1
{@
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2),
Mod: ( 1 0 -1 -1 0 0 0 0 0)
@}
Intersection Matrix:
[-1 2 0 2]
[ 2 -1 2 0]
[ 0 2 -1 2]
[ 2 0 2 -1]
Stabilizer Group Name:
D10
MatrixGroup(9, Integer Ring)
Generators:
[ 4 1 1 1 0 2 0 2 2]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 -1 0 0 -1]
[-1 0 0 0 0 0 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 9 2 4 4 2 4 2 2 4]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-4 -1 -1 -2 -1 -2 -1 -1 -2]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
2
{@
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 1 0 0 -1 0 -1 0 0 0)
@}
Intersection Matrix:
[-1 2 0 2]
[ 2 -1 2 0]
[ 0 2 -1 2]
[ 2 0 2 -1]
Stabilizer Group Name:
D10
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 1 0 0 2 1 0]
[-1 0 0 -1 0 0 -1 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 0 1 0 0 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 1 0 0 0 0]
[11 2 5 5 3 4 3 4 4]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-5 -1 -2 -2 -1 -2 -2 -2 -2]
[-5 -1 -2 -2 -2 -2 -1 -2 -2]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-4 -1 -2 -2 -1 -1 -1 -2 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
3
{@
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1)
@}
Intersection Matrix:
[-1 3 1 1]
[ 3 -1 1 1]
[ 1 1 -1 3]
[ 1 1 3 -1]
Stabilizer Group Name:
D10
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 0 0 1 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 7 2 3 3 3 2 3 2 0]
[-2 0 -1 -1 -1 -1 -1 0 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[10 2 4 5 3 4 2 3 4]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-4 -1 -1 -2 -1 -2 -1 -1 -2]
[-5 -1 -2 -2 -2 -2 -1 -2 -2]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-3 -1 -1 -2 -1 -1 0 -1 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
4
{@
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1)
@}
Intersection Matrix:
[-1 0 0 1]
[ 0 -1 1 0]
[ 0 1 -1 0]
[ 1 0 0 -1]
Stabilizer Group Name:
F5
MatrixGroup(9, Integer Ring)
Generators:
[10 3 2 4 4 2 3 4 5]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[-2 0 0 -1 -1 0 -1 -1 -1]
[-4 -1 -1 -2 -1 -1 -1 -2 -2]
[-5 -2 -1 -2 -2 -1 -2 -2 -2]
[-2 -1 0 -1 -1 0 0 -1 -1]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-4 -1 -1 -2 -2 -1 -1 -1 -2]
[-4 -1 -1 -1 -2 -1 -1 -2 -2]
[12 5 3 5 4 3 5 3 5]
[-5 -2 -1 -2 -2 -2 -2 -1 -2]
[-4 -1 -1 -2 -1 -1 -2 -1 -2]
[-4 -2 -1 -2 -1 -1 -2 -1 -1]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-4 -2 -1 -2 -1 -1 -1 -1 -2]
[-5 -2 -2 -2 -2 -1 -2 -1 -2]
[-2 -1 0 -1 -1 0 -1 0 -1]
[-5 -2 -1 -2 -2 -1 -2 -2 -2]
5
{@
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1)
@}
Intersection Matrix:
[-1 1 0 0]
[ 1 -1 0 0]
[ 0 0 -1 1]
[ 0 0 1 -1]
Stabilizer Group Name:
F5
MatrixGroup(9, Integer Ring)
Generators:
[ 5 1 2 2 0 2 1 1 3]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-1 0 0 0 0 -1 0 0 -1]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-1 0 -1 0 0 0 0 0 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-1 0 0 -1 0 0 0 0 -1]
[ 0 0 0 0 1 0 0 0 0]
[11 3 4 2 5 4 3 5 4]
[-5 -1 -2 -1 -2 -2 -2 -2 -2]
[-4 -1 -1 -1 -2 -2 -1 -2 -1]
[-2 0 -1 0 -1 -1 0 -1 -1]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-4 -1 -2 -1 -2 -1 -1 -2 -1]
[-5 -2 -2 -1 -2 -2 -1 -2 -2]
[-3 -1 -1 0 -1 -1 -1 -2 -1]
[-4 -1 -1 -1 -2 -1 -1 -2 -2]
6
{@
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2),
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1)
@}
Intersection Matrix:
[-1 0 2 0 2 1 1 1 2 2]
[ 0 -1 1 1 2 0 1 2 2 2]
[ 2 1 -1 2 1 2 2 1 0 0]
[ 0 1 2 -1 2 1 0 2 1 2]
[ 2 2 1 2 -1 1 2 0 0 1]
[ 1 0 2 1 1 -1 0 2 2 2]
[ 1 1 2 0 2 0 -1 2 2 1]
[ 1 2 1 2 0 2 2 -1 1 0]
[ 2 2 0 1 0 2 2 1 -1 1]
[ 2 2 0 2 1 2 1 0 1 -1]
Stabilizer Group Name:
C2^3
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 3 0 1 1 0 1 0 1 2]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 0 -1]
[-1 0 0 0 0 0 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[ 0 0 0 0 0 0 1 0 0]
[-1 0 0 -1 0 0 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
7
{@
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2),
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2),
Mod: (0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1 1 1 2 0 2 2 1 2 0]
[ 1 -1 2 1 1 2 2 0 2 0]
[ 1 2 -1 0 2 1 0 2 1 2]
[ 2 1 0 -1 2 1 1 2 0 2]
[ 0 1 2 2 -1 2 2 0 1 1]
[ 2 2 1 1 2 -1 0 2 0 1]
[ 2 2 0 1 2 0 -1 1 1 2]
[ 1 0 2 2 0 2 1 -1 2 1]
[ 2 2 1 0 1 0 1 2 -1 2]
[ 0 0 2 2 1 1 2 1 2 -1]
Stabilizer Group Name:
C2^3
MatrixGroup(9, Integer Ring)
Generators:
[12 4 4 6 4 5 3 4 3]
[-4 -1 -1 -2 -1 -2 -1 -2 -1]
[-4 -1 -1 -2 -2 -2 -1 -1 -1]
[-6 -2 -2 -3 -2 -2 -2 -2 -2]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[-5 -2 -2 -2 -2 -2 -1 -2 -1]
[-3 -1 -1 -2 -1 -1 0 -1 -1]
[-4 -2 -1 -2 -1 -2 -1 -1 -1]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
8
{@
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 1 -1 -1 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 0 0 1 0 0 0 0 0]
[ 0 -1 0 0 0 0 0 0 0 1]
[ 0 0 -1 0 0 1 0 0 0 0]
[ 0 0 0 -1 0 0 1 0 0 0]
[ 1 0 0 0 -1 0 0 0 0 0]
[ 0 0 1 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 -1 1 0]
[ 0 0 0 0 0 0 0 1 -1 0]
[ 0 1 0 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C2^3
MatrixGroup(9, Integer Ring)
Generators:
[12 3 5 6 4 4 4 4 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-5 -1 -2 -2 -2 -2 -2 -2 -1]
[-6 -2 -2 -3 -2 -2 -2 -2 -2]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[-4 -1 -2 -2 -2 -1 -1 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -2 -1]
[-4 -1 -2 -2 -1 -1 -2 -1 -1]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
9
{@
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 0 0 0 0 0 0 0 0]
[ 1 -1 0 0 0 0 0 0 0 0]
[ 0 0 -1 0 0 1 0 0 0 0]
[ 0 0 0 -1 0 0 0 0 0 1]
[ 0 0 0 0 -1 0 0 1 0 0]
[ 0 0 1 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 -1 0 1 0]
[ 0 0 0 0 1 0 0 -1 0 0]
[ 0 0 0 0 0 0 1 0 -1 0]
[ 0 0 0 1 0 0 0 0 0 -1]
Stabilizer Group Name:
C2^3
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 4 1 1 1 0 2 0 2 2]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 -1 0 0 -1]
[-1 0 0 0 0 0 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
10
{@
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 1 0 2 0 3 2 1 2 2 2 0 0 0 1 0 1 1 1 2]
[ 1 -1 0 1 1 1 0 0 1 2 2 0 1 2 2 2 2 0 3 0]
[ 0 0 -1 2 1 2 2 1 1 1 3 1 0 0 2 2 1 0 2 0]
[ 2 1 2 -1 0 0 0 2 2 1 0 1 3 2 2 1 0 0 1 1]
[ 0 1 1 0 -1 2 1 2 3 2 1 0 2 1 2 0 0 0 1 2]
[ 3 1 2 0 2 -1 0 1 0 0 0 2 2 2 1 2 1 1 1 0]
[ 2 0 2 0 1 0 -1 0 1 2 0 0 2 3 1 1 2 1 2 1]
[ 1 0 1 2 2 1 0 -1 0 2 1 0 0 2 0 1 3 2 2 1]
[ 2 1 1 2 3 0 1 0 -1 0 1 2 0 1 0 2 2 2 1 0]
[ 2 2 1 1 2 0 2 2 0 -1 1 3 1 0 1 2 0 1 0 0]
[ 2 2 3 0 1 0 0 1 1 1 -1 1 2 2 0 0 1 2 0 2]
[ 0 0 1 1 0 2 0 0 2 3 1 -1 1 2 1 0 2 1 2 2]
[ 0 1 0 3 2 2 2 0 0 1 2 1 -1 0 0 1 2 2 1 1]
[ 0 2 0 2 1 2 3 2 1 0 2 2 0 -1 1 1 0 1 0 1]
[ 1 2 2 2 2 1 1 0 0 1 0 1 0 1 -1 0 2 3 0 2]
[ 0 2 2 1 0 2 1 1 2 2 0 0 1 1 0 -1 1 2 0 3]
[ 1 2 1 0 0 1 2 3 2 0 1 2 2 0 2 1 -1 0 0 1]
[ 1 0 0 0 0 1 1 2 2 1 2 1 2 1 3 2 0 -1 2 0]
[ 1 3 2 1 1 1 2 2 1 0 0 2 1 0 0 0 0 2 -1 2]
[ 2 0 0 1 2 0 1 1 0 0 2 2 1 1 2 3 1 0 2 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 1 0 0 1 1 2 0]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 0 -1 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
11
{@
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 2 1 1 0 1 0 1 1 1 1 2 1 0 1 1 0 0]
[ 1 -1 2 1 1 1 1 0 1 1 1 0 1 0 1 0 1 1 2 0]
[ 1 2 -1 0 0 0 1 1 1 1 1 1 1 1 0 1 1 1 0 2]
[ 2 1 0 -1 1 0 1 1 1 1 1 1 1 0 0 2 1 0 1 1]
[ 1 1 0 1 -1 1 1 1 1 1 0 1 0 0 1 0 1 2 1 2]
[ 1 1 0 0 1 -1 1 1 0 1 2 0 1 1 0 1 2 1 1 1]
[ 0 1 1 1 1 1 -1 1 0 2 0 2 1 1 0 1 1 1 1 0]
[ 1 0 1 1 1 1 1 -1 2 1 1 0 2 1 0 0 0 1 1 1]
[ 0 1 1 1 1 0 0 2 -1 1 1 1 0 1 1 1 2 1 1 0]
[ 1 1 1 1 1 1 2 1 1 -1 1 0 0 1 2 1 0 0 0 1]
[ 1 1 1 1 0 2 0 1 1 1 -1 2 0 0 1 1 0 1 1 1]
[ 1 0 1 1 1 0 2 0 1 0 2 -1 1 1 1 0 1 1 1 1]
[ 1 1 1 1 0 1 1 2 0 0 0 1 -1 0 2 1 1 1 1 1]
[ 2 0 1 0 0 1 1 1 1 1 0 1 0 -1 1 1 1 1 2 1]
[ 1 1 0 0 1 0 0 0 1 2 1 1 2 1 -1 1 1 1 1 1]
[ 0 0 1 2 0 1 1 0 1 1 1 0 1 1 1 -1 1 2 1 1]
[ 1 1 1 1 1 2 1 0 2 0 0 1 1 1 1 1 -1 0 0 1]
[ 1 1 1 0 2 1 1 1 1 0 1 1 1 1 1 2 0 -1 0 0]
[ 0 2 0 1 1 1 1 1 1 0 1 1 1 2 1 1 0 0 -1 1]
[ 0 0 2 1 2 1 0 1 0 1 1 1 1 1 1 1 1 0 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 3 0 1 1 0 1 0 1 2]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 -1 0 0 -1]
[-1 0 0 0 0 0 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[ 0 0 0 0 0 0 1 0 0]
[-1 0 0 -1 0 0 0 0 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[ 4 0 2 1 0 1 1 2 2]
[ 0 1 0 0 0 0 0 0 0]
[-2 0 -1 0 0 -1 -1 -1 -1]
[-1 0 0 0 0 0 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-1 0 -1 0 0 0 0 0 -1]
[-1 0 -1 0 0 0 0 -1 0]
[-2 0 -1 -1 0 0 -1 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
12
{@
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 0 2 1 1 1 1 1 0 1 1 1 0 1 0 1 2 0 1 1]
[ 0 -1 1 1 2 1 1 0 0 1 1 0 1 1 0 1 1 1 2 1]
[ 2 1 -1 1 1 1 0 1 1 1 1 0 2 0 1 1 0 1 1 0]
[ 1 1 1 -1 0 1 2 1 1 1 0 1 0 1 0 1 0 2 1 1]
[ 1 2 1 0 -1 1 1 2 1 1 0 1 0 0 1 1 1 1 0 1]
[ 1 1 1 1 1 -1 0 0 1 1 1 1 0 1 2 0 0 1 1 2]
[ 1 1 0 2 1 0 -1 1 1 1 1 0 1 0 2 1 1 0 1 1]
[ 1 0 1 1 2 0 1 -1 1 0 1 1 1 2 1 0 0 1 1 1]
[ 0 0 1 1 1 1 1 1 -1 2 2 1 1 0 0 0 1 1 1 1]
[ 1 1 1 1 1 1 1 0 2 -1 0 1 1 2 1 1 1 0 0 0]
[ 1 1 1 0 0 1 1 1 2 0 -1 0 0 1 1 2 1 1 1 1]
[ 1 0 0 1 1 1 0 1 1 1 0 -1 1 0 1 2 1 1 2 1]
[ 0 1 2 0 0 0 1 1 1 1 0 1 -1 1 1 1 1 1 1 2]
[ 1 1 0 1 0 1 0 2 0 2 1 0 1 -1 1 1 1 1 1 1]
[ 0 0 1 0 1 2 2 1 0 1 1 1 1 1 -1 1 1 1 1 0]
[ 1 1 1 1 1 0 1 0 0 1 2 2 1 1 1 -1 0 1 0 1]
[ 2 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 -1 2 1 1]
[ 0 1 1 2 1 1 0 1 1 0 1 1 1 1 1 1 2 -1 0 0]
[ 1 2 1 1 0 1 1 1 1 0 1 2 1 1 1 0 1 0 -1 0]
[ 1 1 0 1 1 2 1 1 1 0 1 1 2 1 0 1 1 0 0 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 0 1 0 0 0 1 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[12 3 5 6 4 4 4 4 3]
[-3 0 -1 -2 -1 -1 -1 -1 -1]
[-5 -1 -2 -2 -2 -2 -2 -2 -1]
[-6 -2 -2 -3 -2 -2 -2 -2 -2]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[-4 -1 -2 -2 -2 -1 -1 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -2 -1]
[-4 -1 -2 -2 -1 -1 -2 -1 -1]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
13
{@
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2),
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2),
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2),
Mod: (0 1 0 0 0 0 0 0 0)
@}
Intersection Matrix:
[-1 0 2 1 1 1 1 0 0 1 1 1 0 1 2 0 1 1 1 1]
[ 0 -1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 2 1 2 0]
[ 2 1 -1 0 1 0 0 1 1 1 1 1 1 1 0 2 0 1 1 1]
[ 1 1 0 -1 1 0 0 1 2 1 1 1 1 0 1 1 0 2 1 1]
[ 1 1 1 1 -1 2 1 0 1 2 1 0 1 1 1 0 1 0 1 0]
[ 1 1 0 0 2 -1 0 2 1 0 1 1 1 1 1 1 0 1 1 1]
[ 1 1 0 0 1 0 -1 1 1 1 0 2 2 1 1 1 0 1 1 1]
[ 0 0 1 1 0 2 1 -1 0 2 1 1 0 1 1 1 1 1 1 1]
[ 0 0 1 2 1 1 1 0 -1 1 1 1 0 2 1 1 1 0 1 1]
[ 1 1 1 1 2 0 1 2 1 -1 0 1 1 0 0 1 1 1 0 1]
[ 1 1 1 1 1 1 0 1 1 0 -1 2 2 0 0 1 1 1 0 1]
[ 1 1 1 1 0 1 2 1 1 1 2 -1 0 1 1 0 1 0 1 0]
[ 0 0 1 1 1 1 2 0 0 1 2 0 -1 1 1 1 1 1 1 1]
[ 1 1 1 0 1 1 1 1 2 0 0 1 1 -1 0 1 1 2 0 1]
[ 2 1 0 1 1 1 1 1 1 0 0 1 1 0 -1 2 1 1 0 1]
[ 0 1 2 1 0 1 1 1 1 1 1 0 1 1 2 -1 1 0 1 0]
[ 1 2 0 0 1 0 0 1 1 1 1 1 1 1 1 1 -1 1 0 2]
[ 1 1 1 2 0 1 1 1 0 1 1 0 1 2 1 0 1 -1 1 0]
[ 1 2 1 1 1 1 1 1 1 0 0 1 1 0 0 1 0 1 -1 2]
[ 1 0 1 1 0 1 1 1 1 1 1 0 1 1 1 0 2 0 2 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[10 2 5 4 2 4 3 3 4]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-5 -1 -2 -2 -1 -2 -2 -2 -2]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[ 9 2 4 4 2 4 2 2 4]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-4 -1 -1 -2 -1 -2 -1 -1 -2]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-2 0 -1 -1 -1 -1 0 0 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
14
{@
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2)
@}
Intersection Matrix:
[-1 2 0 1 1 0 1 0 1 1 2 0 1 1 1 0 1 1 1 1]
[ 2 -1 1 1 0 1 0 1 1 1 0 1 1 1 0 2 1 1 0 1]
[ 0 1 -1 1 1 0 1 0 1 0 1 1 2 1 0 1 1 1 2 1]
[ 1 1 1 -1 2 2 1 1 0 1 1 0 1 1 0 1 0 1 1 0]
[ 1 0 1 2 -1 0 0 1 1 1 1 1 1 1 1 1 1 0 0 2]
[ 0 1 0 2 0 -1 1 0 2 1 1 1 1 0 1 1 1 1 1 1]
[ 1 0 1 1 0 1 -1 0 0 1 1 1 1 2 1 1 2 1 0 1]
[ 0 1 0 1 1 0 0 -1 1 1 1 1 1 1 1 1 2 2 1 0]
[ 1 1 1 0 1 2 0 1 -1 0 1 1 1 2 1 0 1 0 1 1]
[ 1 1 0 1 1 1 1 1 0 -1 0 2 1 1 1 0 1 0 2 1]
[ 2 0 1 1 1 1 1 1 1 0 -1 2 0 0 1 1 1 1 1 0]
[ 0 1 1 0 1 1 1 1 1 2 2 -1 1 1 0 1 0 1 0 1]
[ 1 1 2 1 1 1 1 1 1 1 0 1 -1 0 2 0 1 1 0 0]
[ 1 1 1 1 1 0 2 1 2 1 0 1 0 -1 1 1 0 1 1 0]
[ 1 0 0 0 1 1 1 1 1 1 1 0 2 1 -1 2 0 1 1 1]
[ 0 2 1 1 1 1 1 1 0 0 1 1 0 1 2 -1 1 0 1 1]
[ 1 1 1 0 1 1 2 2 1 1 1 0 1 0 0 1 -1 0 1 1]
[ 1 1 1 1 0 1 1 2 0 0 1 1 1 1 1 0 0 -1 1 2]
[ 1 0 2 1 0 1 0 1 1 2 1 0 0 1 1 1 1 1 -1 1]
[ 1 1 1 0 2 1 1 0 1 1 0 1 0 0 1 1 1 2 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[10 2 5 4 2 4 3 3 4]
[-2 0 -1 -1 0 -1 -1 0 -1]
[-5 -1 -2 -2 -1 -2 -2 -2 -2]
[-4 -1 -2 -1 -1 -2 -1 -1 -2]
[-2 0 -1 -1 0 -1 0 -1 -1]
[-4 -1 -2 -2 -1 -1 -1 -1 -2]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-4 -1 -2 -2 -1 -2 -1 -1 -1]
[ 2 0 1 0 0 0 1 1 0]
[ 0 1 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 -1 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[ 0 0 0 0 0 1 0 0 0]
[-1 0 -1 0 0 0 0 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
15
{@
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1)
@}
Intersection Matrix:
[-1 1 0 1 1 1 2 0 1 1 1 2 1 0 0 1 1 0 1 1]
[ 1 -1 1 2 0 0 1 1 1 1 1 0 0 2 1 1 1 1 1 0]
[ 0 1 -1 0 1 1 2 1 0 1 1 2 1 1 1 0 1 1 0 1]
[ 1 2 0 -1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 2]
[ 1 0 1 1 -1 0 1 2 2 1 0 0 0 1 1 1 1 1 1 1]
[ 1 0 1 1 0 -1 1 1 1 1 1 0 0 1 1 2 0 2 1 1]
[ 2 1 2 1 1 1 -1 1 1 0 0 0 1 1 1 1 0 1 1 0]
[ 0 1 1 1 2 1 1 -1 0 1 2 1 1 0 0 1 1 0 1 1]
[ 1 1 0 0 2 1 1 0 -1 1 2 1 1 1 1 0 1 1 0 1]
[ 1 1 1 1 1 1 0 1 1 -1 0 1 0 1 2 1 0 1 2 0]
[ 1 1 1 1 0 1 0 2 2 0 -1 1 1 1 1 1 0 1 1 0]
[ 2 0 2 1 0 0 0 1 1 1 1 -1 0 1 1 1 1 1 1 1]
[ 1 0 1 1 0 0 1 1 1 0 1 0 -1 1 2 1 1 1 2 1]
[ 0 2 1 0 1 1 1 0 1 1 1 1 1 -1 0 1 1 0 1 2]
[ 0 1 1 1 1 1 1 0 1 2 1 1 2 0 -1 1 1 0 0 1]
[ 1 1 0 0 1 2 1 1 0 1 1 1 1 1 1 -1 2 0 0 1]
[ 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 2 -1 2 1 0]
[ 0 1 1 1 1 2 1 0 1 1 1 1 1 0 0 0 2 -1 1 1]
[ 1 1 0 0 1 1 1 1 0 2 1 1 2 1 0 0 1 1 -1 1]
[ 1 0 1 2 1 1 0 1 1 0 0 1 1 2 1 1 0 1 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 7 2 3 3 3 2 3 2 0]
[-2 0 -1 -1 -1 -1 -1 0 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 2 2 3 3 2 2 1 0]
[-2 0 -1 -1 -1 -1 -1 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 -1 -1 -1 -1 0 -1 0 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
16
{@
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2)
@}
Intersection Matrix:
[-1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 2 2 0 1]
[ 1 -1 1 2 1 2 1 1 1 1 0 0 0 1 1 0 1 0 1 1]
[ 0 1 -1 0 2 1 1 1 2 1 1 1 1 1 0 0 1 1 1 0]
[ 0 2 0 -1 1 0 0 1 1 1 1 2 1 1 0 1 1 1 1 1]
[ 1 1 2 1 -1 0 1 0 0 1 0 1 1 1 1 1 1 1 0 2]
[ 1 2 1 0 0 -1 1 0 1 1 1 1 2 1 1 1 0 1 0 1]
[ 1 1 1 0 1 1 -1 1 0 0 1 2 0 1 1 1 1 0 2 1]
[ 1 1 1 1 0 0 1 -1 1 0 1 1 1 2 2 0 1 1 0 1]
[ 1 1 2 1 0 1 0 1 -1 0 1 1 0 0 1 2 1 1 1 1]
[ 1 1 1 1 1 1 0 0 0 -1 2 1 0 1 2 1 1 1 1 0]
[ 1 0 1 1 0 1 1 1 1 2 -1 1 1 1 0 0 1 0 1 2]
[ 1 0 1 2 1 1 2 1 1 1 1 -1 1 0 1 1 0 1 0 0]
[ 0 0 1 1 1 2 0 1 0 0 1 1 -1 1 1 1 2 1 1 1]
[ 1 1 1 1 1 1 1 2 0 1 1 0 1 -1 0 2 0 1 1 0]
[ 0 1 0 0 1 1 1 2 1 2 0 1 1 0 -1 1 1 1 1 1]
[ 1 0 0 1 1 1 1 0 2 1 0 1 1 2 1 -1 1 0 1 1]
[ 2 1 1 1 1 0 1 1 1 1 1 0 2 0 1 1 -1 0 1 0]
[ 2 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 -1 2 1]
[ 0 1 1 1 0 0 2 0 1 1 1 0 1 1 1 1 1 2 -1 1]
[ 1 1 0 1 2 1 1 1 1 0 2 0 1 0 1 1 0 1 1 -1]
Stabilizer Group Name:
C2^2
MatrixGroup(9, Integer Ring)
Generators:
[ 4 1 1 1 0 2 0 2 2]
[-1 0 0 0 0 -1 0 -1 0]
[-1 0 0 0 0 -1 0 0 -1]
[-1 0 0 0 0 0 0 -1 -1]
[ 0 0 0 0 1 0 0 0 0]
[-2 -1 -1 0 0 -1 0 -1 -1]
[ 0 0 0 0 0 0 1 0 0]
[-2 -1 0 -1 0 -1 0 -1 -1]
[-2 0 -1 -1 0 -1 0 -1 -1]
[ 2 1 0 0 0 1 0 1 0]
[-1 0 0 0 0 -1 0 -1 0]
[ 0 0 1 0 0 0 0 0 0]
[ 0 0 0 1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 0 0]
[-1 -1 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 1 0 0]
[-1 -1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 1]
17
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 1 0 0 -1 0 0 0 0 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2)
@}
Intersection Matrix:
[-1 1 0 1 1 0 0 0 3 0 1 1 1 0 2 1 2 2 1 1 2 0 2 2 1 0 1 1 1 2 1 2 0 1 2 2 1 1 1 0]
[ 1 -1 1 2 2 1 0 1 1 1 2 0 1 1 0 1 2 0 1 3 1 2 1 2 1 2 0 0 0 1 0 1 0 0 1 1 2 2 2 1]
[ 0 1 -1 2 1 0 1 0 2 1 1 1 1 0 1 1 1 2 2 1 3 0 2 2 0 1 1 2 1 2 0 2 0 1 1 2 1 0 1 0]
[ 1 2 2 -1 0 1 2 1 1 0 0 2 2 1 2 0 0 1 1 0 0 1 1 1 1 0 2 1 2 1 3 1 1 2 2 1 0 1 0 1]
[ 1 2 1 0 -1 2 2 0 1 1 0 2 2 1 2 0 0 1 1 0 1 1 0 1 1 0 3 2 1 1 2 1 1 2 1 2 0 0 1 1]
[ 0 1 0 1 2 -1 1 1 2 0 1 1 1 0 1 1 1 2 2 1 2 0 3 2 0 1 0 1 2 2 1 2 0 1 2 1 1 1 0 0]
[ 0 0 1 2 2 1 -1 1 2 1 2 0 0 1 1 2 3 1 0 2 1 1 1 1 2 1 0 0 0 1 0 1 1 0 1 1 2 2 2 1]
[ 0 1 0 1 0 1 1 -1 2 0 1 1 1 0 1 1 1 2 2 1 2 0 1 2 0 1 2 1 0 2 1 2 0 1 2 3 1 1 2 0]
[ 3 1 2 1 1 2 2 2 -1 2 1 1 1 2 0 1 0 0 1 1 0 2 0 0 1 2 1 1 1 0 1 0 2 1 0 0 1 1 1 2]
[ 0 1 1 0 1 0 1 0 2 -1 1 1 1 0 1 1 1 2 2 1 1 0 2 2 0 1 1 0 1 2 2 2 0 1 3 2 1 2 1 0]
[ 1 2 1 0 0 1 2 1 1 1 -1 1 2 0 2 0 0 1 1 0 1 1 1 1 1 0 2 2 2 0 2 2 1 3 1 1 1 0 0 2]
[ 1 0 1 2 2 1 0 1 1 1 1 -1 0 0 0 2 2 1 1 2 1 1 1 1 1 2 0 0 0 0 0 2 1 1 1 1 3 2 2 2]
[ 1 1 1 2 2 1 0 1 1 1 2 0 -1 1 0 3 2 2 1 1 1 0 1 0 1 2 0 0 0 1 0 1 2 0 1 1 2 2 2 1]
[ 0 1 0 1 1 0 1 0 2 0 0 0 1 -1 1 1 1 2 2 1 2 0 2 2 0 1 1 1 1 1 1 3 0 2 2 2 2 1 1 1]
[ 2 0 1 2 2 1 1 1 0 1 2 0 0 1 -1 2 1 1 2 2 1 1 1 1 0 3 0 0 0 1 0 1 1 0 1 1 2 2 2 1]
[ 1 1 1 0 0 1 2 1 1 1 0 2 3 1 2 -1 0 0 1 1 1 2 1 2 1 0 2 2 2 1 2 1 0 2 1 1 0 0 0 1]
[ 2 2 1 0 0 1 3 1 0 1 0 2 2 1 1 0 -1 1 2 0 1 1 1 1 0 1 2 2 2 1 2 1 1 2 1 1 0 0 0 1]
[ 2 0 2 1 1 2 1 2 0 2 1 1 2 2 1 0 1 -1 0 2 0 3 0 1 2 1 1 1 1 0 1 0 1 1 0 0 1 1 1 2]
[ 1 1 2 1 1 2 0 2 1 2 1 1 1 2 2 1 2 0 -1 1 0 2 0 0 3 0 1 1 1 0 1 0 2 1 0 0 1 1 1 2]
[ 1 3 1 0 0 1 2 1 1 1 0 2 1 1 2 1 0 2 1 -1 1 0 1 0 1 0 2 2 2 1 2 1 2 2 1 1 0 0 0 1]
[ 2 1 3 0 1 2 1 2 0 1 1 1 1 2 1 1 1 0 0 1 -1 2 0 0 2 1 1 0 1 0 2 0 2 1 1 0 1 2 1 2]
[ 0 2 0 1 1 0 1 0 2 0 1 1 0 0 1 2 1 3 2 0 2 -1 2 1 0 1 1 1 1 2 1 2 1 1 2 2 1 1 1 0]
[ 2 1 2 1 0 3 1 1 0 2 1 1 1 2 1 1 1 0 0 1 0 2 -1 0 2 1 2 1 0 0 1 0 2 1 0 1 1 1 2 2]
[ 2 2 2 1 1 2 1 2 0 2 1 1 0 2 1 2 1 1 0 0 0 1 0 -1 2 1 1 1 1 0 1 0 3 1 0 0 1 1 1 2]
[ 1 1 0 1 1 0 2 0 1 0 1 1 1 0 0 1 0 2 3 1 2 0 2 2 -1 2 1 1 1 2 1 2 0 1 2 2 1 1 1 0]
[ 0 2 1 0 0 1 1 1 2 1 0 2 2 1 3 0 1 1 0 0 1 1 1 1 2 -1 2 2 2 1 2 1 1 2 1 1 0 0 0 1]
[ 1 0 1 2 3 0 0 2 1 1 2 0 0 1 0 2 2 1 1 2 1 1 2 1 1 2 -1 0 1 1 0 1 1 0 1 0 2 2 1 1]
[ 1 0 2 1 2 1 0 1 1 0 2 0 0 1 0 2 2 1 1 2 0 1 1 1 1 2 0 -1 0 1 1 1 1 0 2 1 2 3 2 1]
[ 1 0 1 2 1 2 0 0 1 1 2 0 0 1 0 2 2 1 1 2 1 1 0 1 1 2 1 0 -1 1 0 1 1 0 1 2 2 2 3 1]
[ 2 1 2 1 1 2 1 2 0 2 0 0 1 1 1 1 1 0 0 1 0 2 0 0 2 1 1 1 1 -1 1 1 2 2 0 0 2 1 1 3]
[ 1 0 0 3 2 1 0 1 1 2 2 0 0 1 0 2 2 1 1 2 2 1 1 1 1 2 0 1 0 1 -1 1 1 0 0 1 2 1 2 1]
[ 2 1 2 1 1 2 1 2 0 2 2 2 1 3 1 1 1 0 0 1 0 2 0 0 2 1 1 1 1 1 1 -1 2 0 0 0 0 1 1 1]
[ 0 0 0 1 1 0 1 0 2 0 1 1 2 0 1 0 1 1 2 2 2 1 2 3 0 1 1 1 1 2 1 2 -1 1 2 2 1 1 1 0]
[ 1 0 1 2 2 1 0 1 1 1 3 1 0 2 0 2 2 1 1 2 1 1 1 1 1 2 0 0 0 2 0 0 1 -1 1 1 1 2 2 0]
[ 2 1 1 2 1 2 1 2 0 3 1 1 1 2 1 1 1 0 0 1 1 2 0 0 2 1 1 2 1 0 0 0 2 1 -1 0 1 0 1 2]
[ 2 1 2 1 2 1 1 3 0 2 1 1 1 2 1 1 1 0 0 1 0 2 1 0 2 1 0 1 2 0 1 0 2 1 0 -1 1 1 0 2]
[ 1 2 1 0 0 1 2 1 1 1 1 3 2 2 2 0 0 1 1 0 1 1 1 1 1 0 2 2 2 2 2 0 1 1 1 1 -1 0 0 0]
[ 1 2 0 1 0 1 2 1 1 2 0 2 2 1 2 0 0 1 1 0 2 1 1 1 1 0 2 3 2 1 1 1 1 2 0 1 0 -1 0 1]
[ 1 2 1 0 1 0 2 2 1 1 0 2 2 1 2 0 0 1 1 0 1 1 2 1 1 0 1 2 3 1 2 1 1 2 1 0 0 0 -1 1]
[ 0 1 0 1 1 0 1 0 2 0 2 2 1 1 1 1 1 2 2 1 2 0 2 2 0 1 1 1 1 3 1 1 0 0 2 2 0 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 2 1 0 1 0 0 1 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-1 -1 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 0 0 0 0 0 1 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 1 0 0 0 0]
D7(9):C3⋊S3⋊C2
order := 36,
length := 2419200,
subgroup := MatrixGroup(9, Integer Ring) of order 2^2 * 3^2
Generators:
[ 9 5 3 2 2 2 4 3 3]
[-4 -2 -1 -1 -1 -1 -2 -1 -2]
[-3 -2 -1 -1 0 -1 -1 -1 -1]
[-4 -2 -1 -1 -1 -1 -2 -2 -1]
[-4 -2 -2 -1 -1 -1 -2 -1 -1]
[-1 -1 0 0 0 0 -1 0 0]
[-3 -2 -1 0 -1 -1 -1 -1 -1]
[-2 -1 -1 0 0 0 -1 -1 -1]
[-3 -2 -1 -1 -1 0 -1 -1 -1]
[ 7 2 3 3 2 2 3 3 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]>
Orbit type:{2,2,4,4,6,6,12,12,12,12,12,12,12,12,12,36,36,36}
Orbit:
1
{@
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
C3:S3
MatrixGroup(9, Integer Ring)
Generators:
[ 7 2 3 3 2 2 3 3 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
2
{@
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
C3:S3
MatrixGroup(9, Integer Ring)
Generators:
[ 7 2 3 3 2 2 3 3 0]
[-2 0 -1 -1 0 -1 -1 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -1 -2 -1 -1 -1 -1 0]
[-2 0 -1 -1 -1 0 -1 -1 0]
[-2 -1 -1 -1 0 0 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -1 -2 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
3
{@
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1)
@}
Intersection Matrix:
[-1 2 1 1]
[ 2 -1 1 1]
[ 1 1 -1 2]
[ 1 1 2 -1]
Stabilizer Group Name:
C3^2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
4
{@
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1)
@}
Intersection Matrix:
[-1 1 1 2]
[ 1 -1 2 1]
[ 1 2 -1 1]
[ 2 1 1 -1]
Stabilizer Group Name:
C3^2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
5
{@
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1)
@}
Intersection Matrix:
[-1 2 1 1 2 1]
[ 2 -1 1 1 2 1]
[ 1 1 -1 2 1 2]
[ 1 1 2 -1 1 2]
[ 2 2 1 1 -1 1]
[ 1 1 2 2 1 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[ 7 2 0 3 2 2 3 3 3]
[-2 0 0 -1 0 -1 -1 -1 -1]
[ 0 0 1 0 0 0 0 0 0]
[-3 -1 0 -2 -1 -1 -1 -1 -1]
[-2 0 0 -1 -1 0 -1 -1 -1]
[-2 -1 0 -1 0 0 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -2 -1]
[-3 -1 0 -1 -1 -1 -2 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
6
{@
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 2 1 1 2]
[ 1 -1 1 2 2 1]
[ 2 1 -1 1 1 2]
[ 1 2 1 -1 2 1]
[ 1 2 1 2 -1 1]
[ 2 1 2 1 1 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[16 5 6 6 5 5 6 6 6]
[-5 -2 -2 -2 -1 -1 -2 -2 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
[-6 -2 -2 -3 -2 -2 -2 -2 -2]
[-5 -1 -2 -2 -1 -2 -2 -2 -2]
[-5 -1 -2 -2 -2 -1 -2 -2 -2]
[-6 -2 -2 -2 -2 -2 -2 -3 -2]
[-6 -2 -2 -2 -2 -2 -3 -2 -2]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
[ 7 2 0 3 2 2 3 3 3]
[-2 -1 0 -1 0 0 -1 -1 -1]
[ 0 0 1 0 0 0 0 0 0]
[-3 -1 0 -2 -1 -1 -1 -1 -1]
[-2 0 0 -1 0 -1 -1 -1 -1]
[-2 0 0 -1 -1 0 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -2 -1]
[-3 -1 0 -1 -1 -1 -2 -1 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
7
{@
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2),
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2),
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1)
@}
Intersection Matrix:
[-1 2 2 2 2 0 2 0 0 1 2 0]
[ 2 -1 0 0 0 2 0 2 2 2 1 2]
[ 2 0 -1 1 0 2 0 2 2 2 0 2]
[ 2 0 1 -1 0 2 0 2 2 2 0 2]
[ 2 0 0 0 -1 2 1 2 2 2 0 2]
[ 0 2 2 2 2 -1 2 0 1 0 2 0]
[ 2 0 0 0 1 2 -1 2 2 2 0 2]
[ 0 2 2 2 2 0 2 -1 0 0 2 1]
[ 0 2 2 2 2 1 2 0 -1 0 2 0]
[ 1 2 2 2 2 0 2 0 0 -1 2 0]
[ 2 1 0 0 0 2 0 2 2 2 -1 2]
[ 0 2 2 2 2 0 2 1 0 0 2 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[10 3 6 3 3 3 3 3 3]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
8
{@
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1)
@}
Intersection Matrix:
[-1 2 0 0 1 2 2 2 2 0 0 2]
[ 2 -1 2 2 2 1 0 0 0 2 2 0]
[ 0 2 -1 1 0 2 2 2 2 0 0 2]
[ 0 2 1 -1 0 2 2 2 2 0 0 2]
[ 1 2 0 0 -1 2 2 2 2 0 0 2]
[ 2 1 2 2 2 -1 0 0 0 2 2 0]
[ 2 0 2 2 2 0 -1 1 0 2 2 0]
[ 2 0 2 2 2 0 1 -1 0 2 2 0]
[ 2 0 2 2 2 0 0 0 -1 2 2 1]
[ 0 2 0 0 0 2 2 2 2 -1 1 2]
[ 0 2 0 0 0 2 2 2 2 1 -1 2]
[ 2 0 2 2 2 0 0 0 1 2 2 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
9
{@
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 1 1 1 1 0 1 1 1 0 2 1]
[ 1 -1 1 1 0 1 1 0 1 1 1 2]
[ 1 1 -1 1 1 2 0 1 1 1 0 1]
[ 1 1 1 -1 2 1 1 1 0 1 1 0]
[ 1 0 1 2 -1 1 1 0 1 1 1 1]
[ 0 1 2 1 1 -1 1 1 1 0 1 1]
[ 1 1 0 1 1 1 -1 1 1 2 0 1]
[ 1 0 1 1 0 1 1 -1 2 1 1 1]
[ 1 1 1 0 1 1 1 2 -1 1 1 0]
[ 0 1 1 1 1 0 2 1 1 -1 1 1]
[ 2 1 0 1 1 1 0 1 1 1 -1 1]
[ 1 2 1 0 1 1 1 1 0 1 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[10 3 6 3 3 3 3 3 3]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
10
{@
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 1 0 0 -1 0 0 0 0 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1)
@}
Intersection Matrix:
[-1 2 1 1 1 1 1 1 0 1 1 0]
[ 2 -1 0 1 0 1 1 1 1 1 1 1]
[ 1 0 -1 1 0 1 1 1 1 1 1 2]
[ 1 1 1 -1 1 0 1 2 1 1 0 1]
[ 1 0 0 1 -1 1 1 1 2 1 1 1]
[ 1 1 1 0 1 -1 1 1 1 2 0 1]
[ 1 1 1 1 1 1 -1 0 1 0 2 1]
[ 1 1 1 2 1 1 0 -1 1 0 1 1]
[ 0 1 1 1 2 1 1 1 -1 1 1 0]
[ 1 1 1 1 1 2 0 0 1 -1 1 1]
[ 1 1 1 0 1 0 2 1 1 1 -1 1]
[ 0 1 2 1 1 1 1 1 0 1 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[10 3 3 3 3 3 3 3 6]
[-3 0 -1 -1 -1 -1 -1 -1 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 0 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
11
{@
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0)
@}
Intersection Matrix:
[-1 0 2 1 1 1 1 1 1 1 1 0]
[ 0 -1 1 2 1 1 1 1 1 1 1 0]
[ 2 1 -1 0 1 1 1 1 0 1 1 1]
[ 1 2 0 -1 1 1 1 1 0 1 1 1]
[ 1 1 1 1 -1 0 0 2 1 1 1 1]
[ 1 1 1 1 0 -1 0 1 1 1 2 1]
[ 1 1 1 1 0 0 -1 1 1 2 1 1]
[ 1 1 1 1 2 1 1 -1 1 0 0 1]
[ 1 1 0 0 1 1 1 1 -1 1 1 2]
[ 1 1 1 1 1 1 2 0 1 -1 0 1]
[ 1 1 1 1 1 2 1 0 1 0 -1 1]
[ 0 0 1 1 1 1 1 1 2 1 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
12
{@
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1),
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 1 1 1 1 1 2 0 1 0 1 1]
[ 1 -1 1 2 0 0 1 1 1 1 1 1]
[ 1 1 -1 1 1 1 0 2 1 1 1 0]
[ 1 2 1 -1 1 1 1 1 0 1 0 1]
[ 1 0 1 1 -1 0 1 1 2 1 1 1]
[ 1 0 1 1 0 -1 1 1 1 1 2 1]
[ 2 1 0 1 1 1 -1 1 1 1 1 0]
[ 0 1 2 1 1 1 1 -1 1 0 1 1]
[ 1 1 1 0 2 1 1 1 -1 1 0 1]
[ 0 1 1 1 1 1 1 0 1 -1 1 2]
[ 1 1 1 0 1 2 1 1 0 1 -1 1]
[ 1 1 0 1 1 1 0 1 1 2 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[10 3 6 3 3 3 3 3 3]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
13
{@
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 1 2 0 2 3 1 1 1 0]
[ 1 -1 0 0 1 1 1 1 2 2 3 1]
[ 1 0 -1 0 1 1 1 1 2 3 2 1]
[ 1 0 0 -1 1 1 1 1 3 2 2 1]
[ 2 1 1 1 -1 3 0 0 1 1 1 2]
[ 0 1 1 1 3 -1 2 2 1 1 1 0]
[ 2 1 1 1 0 2 -1 0 1 1 1 3]
[ 3 1 1 1 0 2 0 -1 1 1 1 2]
[ 1 2 2 3 1 1 1 1 -1 0 0 1]
[ 1 2 3 2 1 1 1 1 0 -1 0 1]
[ 1 3 2 2 1 1 1 1 0 0 -1 1]
[ 0 1 1 1 2 0 3 2 1 1 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
14
{@
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 1 0 0 0]
[ 0 -1 0 0 0 0 0 0 0 0 1 0]
[ 0 0 -1 0 0 0 0 0 0 0 0 1]
[ 0 0 0 -1 0 0 1 0 0 0 0 0]
[ 0 0 0 0 -1 0 0 1 0 0 0 0]
[ 0 0 0 0 0 -1 0 0 0 1 0 0]
[ 0 0 0 1 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 1 0 0 -1 0 0 0 0]
[ 1 0 0 0 0 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 1 0 0 0 -1 0 0]
[ 0 1 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 1 0 0 0 0 0 0 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
15
{@
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1)
@}
Intersection Matrix:
[-1 0 0 0 0 0 1 0 0 0 0 0]
[ 0 -1 0 0 0 0 0 1 0 0 0 0]
[ 0 0 -1 0 0 0 0 0 0 0 1 0]
[ 0 0 0 -1 0 0 0 0 1 0 0 0]
[ 0 0 0 0 -1 0 0 0 0 1 0 0]
[ 0 0 0 0 0 -1 0 0 0 0 0 1]
[ 1 0 0 0 0 0 -1 0 0 0 0 0]
[ 0 1 0 0 0 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 -1 0 0 0]
[ 0 0 0 0 1 0 0 0 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 1 0 0 0 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
16
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2)
@}
Intersection Matrix:
[-1 1 1 0 0 1 1 1 1 0 0 0 2 2 1 1 2 1 1 1 0 0 1 0 0 0 1 1 0 1 2 1 1 2 0 1]
[ 1 -1 0 0 1 1 0 2 1 1 2 1 1 1 0 0 0 1 1 0 0 0 1 1 1 0 2 1 2 1 1 2 1 0 1 0]
[ 1 0 -1 0 2 0 0 2 1 0 2 2 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1 2 1 1 1 0 1 1]
[ 0 0 0 -1 1 0 0 2 1 0 1 1 2 1 1 1 1 1 1 0 0 0 1 0 0 0 1 1 1 2 2 2 1 1 1 1]
[ 0 1 2 1 -1 2 1 0 1 1 0 0 1 2 1 0 1 2 1 1 1 0 1 1 0 0 1 0 1 0 1 1 1 2 0 0]
[ 1 1 0 0 2 -1 0 1 0 0 1 1 1 0 1 2 1 0 1 1 1 1 0 0 1 1 0 1 0 2 1 1 1 0 2 2]
[ 1 0 0 0 1 0 -1 1 0 0 2 1 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 0 1 2 1 2 2 0 2 1]
[ 1 2 2 2 0 1 1 -1 0 1 0 0 0 1 1 1 1 1 1 2 2 1 0 1 1 1 0 0 0 0 0 0 1 1 1 1]
[ 1 1 1 1 1 0 0 0 -1 1 1 0 1 1 0 2 1 0 2 2 1 0 0 0 2 1 1 1 0 1 0 1 1 0 2 1]
[ 0 1 0 0 1 0 0 1 1 -1 1 1 1 1 2 1 1 1 0 1 1 1 0 1 0 0 0 0 0 2 2 1 2 1 1 2]
[ 0 2 2 1 0 1 2 0 1 1 -1 0 1 1 1 1 2 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 2 0 1]
[ 0 1 2 1 0 1 1 0 0 1 0 -1 1 2 0 1 2 1 2 2 1 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1]
[ 2 1 1 2 1 1 1 0 1 1 1 1 -1 0 1 0 0 1 0 1 2 2 0 2 1 1 0 0 1 0 0 0 1 0 1 1]
[ 2 1 0 1 2 0 1 1 1 1 1 2 0 -1 1 1 0 0 0 0 1 2 1 1 1 2 0 1 1 1 0 0 0 0 1 1]
[ 1 0 1 1 1 1 1 1 0 2 1 0 1 1 -1 1 1 0 2 1 0 0 1 0 2 1 2 2 1 0 0 1 0 0 1 0]
[ 1 0 1 1 0 2 1 1 2 1 1 1 0 1 1 -1 0 2 0 0 1 1 1 2 0 0 1 0 2 0 1 1 1 1 0 0]
[ 2 0 0 1 1 1 0 1 1 1 2 2 0 0 1 0 -1 1 0 0 1 1 1 2 1 1 1 0 2 1 0 1 1 0 1 0]
[ 1 1 0 1 2 0 1 1 0 1 1 1 1 0 0 2 1 -1 1 1 0 1 1 0 2 2 1 2 0 1 0 0 0 0 1 1]
[ 1 1 0 1 1 1 1 1 2 0 1 2 0 0 2 0 0 1 -1 0 1 2 1 2 0 1 0 0 1 1 1 0 1 1 0 1]
[ 1 0 0 0 1 1 1 2 2 1 1 2 1 0 1 0 0 1 0 -1 0 1 2 1 0 1 1 1 2 1 1 1 0 1 0 0]
[ 0 0 0 0 1 1 1 2 1 1 1 1 2 1 0 1 1 0 1 0 -1 0 2 0 1 1 2 2 1 1 1 1 0 1 0 0]
[ 0 0 1 0 0 1 0 1 0 1 1 0 2 2 0 1 1 1 2 1 0 -1 1 0 1 0 2 1 1 1 1 2 1 1 1 0]
[ 1 1 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 1 2 2 1 -1 1 1 0 0 0 0 1 1 1 2 0 2 2]
[ 0 1 1 0 1 0 1 1 0 1 0 0 2 1 0 2 2 0 2 1 0 0 1 -1 1 1 1 2 0 1 1 1 0 1 1 1]
[ 0 1 1 0 0 1 1 1 2 0 0 1 1 1 2 0 1 2 0 0 1 1 1 1 -1 0 0 0 1 1 2 1 1 2 0 1]
[ 0 0 1 0 0 1 0 1 1 0 1 0 1 2 1 0 1 2 1 1 1 0 0 1 0 -1 1 0 1 1 2 2 2 1 1 1]
[ 1 2 1 1 1 0 1 0 1 0 0 1 0 0 2 1 1 1 0 1 2 2 0 1 0 1 -1 0 0 1 1 0 1 1 1 2]
[ 1 1 1 1 0 1 0 0 1 0 1 1 0 1 2 0 0 2 0 1 2 1 0 2 0 0 0 -1 1 1 1 1 2 1 1 1]
[ 0 2 1 1 1 0 1 0 0 0 0 0 1 1 1 2 2 0 1 2 1 1 0 0 1 1 0 1 -1 1 1 0 1 1 1 2]
[ 1 1 2 2 0 2 2 0 1 2 0 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 0 0 0 1 0 0]
[ 2 1 1 2 1 1 1 0 0 2 1 1 0 0 0 1 0 0 1 1 1 1 1 1 2 2 1 1 1 0 -1 0 0 0 1 0]
[ 1 2 1 2 1 1 2 0 1 1 0 1 0 0 1 1 1 0 0 1 1 2 1 1 1 2 0 1 0 0 0 -1 0 1 0 1]
[ 1 1 1 1 1 1 2 1 1 2 0 1 1 0 0 1 1 0 1 0 0 1 2 0 1 2 1 2 1 0 0 0 -1 1 0 0]
[ 2 0 0 1 2 0 0 1 0 1 2 1 0 0 0 1 0 0 1 1 1 1 0 1 2 1 1 1 1 1 0 1 1 -1 2 1]
[ 0 1 1 1 0 2 2 1 2 1 0 1 1 1 1 0 1 1 0 0 0 1 2 1 0 1 1 1 1 0 1 0 0 2 -1 0]
[ 1 0 1 1 0 2 1 1 1 2 1 1 1 1 0 0 0 1 1 0 0 0 2 1 1 1 2 1 2 0 0 1 0 1 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
17
{@
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2),
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0)
@}
Intersection Matrix:
[-1 1 1 1 0 1 0 1 0 2 0 1 2 0 1 0 2 0 1 0 2 1 0 0 2 1 1 0 1 1 0 1 1 1 1 1]
[ 1 -1 1 2 0 1 1 2 2 0 1 1 0 1 0 2 0 2 0 1 1 0 0 1 1 1 0 1 0 0 0 1 1 1 1 1]
[ 1 1 -1 0 1 2 2 1 1 1 2 0 0 0 0 1 1 0 0 1 0 1 1 0 1 1 2 0 2 0 1 1 1 1 1 0]
[ 1 2 0 -1 2 1 1 0 0 1 1 0 1 1 1 0 1 0 1 1 0 2 2 1 0 0 1 0 2 1 1 0 1 0 1 1]
[ 0 0 1 2 -1 1 0 2 1 1 1 1 1 0 1 1 1 1 0 0 2 0 0 0 2 1 1 1 0 0 0 2 1 1 1 1]
[ 1 1 2 1 1 -1 0 0 1 1 0 1 1 2 2 0 0 1 2 0 1 0 1 1 0 1 0 2 0 1 1 1 0 0 1 1]
[ 0 1 2 1 0 0 -1 1 0 1 0 1 2 1 2 0 1 1 1 0 2 1 1 1 1 0 0 1 0 1 0 1 1 0 1 2]
[ 1 2 1 0 2 0 1 -1 0 1 0 1 1 1 1 0 1 0 2 1 0 1 1 1 0 1 1 1 1 2 2 0 0 1 0 0]
[ 0 2 1 0 1 1 0 0 -1 1 0 1 2 0 1 0 2 0 1 1 1 2 1 1 1 0 1 0 1 2 1 0 1 1 0 1]
[ 2 0 1 1 1 1 1 1 1 -1 1 1 0 1 0 2 0 2 0 2 0 1 1 2 0 0 0 1 0 1 1 0 1 1 0 1]
[ 0 1 2 1 1 0 0 0 0 1 -1 2 2 1 1 0 1 1 2 1 1 1 0 1 1 1 0 1 0 2 1 0 0 1 0 1]
[ 1 1 0 0 1 1 1 1 1 1 2 -1 0 1 1 1 1 0 0 0 1 1 2 1 0 0 1 0 2 0 0 1 2 0 2 1]
[ 2 0 0 1 1 1 2 1 2 0 2 0 -1 1 0 2 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 0]
[ 0 1 0 1 0 2 1 1 0 1 1 1 1 -1 0 1 2 0 0 1 1 1 0 0 2 1 2 0 1 1 1 1 1 2 0 0]
[ 1 0 0 1 1 2 2 1 1 0 1 1 0 0 -1 2 1 1 0 2 0 1 0 1 1 1 1 0 1 1 1 0 1 2 0 0]
[ 0 2 1 0 1 0 0 0 0 2 0 1 2 1 2 -1 1 0 2 0 1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 1]
[ 2 0 1 1 1 0 1 1 2 0 1 1 0 2 1 1 -1 2 1 1 0 0 1 1 0 1 0 2 0 0 1 1 0 0 1 1]
[ 0 2 0 0 1 1 1 0 0 2 1 0 1 0 1 0 2 -1 1 0 1 1 1 0 1 1 2 0 2 1 1 1 1 1 1 0]
[ 1 0 0 1 0 2 1 2 1 0 2 0 0 0 0 2 1 1 -1 1 1 1 1 1 1 0 1 0 1 0 0 1 2 1 1 1]
[ 0 1 1 1 0 0 0 1 1 2 1 0 1 1 2 0 1 0 1 -1 2 0 1 0 1 1 1 1 1 0 0 2 1 0 2 1]
[ 2 1 0 0 2 1 2 0 1 0 1 1 0 1 0 1 0 1 1 2 -1 1 1 1 0 1 1 1 1 1 2 0 0 1 0 0]
[ 1 0 1 2 0 0 1 1 2 1 1 1 0 1 1 1 0 1 1 0 1 -1 0 0 1 2 1 2 0 0 1 2 0 1 1 0]
[ 0 0 1 2 0 1 1 1 1 1 0 2 1 0 0 1 1 1 1 1 1 0 -1 0 2 2 1 1 0 1 1 1 0 2 0 0]
[ 0 1 0 1 0 1 1 1 1 2 1 1 1 0 1 0 1 0 1 0 1 0 0 -1 2 2 2 1 1 0 1 2 0 1 1 0]
[ 2 1 1 0 2 0 1 0 1 0 1 0 0 2 1 1 0 1 1 1 0 1 2 2 -1 0 0 1 1 1 1 0 1 0 1 1]
[ 1 1 1 0 1 1 0 1 0 0 1 0 1 1 1 1 1 1 0 1 1 2 2 2 0 -1 0 0 1 1 0 0 2 0 1 2]
[ 1 0 2 1 1 0 0 1 1 0 0 1 1 2 1 1 0 2 1 1 1 1 1 2 0 0 -1 1 0 1 0 0 1 0 1 2]
[ 0 1 0 0 1 2 1 1 0 1 1 0 1 0 0 1 2 0 0 1 1 2 1 1 1 0 1 -1 2 1 0 0 2 1 1 1]
[ 1 0 2 2 0 0 0 1 1 0 0 2 1 1 1 1 0 2 1 1 1 0 0 1 1 1 0 2 -1 1 1 1 0 1 0 1]
[ 1 0 0 1 0 1 1 2 2 1 2 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 1 1 1 -1 0 2 1 0 2 1]
[ 0 0 1 1 0 1 0 2 1 1 1 0 1 1 1 1 1 1 0 0 2 1 1 1 1 0 0 0 1 0 -1 1 2 0 2 2]
[ 1 1 1 0 2 1 1 0 0 0 0 1 1 1 0 1 1 1 1 2 0 2 1 2 0 0 0 0 1 2 1 -1 1 1 0 1]
[ 1 1 1 1 1 0 1 0 1 1 0 2 1 1 1 0 0 1 2 1 0 0 0 0 1 2 1 2 0 1 2 1 -1 1 0 0]
[ 1 1 1 0 1 0 0 1 1 1 1 0 1 2 2 0 0 1 1 0 1 1 2 1 0 0 0 1 1 0 0 1 1 -1 2 2]
[ 1 1 1 1 1 1 1 0 0 0 0 2 1 0 0 1 1 1 1 2 0 1 0 1 1 1 1 1 0 2 2 0 0 2 -1 0]
[ 1 1 0 1 1 1 2 0 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 1 2 2 1 1 1 2 1 0 2 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
18
{@
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 0 1 2 1 2 0 0 2 1 2 0 0 1 2 2 0 1 0 2 1 2 1 1 1 3 1 1 1 0 1 1 1 1 1]
[ 1 -1 1 2 1 1 2 0 1 0 0 1 1 2 0 1 2 2 1 0 0 1 1 0 1 2 1 1 2 0 1 3 1 1 1 2]
[ 0 1 -1 1 3 0 2 1 1 2 2 1 1 0 1 1 1 1 2 0 1 1 1 0 2 2 2 2 1 1 1 1 0 1 0 0]
[ 1 2 1 -1 1 0 0 1 1 2 1 2 2 0 1 1 1 1 0 2 1 0 0 1 2 1 1 1 1 3 0 0 1 2 2 1]
[ 2 1 3 1 -1 2 0 1 1 0 0 1 1 2 1 1 1 1 0 2 1 1 1 2 0 0 0 0 1 1 1 1 2 1 2 2]
[ 1 1 0 0 2 -1 1 1 2 1 2 2 2 1 0 0 1 1 1 1 1 1 0 0 3 2 1 1 2 2 0 1 1 1 1 0]
[ 2 2 2 0 0 1 -1 1 2 1 1 1 1 1 2 0 1 1 1 3 1 0 1 1 1 1 0 0 0 2 1 0 2 2 1 1]
[ 0 0 1 1 1 1 1 -1 1 1 0 2 0 1 1 1 3 1 1 1 1 0 2 0 1 2 2 0 1 1 0 2 2 2 1 2]
[ 0 1 1 1 1 2 2 1 -1 2 0 1 1 0 1 3 1 1 0 0 1 1 1 2 0 0 2 2 1 1 1 1 0 1 2 2]
[ 2 0 2 2 0 1 1 1 2 -1 1 1 1 3 0 0 1 1 1 1 1 2 1 1 1 1 0 0 2 0 1 2 2 0 1 1]
[ 1 0 2 1 0 2 1 0 0 1 -1 1 1 1 1 2 2 2 0 1 0 0 1 1 0 1 1 1 1 1 1 2 1 2 2 3]
[ 2 1 1 2 1 2 1 2 1 1 1 -1 1 1 2 1 0 2 2 1 0 1 1 1 0 1 0 2 0 0 3 1 0 1 0 1]
[ 0 1 1 2 1 2 1 0 1 1 1 1 -1 1 2 1 2 0 2 1 2 1 3 1 0 1 2 0 0 0 1 1 2 1 0 1]
[ 0 2 0 0 2 1 1 1 0 3 1 1 1 -1 2 2 1 1 1 1 1 0 1 1 1 1 2 2 0 2 1 0 0 2 1 1]
[ 1 0 1 1 1 0 2 1 1 0 1 2 2 2 -1 1 1 1 0 0 1 2 0 1 2 1 1 1 3 1 0 2 1 0 2 1]
[ 2 1 1 1 1 0 0 1 3 0 2 1 1 2 1 -1 1 1 2 2 1 1 1 0 2 2 0 0 1 1 1 1 2 1 0 0]
[ 2 2 1 1 1 1 1 3 1 1 2 0 2 1 1 1 -1 1 1 1 1 2 0 2 1 0 0 2 1 1 2 0 0 0 1 0]
[ 0 2 1 1 1 1 1 1 1 1 2 2 0 1 1 1 1 -1 1 1 3 2 2 2 1 0 2 0 1 1 0 0 2 0 1 0]
[ 1 1 2 0 0 1 1 1 0 1 0 2 2 1 0 2 1 1 -1 1 1 1 0 2 1 0 1 1 2 2 0 1 1 1 3 2]
[ 0 0 0 2 2 1 3 1 0 1 1 1 1 1 0 2 1 1 1 -1 1 2 1 1 1 1 2 2 2 0 1 2 0 0 1 1]
[ 2 0 1 1 1 1 1 1 1 1 0 0 2 1 1 1 1 3 1 1 -1 0 0 0 1 2 0 2 1 1 2 2 0 2 1 2]
[ 1 1 1 0 1 1 0 0 1 2 0 1 1 0 2 1 2 2 1 2 0 -1 1 0 1 2 1 1 0 2 1 1 1 3 1 2]
[ 2 1 1 0 1 0 1 2 1 1 1 1 3 1 0 1 0 2 0 1 0 1 -1 1 2 1 0 2 2 2 1 1 0 1 2 1]
[ 1 0 0 1 2 0 1 0 2 1 1 1 1 1 1 0 2 2 2 1 0 0 1 -1 2 3 1 1 1 1 1 2 1 2 0 1]
[ 1 1 2 2 0 3 1 1 0 1 0 0 0 1 2 2 1 1 1 1 1 1 2 2 -1 0 1 1 0 0 2 1 1 1 1 2]
[ 1 2 2 1 0 2 1 2 0 1 1 1 1 1 1 2 0 0 0 1 2 2 1 3 0 -1 1 1 1 1 1 0 1 0 2 1]
[ 3 1 2 1 0 1 0 2 2 0 1 0 2 2 1 0 0 2 1 2 0 1 0 1 1 1 -1 1 1 1 2 1 1 1 1 1]
[ 1 1 2 1 0 1 0 0 2 0 1 2 0 2 1 0 2 0 1 2 2 1 2 1 1 1 1 -1 1 1 0 1 3 1 1 1]
[ 1 2 1 1 1 2 0 1 1 2 1 0 0 0 3 1 1 1 2 2 1 0 2 1 0 1 1 1 -1 1 2 0 1 2 0 1]
[ 1 0 1 3 1 2 2 1 1 0 1 0 0 2 1 1 1 1 2 0 1 2 2 1 0 1 1 1 1 -1 2 2 1 0 0 1]
[ 0 1 1 0 1 0 1 0 1 1 1 3 1 1 0 1 2 0 0 1 2 1 1 1 2 1 2 0 2 2 -1 1 2 1 2 1]
[ 1 3 1 0 1 1 0 2 1 2 2 1 1 0 2 1 0 0 1 2 2 1 1 2 1 0 1 1 0 2 1 -1 1 1 1 0]
[ 1 1 0 1 2 1 2 2 0 2 1 0 2 0 1 2 0 2 1 0 0 1 0 1 1 1 1 3 1 1 2 1 -1 1 1 1]
[ 1 1 1 2 1 1 2 2 1 0 2 1 1 2 0 1 0 0 1 0 2 3 1 2 1 0 1 1 2 0 1 1 1 -1 1 0]
[ 1 1 0 2 2 1 1 1 2 1 2 0 0 1 2 0 1 1 3 1 1 1 2 0 1 2 1 1 0 0 2 1 1 1 -1 0]
[ 1 2 0 1 2 0 1 2 2 1 3 1 1 1 1 0 0 0 2 1 2 2 1 1 2 1 1 1 1 1 1 0 1 0 0 -1]
Stabilizer Group Name:
C1
MatrixGroup(9, Integer Ring) of order 1
D7(10):S3≀C2
order := 72,
length := 2419200,
subgroup := MatrixGroup(9, Integer Ring) of order 2^3 * 3^2
Generators:
[ 3 1 0 2 1 1 1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[ 9 5 3 4 2 2 3 2 3]
[-4 -2 -1 -2 -1 -1 -1 -1 -2]
[-3 -2 -1 -1 0 -1 -1 -1 -1]
[-2 -1 -1 -1 0 0 -1 0 -1]
[-4 -2 -2 -2 -1 -1 -1 -1 -1]
[-1 -1 0 -1 0 0 0 0 0]
[-4 -2 -1 -2 -1 -1 -2 -1 -1]
[-3 -2 -1 -1 -1 -1 -1 0 -1]
[-3 -2 -1 -1 -1 0 -1 -1 -1]
[ 7 3 3 2 3 3 2 2 0]
[-3 -1 -1 -1 -1 -2 -1 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]>
Orbit type:{2,2,4,4,6,6,12,12,12,24,24,24,36,36,36}
Orbit:
1
{@
Mod: ( 4 -1 -1 -2 -1 -1 -2 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -1 0 -2 -1)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
S3^2
MatrixGroup(9, Integer Ring)
Generators:
[ 7 3 3 2 0 3 2 2 3]
[ 0 0 0 0 1 0 0 0 0]
[-3 -2 -1 -1 0 -1 -1 -1 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-2 -1 -1 0 0 -1 0 -1 -1]
[-2 -1 -1 0 0 -1 -1 0 -1]
[-3 -1 -1 -1 0 -2 -1 -1 -1]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
[ 7 3 3 2 3 3 2 2 0]
[-3 -1 -1 -1 -1 -2 -1 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
14
{@
Mod: ( 2 -1 -1 0 -1 -1 0 0 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 0 -1)
@}
Intersection Matrix:
[-1 1]
[ 1 -1]
Stabilizer Group Name:
S3^2
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
[ 7 3 3 2 3 0 2 2 3]
[ 0 0 0 0 0 1 0 0 0]
[-3 -1 -1 -1 -2 0 -1 -1 -1]
[-2 -1 -1 -1 -1 0 0 0 -1]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-2 -1 -1 0 -1 0 0 -1 -1]
[-2 -1 -1 0 -1 0 -1 0 -1]
[-3 -2 -1 -1 -1 0 -1 -1 -1]
[ 7 3 3 2 3 3 2 2 0]
[-3 -1 -1 -1 -1 -2 -1 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-2 -1 -1 -1 -1 -1 0 0 0]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-2 -1 -1 0 -1 -1 0 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
3
{@
Mod: ( 3 -1 -1 -2 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -2 -1),
Mod: ( 2 0 -1 -1 0 0 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -2 -1)
@}
Intersection Matrix:
[-1 2 1 1]
[ 2 -1 1 1]
[ 1 1 -1 2]
[ 1 1 2 -1]
Stabilizer Group Name:
C3*S3
MatrixGroup(9, Integer Ring)
Generators:
[10 3 3 3 6 3 3 3 3]
[-6 -2 -2 -2 -3 -2 -2 -2 -2]
[-3 -1 -1 -1 -2 0 -1 -1 -1]
[-3 -1 -1 0 -2 -1 -1 -1 -1]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 -1 0]
[-3 -1 -1 -1 -2 -1 0 -1 -1]
[-3 -1 -1 -1 -2 -1 -1 0 -1]
[-3 0 -1 -1 -2 -1 -1 -1 -1]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
4
{@
Mod: ( 3 -1 -1 0 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 0 -1),
Mod: ( 1 0 -1 0 0 0 0 0 -1),
Mod: ( 4 -2 -1 -1 -2 -2 -1 -1 -1)
@}
Intersection Matrix:
[-1 2 1 1]
[ 2 -1 1 1]
[ 1 1 -1 2]
[ 1 1 2 -1]
Stabilizer Group Name:
C3*S3
MatrixGroup(9, Integer Ring)
Generators:
[10 6 3 3 3 3 3 3 3]
[-3 -2 0 -1 -1 -1 -1 -1 -1]
[-3 -2 -1 -1 0 -1 -1 -1 -1]
[-3 -2 -1 0 -1 -1 -1 -1 -1]
[-3 -2 -1 -1 -1 -1 -1 -1 0]
[-6 -3 -2 -2 -2 -2 -2 -2 -2]
[-3 -2 -1 -1 -1 -1 0 -1 -1]
[-3 -2 -1 -1 -1 -1 -1 0 -1]
[-3 -2 -1 -1 -1 0 -1 -1 -1]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[10 3 6 3 3 3 3 3 3]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
5
{@
Mod: (0 0 1 0 0 0 0 0 0),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -2 -3),
Mod: ( 3 0 -1 -1 -1 -2 -1 -1 -1),
Mod: ( 3 -2 -1 -1 0 -1 -1 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 -1 -1 0),
Mod: ( 3 -1 -1 -1 -2 0 -1 -1 -1)
@}
Intersection Matrix:
[-1 2 1 1 2 1]
[ 2 -1 1 1 2 1]
[ 1 1 -1 2 1 2]
[ 1 1 2 -1 1 2]
[ 2 2 1 1 -1 1]
[ 1 1 2 2 1 -1]
Stabilizer Group Name:
D6
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 0 2 1 1 1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
[ 7 3 0 2 3 3 2 2 3]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[ 0 0 1 0 0 0 0 0 0]
[-2 -1 0 -1 -1 -1 0 0 -1]
[-3 -2 0 -1 -1 -1 -1 -1 -1]
[-3 -1 0 -1 -1 -2 -1 -1 -1]
[-2 -1 0 0 -1 -1 0 -1 -1]
[-2 -1 0 0 -1 -1 -1 0 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
6
{@
Mod: ( 3 -1 -1 -1 0 -2 -1 -1 -1),
Mod: (0 0 0 0 0 0 0 0 1),
Mod: ( 3 -2 -1 -1 -1 0 -1 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -1 -1 -2),
Mod: ( 6 -2 -3 -2 -2 -2 -2 -2 -2),
Mod: ( 3 0 -1 -1 -2 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 2 1 1 2]
[ 1 -1 1 2 2 1]
[ 2 1 -1 1 1 2]
[ 1 2 1 -1 2 1]
[ 1 2 1 2 -1 1]
[ 2 1 2 1 1 -1]
Stabilizer Group Name:
D6
MatrixGroup(9, Integer Ring)
Generators:
[10 3 3 3 3 3 3 3 6]
[-3 0 -1 -1 -1 -1 -1 -1 -2]
[-6 -2 -2 -2 -2 -2 -2 -2 -3]
[-3 -1 -1 0 -1 -1 -1 -1 -2]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-3 -1 -1 -1 -1 -1 0 -1 -2]
[-3 -1 -1 -1 -1 -1 -1 0 -2]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[ 6 2 0 1 2 2 3 2 3]
[-2 0 0 0 -1 -1 -1 -1 -1]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 0 -1]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-2 -1 0 0 -1 0 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -2 -1 -1]
[-2 -1 0 0 -1 -1 -1 0 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
[ 7 3 0 2 3 3 2 2 3]
[-3 -2 0 -1 -1 -1 -1 -1 -1]
[ 0 0 1 0 0 0 0 0 0]
[-2 -1 0 -1 -1 -1 0 0 -1]
[-3 -1 0 -1 -1 -2 -1 -1 -1]
[-3 -1 0 -1 -2 -1 -1 -1 -1]
[-2 -1 0 0 -1 -1 0 -1 -1]
[-2 -1 0 0 -1 -1 -1 0 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
7
{@
Mod: ( 2 -1 0 0 -1 -1 -1 -1 0),
Mod: ( 5 -2 -1 -1 -2 -2 -2 -2 -2),
Mod: ( 4 -2 -1 -2 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -2 -1 -1 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -2 -1),
Mod: ( 1 0 -1 -1 0 0 0 0 0),
Mod: ( 4 -2 -1 -2 -1 -2 -1 -1 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -1 -1 -2),
Mod: ( 2 -1 -1 0 0 0 -1 -1 -1),
Mod: ( 2 0 -1 0 0 -1 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 0 -1 -1 -1),
Mod: ( 1 0 0 -1 0 0 0 0 -1)
@}
Intersection Matrix:
[-1 0 1 1 0 2 1 3 1 1 1 2]
[ 0 -1 1 1 0 3 1 2 1 1 1 2]
[ 1 1 -1 0 1 1 0 1 2 3 2 1]
[ 1 1 0 -1 1 1 0 1 3 2 2 1]
[ 0 0 1 1 -1 2 1 2 1 1 1 3]
[ 2 3 1 1 2 -1 1 0 1 1 1 0]
[ 1 1 0 0 1 1 -1 1 2 2 3 1]
[ 3 2 1 1 2 0 1 -1 1 1 1 0]
[ 1 1 2 3 1 1 2 1 -1 0 0 1]
[ 1 1 3 2 1 1 2 1 0 -1 0 1]
[ 1 1 2 2 1 1 3 1 0 0 -1 1]
[ 2 2 1 1 3 0 1 0 1 1 1 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 0 2 1 1 1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
8
{@
Mod: ( 2 0 -1 0 -1 -1 -1 0 -1),
Mod: ( 2 -1 -1 0 -1 -1 -1 0 0),
Mod: ( 2 -1 -1 0 0 -1 -1 0 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 0 -1),
Mod: (0 0 0 0 0 0 0 1 0),
Mod: ( 3 -1 -2 -1 -1 -1 -1 0 -1),
Mod: ( 2 -1 0 0 -1 -1 -1 0 -1),
Mod: ( 3 -2 -1 -1 -1 -1 -1 0 -1),
Mod: ( 3 -1 -1 -1 -1 -2 -1 0 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -1 0 -2),
Mod: ( 3 -1 -1 -1 -2 -1 -1 0 -1),
Mod: ( 5 -2 -2 -1 -2 -2 -2 -1 -2)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 1 0 0 0 0]
[ 0 -1 0 0 0 0 0 0 0 1 0 0]
[ 0 0 -1 0 0 0 0 0 0 0 1 0]
[ 0 0 0 -1 0 0 0 0 1 0 0 0]
[ 0 0 0 0 -1 0 0 0 0 0 0 1]
[ 0 0 0 0 0 -1 1 0 0 0 0 0]
[ 0 0 0 0 0 1 -1 0 0 0 0 0]
[ 1 0 0 0 0 0 0 -1 0 0 0 0]
[ 0 0 0 1 0 0 0 0 -1 0 0 0]
[ 0 1 0 0 0 0 0 0 0 -1 0 0]
[ 0 0 1 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 1 0 0 0 0 0 0 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 6 2 3 1 2 2 3 2 0]
[-2 0 -1 0 -1 -1 -1 -1 0]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-1 0 -1 0 0 0 -1 0 0]
[-2 -1 -1 0 0 -1 -1 -1 0]
[-2 -1 -1 0 -1 0 -1 -1 0]
[-3 -1 -1 -1 -1 -1 -2 -1 0]
[-2 -1 -1 0 -1 -1 -1 0 0]
[ 0 0 0 0 0 0 0 0 1]
[ 6 2 0 1 2 2 3 2 3]
[-2 0 0 0 -1 -1 -1 -1 -1]
[ 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 0 -1 0 -1]
[-2 -1 0 0 0 -1 -1 -1 -1]
[-2 -1 0 0 -1 0 -1 -1 -1]
[-3 -1 0 -1 -1 -1 -2 -1 -1]
[-2 -1 0 0 -1 -1 -1 0 -1]
[-3 -1 0 -1 -1 -1 -1 -1 -2]
9
{@
Mod: ( 4 -1 -2 -2 -1 -1 -1 -2 -1),
Mod: ( 1 0 0 -1 0 0 0 -1 0),
Mod: ( 6 -2 -2 -2 -2 -2 -2 -3 -2),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -2 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -2 -1),
Mod: ( 3 0 -1 -1 -1 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -1 0 -1 -2 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -1 -2 -2),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -2 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -1 -2 0),
Mod: ( 3 -1 0 -1 -1 -1 -1 -2 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -2 -1)
@}
Intersection Matrix:
[-1 0 0 0 0 0 0 0 0 0 1 0]
[ 0 -1 1 0 0 0 0 0 0 0 0 0]
[ 0 1 -1 0 0 0 0 0 0 0 0 0]
[ 0 0 0 -1 0 0 1 0 0 0 0 0]
[ 0 0 0 0 -1 0 0 0 1 0 0 0]
[ 0 0 0 0 0 -1 0 0 0 0 0 1]
[ 0 0 0 1 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 -1 0 1 0 0]
[ 0 0 0 0 1 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 1 0 -1 0 0]
[ 1 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 1 0 0 0 0 0 -1]
Stabilizer Group Name:
S3
MatrixGroup(9, Integer Ring)
Generators:
[ 3 1 0 2 1 1 1 0 0]
[-1 0 0 -1 0 -1 0 0 0]
[ 0 0 1 0 0 0 0 0 0]
[-2 -1 0 -1 -1 -1 -1 0 0]
[-1 0 0 -1 -1 0 0 0 0]
[-1 -1 0 -1 0 0 0 0 0]
[-1 0 0 -1 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 1 0]
[ 0 0 0 0 0 0 0 0 1]
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
10
{@
Mod: ( 3 -2 -1 -1 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 0 -1 -2),
Mod: ( 5 -2 -2 -1 -2 -2 -1 -2 -2),
Mod: ( 3 -1 -1 -1 0 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -2 0 -1 -1),
Mod: ( 2 -1 -1 0 0 -1 0 -1 -1),
Mod: ( 4 -1 -1 -2 -2 -1 -2 -1 -1),
Mod: ( 3 -1 0 -1 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -2 -2 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -1 -1 -1 -1 -2 -1 0),
Mod: ( 2 -1 0 0 -1 -1 0 -1 -1),
Mod: ( 3 -1 -1 -1 -1 0 -2 -1 -1),
Mod: (0 0 0 0 0 0 1 0 0),
Mod: ( 3 0 -1 -1 -1 -1 -2 -1 -1),
Mod: ( 3 -1 -2 -1 -1 -1 0 -1 -1),
Mod: ( 1 0 0 -1 0 0 -1 0 0),
Mod: ( 3 -1 -1 -1 -2 -1 0 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 0 -1 -1),
Mod: ( 6 -2 -2 -2 -2 -2 -3 -2 -2),
Mod: ( 4 -1 -1 -2 -1 -2 -2 -1 -1),
Mod: ( 2 -1 -1 0 -1 -1 0 -1 0),
Mod: ( 2 0 -1 0 -1 -1 0 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -1 -2 -1 -2),
Mod: ( 4 -2 -1 -2 -1 -1 -2 -1 -1)
@}
Intersection Matrix:
[-1 0 0 2 0 0 2 2 2 2 0 2 0 3 0 2 0 0 2 2 0 1 2 1]
[ 0 -1 0 2 0 0 2 2 2 3 0 2 0 2 0 2 0 0 2 2 1 0 1 2]
[ 0 0 -1 2 0 0 2 2 2 2 0 2 1 2 0 3 0 0 1 2 0 0 2 2]
[ 2 2 2 -1 2 1 1 0 0 0 2 0 2 0 2 0 3 2 0 0 2 2 0 0]
[ 0 0 0 2 -1 0 2 2 2 2 0 3 0 2 0 2 0 1 2 1 0 0 2 2]
[ 0 0 0 1 0 -1 3 2 2 2 0 2 0 2 0 2 1 0 2 2 0 0 2 2]
[ 2 2 2 1 2 3 -1 0 0 0 2 0 2 0 2 0 1 2 0 0 2 2 0 0]
[ 2 2 2 0 2 2 0 -1 1 0 1 0 2 0 3 0 2 2 0 0 2 2 0 0]
[ 2 2 2 0 2 2 0 1 -1 0 3 0 2 0 1 0 2 2 0 0 2 2 0 0]
[ 2 3 2 0 2 2 0 0 0 -1 2 0 2 0 2 0 2 2 0 0 1 2 1 0]
[ 0 0 0 2 0 0 2 1 3 2 -1 2 0 2 1 2 0 0 2 2 0 0 2 2]
[ 2 2 2 0 3 2 0 0 0 0 2 -1 2 0 2 0 2 1 0 1 2 2 0 0]
[ 0 0 1 2 0 0 2 2 2 2 0 2 -1 2 0 1 0 0 3 2 0 0 2 2]
[ 3 2 2 0 2 2 0 0 0 0 2 0 2 -1 2 0 2 2 0 0 2 1 0 1]
[ 0 0 0 2 0 0 2 3 1 2 1 2 0 2 -1 2 0 0 2 2 0 0 2 2]
[ 2 2 3 0 2 2 0 0 0 0 2 0 1 0 2 -1 2 2 1 0 2 2 0 0]
[ 0 0 0 3 0 1 1 2 2 2 0 2 0 2 0 2 -1 0 2 2 0 0 2 2]
[ 0 0 0 2 1 0 2 2 2 2 0 1 0 2 0 2 0 -1 2 3 0 0 2 2]
[ 2 2 1 0 2 2 0 0 0 0 2 0 3 0 2 1 2 2 -1 0 2 2 0 0]
[ 2 2 2 0 1 2 0 0 0 0 2 1 2 0 2 0 2 3 0 -1 2 2 0 0]
[ 0 1 0 2 0 0 2 2 2 1 0 2 0 2 0 2 0 0 2 2 -1 0 3 2]
[ 1 0 0 2 0 0 2 2 2 2 0 2 0 1 0 2 0 0 2 2 0 -1 2 3]
[ 2 1 2 0 2 2 0 0 0 1 2 0 2 0 2 0 2 2 0 0 3 2 -1 0]
[ 1 2 2 0 2 2 0 0 0 0 2 0 2 1 2 0 2 2 0 0 2 3 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[10 3 6 3 3 3 3 3 3]
[-3 0 -2 -1 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 -1 0]
[-3 -1 -2 0 -1 -1 -1 -1 -1]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[-3 -1 -2 -1 -1 -1 0 -1 -1]
[-3 -1 -2 -1 -1 -1 -1 0 -1]
[-6 -2 -3 -2 -2 -2 -2 -2 -2]
11
{@
Mod: ( 4 -1 -2 -1 -1 -1 -1 -2 -2),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -2 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -2 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 -1 0),
Mod: ( 4 -1 -1 -1 -1 -1 -2 -2 -2),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -2 -1),
Mod: ( 2 0 -1 -1 -1 0 0 -1 -1),
Mod: ( 1 0 -1 0 0 0 0 -1 0),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -2 -1),
Mod: ( 1 0 0 0 0 0 -1 -1 0),
Mod: ( 6 -2 -2 -3 -2 -2 -2 -2 -2),
Mod: ( 1 0 0 0 0 0 0 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -2 -1),
Mod: ( 2 -1 -1 -1 0 0 0 -1 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -2 -1),
Mod: ( 3 -1 -1 -2 0 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -1 -2 -2),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -2 -1),
Mod: ( 3 -1 0 -2 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -2 -1 -1 -1 -1 0),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -2 -1),
Mod: ( 2 0 -1 -1 0 -1 0 -1 -1),
Mod: ( 3 -1 -1 -2 -1 0 -1 -1 -1),
Mod: ( 3 0 -1 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 2 0 1 0 0 1 1 1 0 0 0 1 1 1 1 2 2 1 0 1 1]
[ 1 -1 1 1 0 0 2 1 0 0 1 1 0 2 0 1 1 0 1 1 1 1 2 1]
[ 1 1 -1 0 2 1 1 1 1 2 0 2 1 1 0 1 0 0 1 0 0 1 1 1]
[ 2 1 0 -1 2 1 1 1 1 1 1 1 2 1 0 1 0 0 0 0 0 1 1 1]
[ 0 0 2 2 -1 0 1 1 0 0 1 0 0 1 1 1 1 1 1 2 1 1 1 1]
[ 1 0 1 1 0 -1 2 1 0 0 1 1 0 1 0 1 1 1 1 1 0 2 1 2]
[ 0 2 1 1 1 2 -1 0 1 1 1 0 1 0 2 1 1 1 1 1 1 0 0 0]
[ 0 1 1 1 1 1 0 -1 1 0 2 0 0 0 1 1 2 1 2 1 1 0 1 1]
[ 1 0 1 1 0 0 1 1 -1 0 1 1 0 2 1 2 1 0 1 1 0 2 1 1]
[ 1 0 2 1 0 0 1 0 0 -1 2 0 0 1 1 1 2 1 1 1 1 1 1 1]
[ 1 1 0 1 1 1 1 2 1 2 -1 2 1 1 1 0 0 1 0 0 1 1 0 0]
[ 0 1 2 1 0 1 0 0 1 0 2 -1 1 0 1 1 1 1 1 2 1 0 1 1]
[ 0 0 1 2 0 0 1 0 0 0 1 1 -1 1 1 1 2 1 2 1 1 1 1 1]
[ 0 2 1 1 1 1 0 0 2 1 1 0 1 -1 1 0 1 2 1 1 1 0 0 1]
[ 1 0 0 0 1 0 2 1 1 1 1 1 1 1 -1 1 0 0 1 1 0 1 2 2]
[ 1 1 1 1 1 1 1 1 2 1 0 1 1 0 1 -1 1 2 0 0 2 0 0 0]
[ 1 1 0 0 1 1 1 2 1 2 0 1 2 1 0 1 -1 0 0 1 0 1 1 1]
[ 1 0 0 0 1 1 1 1 0 1 1 1 1 2 0 2 0 -1 1 1 0 1 2 1]
[ 2 1 1 0 1 1 1 2 1 1 0 1 2 1 1 0 0 1 -1 0 1 1 0 0]
[ 2 1 0 0 2 1 1 1 1 1 0 2 1 1 1 0 1 1 0 -1 1 1 0 0]
[ 1 1 0 0 1 0 1 1 0 1 1 1 1 1 0 2 0 0 1 1 -1 2 1 2]
[ 0 1 1 1 1 2 0 0 2 1 1 0 1 0 1 0 1 1 1 1 2 -1 1 0]
[ 1 2 1 1 1 1 0 1 1 1 0 1 1 0 2 0 1 2 0 0 1 1 -1 0]
[ 1 1 1 1 1 2 0 1 1 1 0 1 1 1 2 0 1 1 0 0 2 0 0 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
12
{@
Mod: ( 1 0 0 0 0 0 -1 0 -1),
Mod: ( 2 -1 -1 -1 -1 0 0 0 -1),
Mod: ( 2 -1 0 -1 -1 -1 0 0 -1),
Mod: (0 0 0 1 0 0 0 0 0),
Mod: ( 4 -1 -1 -1 -2 -2 -2 -1 -1),
Mod: ( 2 0 -1 -1 0 -1 -1 0 -1),
Mod: ( 4 -2 -1 -1 -2 -1 -2 -1 -1),
Mod: ( 2 0 -1 -1 -1 -1 0 0 -1),
Mod: ( 3 -1 -2 0 -1 -1 -1 -1 -1),
Mod: ( 4 -1 -2 -1 -1 -1 -2 -1 -2),
Mod: ( 5 -2 -2 -2 -2 -2 -2 -1 -1),
Mod: ( 1 0 -1 0 0 0 -1 0 0),
Mod: ( 2 -1 -1 -1 -1 -1 0 0 0),
Mod: ( 2 0 -1 -1 -1 0 -1 0 -1),
Mod: ( 3 -2 -1 0 -1 -1 -1 -1 -1),
Mod: ( 3 -1 -1 0 -1 -1 -1 -1 -2),
Mod: ( 2 -1 0 -1 -1 -1 -1 0 0),
Mod: ( 3 -1 -1 0 -1 -2 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 0 -1),
Mod: ( 4 -2 -1 -1 -1 -2 -2 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -2 -1 -1 -2),
Mod: ( 2 -1 -1 -1 0 0 -1 0 -1),
Mod: ( 3 -1 -1 0 -2 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -2 -2 -2 -1 -2)
@}
Intersection Matrix:
[-1 1 1 0 1 0 1 1 1 0 2 0 2 0 1 0 1 1 1 1 2 0 1 1]
[ 1 -1 0 1 2 1 1 0 1 1 1 1 0 0 1 1 1 2 0 2 0 0 1 1]
[ 1 0 -1 1 1 1 1 0 2 2 1 2 0 1 1 1 0 1 0 1 0 1 1 0]
[ 0 1 1 -1 1 1 1 1 0 1 2 0 1 1 0 0 1 0 1 1 2 1 0 2]
[ 1 2 1 1 -1 1 0 1 1 1 0 1 1 1 1 1 0 0 2 0 1 2 0 0]
[ 0 1 1 1 1 -1 2 0 1 0 1 0 1 0 2 1 1 1 0 1 1 0 2 1]
[ 1 1 1 1 0 2 -1 2 1 1 0 1 1 1 0 1 0 1 2 0 1 1 0 0]
[ 1 0 0 1 1 0 2 -1 1 1 1 1 0 0 2 1 1 1 0 2 0 1 1 1]
[ 1 1 2 0 1 1 1 1 -1 0 1 0 1 1 0 0 2 0 1 1 1 1 0 2]
[ 0 1 2 1 1 0 1 1 0 -1 1 0 2 0 1 0 2 1 1 1 1 0 1 1]
[ 2 1 1 2 0 1 0 1 1 1 -1 1 0 1 1 2 0 1 1 0 0 1 1 0]
[ 0 1 2 0 1 0 1 1 0 0 1 -1 1 0 1 1 1 1 1 1 2 0 1 2]
[ 2 0 0 1 1 1 1 0 1 2 0 1 -1 1 1 2 0 1 0 1 0 1 1 1]
[ 0 0 1 1 1 0 1 0 1 0 1 0 1 -1 2 1 1 2 1 2 1 0 1 1]
[ 1 1 1 0 1 2 0 2 0 1 1 1 1 2 -1 0 1 0 1 0 1 1 0 1]
[ 0 1 1 0 1 1 1 1 0 0 2 1 2 1 0 -1 2 0 1 1 1 1 0 1]
[ 1 1 0 1 0 1 0 1 2 2 0 1 0 1 1 2 -1 1 1 0 1 1 1 0]
[ 1 2 1 0 0 1 1 1 0 1 1 1 1 2 0 0 1 -1 1 0 1 2 0 1]
[ 1 0 0 1 2 0 2 0 1 1 1 1 0 1 1 1 1 1 -1 1 0 0 2 1]
[ 1 2 1 1 0 1 0 2 1 1 0 1 1 2 0 1 0 0 1 -1 1 1 1 0]
[ 2 0 0 2 1 1 1 0 1 1 0 2 0 1 1 1 1 1 0 1 -1 1 1 0]
[ 0 0 1 1 2 0 1 1 1 0 1 0 1 0 1 1 1 2 0 1 1 -1 2 1]
[ 1 1 1 0 0 2 0 1 0 1 1 1 1 1 0 0 1 0 2 1 1 2 -1 1]
[ 1 1 0 2 0 1 0 1 2 1 0 2 1 1 1 1 0 1 1 0 0 1 1 -1]
Stabilizer Group Name:
C3
MatrixGroup(9, Integer Ring)
Generators:
[1 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0]
[0 0 1 0 0 0 0 0 0]
[0 0 0 1 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0]
[0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0]
[0 0 0 0 0 0 0 1 0]
[0 0 0 0 0 0 0 0 1]
13
{@
Mod: ( 1 -1 0 0 0 -1 0 0 0),
Mod: ( 2 -1 0 -1 -1 0 -1 0 -1),
Mod: ( 4 -2 -2 -1 -2 -1 -1 -1 -1),
Mod: ( 2 0 -1 -1 -1 -1 -1 0 0),
Mod: ( 1 0 -1 0 0 -1 0 0 0),
Mod: ( 1 -1 -1 0 0 0 0 0 0),
Mod: ( 1 0 0 0 -1 0 -1 0 0),
Mod: ( 4 -1 -1 -1 -2 -1 -2 -1 -2),
Mod: ( 1 -1 0 0 -1 0 0 0 0),
Mod: ( 4 -2 -1 -1 -1 -1 -2 -1 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -2 -1 -1),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -1 -2),
Mod: ( 1 0 0 0 0 -1 0 0 -1),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -1 -2),
Mod: ( 1 -1 0 0 0 0 -1 0 0),
Mod: ( 1 0 -1 0 -1 0 0 0 0),
Mod: ( 2 -1 -1 -1 0 -1 -1 0 0),
Mod: ( 4 -2 -1 -1 -2 -1 -1 -1 -2),
Mod: ( 4 -1 -2 -1 -2 -2 -1 -1 -1),
Mod: ( 1 0 0 0 0 -1 -1 0 0),
Mod: ( 4 -2 -2 -1 -1 -2 -1 -1 -1),
Mod: ( 1 0 0 0 -1 0 0 0 -1),
Mod: ( 2 -1 -1 -1 -1 0 -1 0 0),
Mod: ( 4 -1 -1 -1 -1 -2 -2 -1 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -1 -2),
Mod: ( 1 -1 0 0 0 0 0 0 -1),
Mod: ( 2 -1 0 -1 0 -1 -1 0 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -2 -1 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 0 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -1 -2),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -1 -2),
Mod: ( 1 0 0 0 -1 -1 0 0 0),
Mod: ( 4 -2 -2 -1 -1 -1 -2 -1 -1),
Mod: ( 4 -1 -1 -1 -2 -2 -1 -1 -2),
Mod: ( 4 -2 -2 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -2 -1 -1 -1 -2 -1 -1 -2)
@}
Intersection Matrix:
[-1 1 1 1 0 0 1 2 0 1 1 2 0 1 0 1 0 1 1 0 0 1 1 1 2 0 0 2 1 1 2 0 1 1 1 0]
[ 1 -1 1 1 2 1 0 0 0 0 2 0 1 2 0 1 1 0 2 1 2 0 0 1 1 0 0 1 0 1 1 1 1 1 1 1]
[ 1 1 -1 1 1 0 1 1 0 1 1 0 2 1 1 0 1 0 0 2 0 1 0 2 1 1 2 0 2 1 0 1 0 1 0 1]
[ 1 1 1 -1 0 1 0 1 1 2 0 1 1 1 1 0 0 2 0 0 1 1 0 1 0 2 1 0 0 1 1 0 1 1 2 2]
[ 0 2 1 0 -1 0 1 2 1 2 0 2 0 0 1 0 0 2 0 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1]
[ 0 1 0 1 0 -1 1 2 0 1 1 1 1 1 0 0 0 1 1 1 0 1 0 2 2 0 1 1 2 1 1 1 0 2 0 1]
[ 1 0 1 0 1 1 -1 0 0 1 1 1 1 2 0 0 1 1 1 0 2 0 0 1 1 1 1 0 0 2 1 0 1 1 2 2]
[ 2 0 1 1 2 2 0 -1 1 0 1 0 1 1 1 1 2 0 1 1 2 0 1 0 0 1 1 0 0 1 0 1 1 0 1 1]
[ 0 0 0 1 1 0 0 1 -1 1 2 1 1 2 0 0 1 0 1 1 1 0 0 2 2 0 1 1 1 2 1 0 1 1 1 1]
[ 1 0 1 2 2 1 1 0 1 -1 1 0 1 1 0 2 1 0 2 1 1 1 1 0 1 0 0 1 1 0 1 2 0 1 0 0]
[ 1 2 1 0 0 1 1 1 2 1 -1 1 1 0 1 1 0 2 0 0 0 2 1 0 0 2 1 0 1 0 1 1 0 1 1 1]
[ 2 0 0 1 2 1 1 0 1 0 1 -1 2 1 1 1 1 0 1 2 1 1 0 1 0 1 1 0 1 0 0 2 0 1 0 1]
[ 0 1 2 1 0 1 1 1 1 1 1 2 -1 0 1 1 1 1 1 0 1 0 2 0 1 0 0 2 0 1 1 0 2 0 1 0]
[ 1 2 1 1 0 1 2 1 2 1 0 1 0 -1 2 1 1 1 0 1 0 1 2 0 0 1 1 1 1 0 0 1 1 0 0 0]
[ 0 0 1 1 1 0 0 1 0 0 1 1 1 2 -1 1 0 1 2 0 1 1 0 1 2 0 0 1 1 1 2 1 0 2 1 1]
[ 1 1 0 0 0 0 0 1 0 2 1 1 1 1 1 -1 1 1 0 1 1 0 0 2 1 1 2 0 1 2 0 0 1 1 1 2]
[ 0 1 1 0 0 0 1 2 1 1 0 1 1 1 0 1 -1 2 1 0 0 2 0 1 1 1 0 1 1 0 2 1 0 2 1 1]
[ 1 0 0 2 2 1 1 0 0 0 2 0 1 1 1 1 2 -1 1 2 1 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0]
[ 1 2 0 0 0 1 1 1 1 2 0 1 1 0 2 0 1 1 -1 1 0 1 1 1 0 2 2 0 1 1 0 0 1 0 1 1]
[ 0 1 2 0 0 1 0 1 1 1 0 2 0 1 0 1 0 2 1 -1 1 1 1 0 1 1 0 1 0 1 2 0 1 1 2 1]
[ 0 2 0 1 0 0 2 2 1 1 0 1 1 0 1 1 0 1 0 1 -1 2 1 1 1 1 1 1 2 0 1 1 0 1 0 0]
[ 1 0 1 1 1 1 0 0 0 1 2 1 0 1 1 0 2 0 1 1 2 -1 1 1 1 0 1 1 0 2 0 0 2 0 1 1]
[ 1 0 0 0 1 0 0 1 0 1 1 0 2 2 0 0 0 1 1 1 1 1 -1 2 1 1 1 0 1 1 1 1 0 2 1 2]
[ 1 1 2 1 1 2 1 0 2 0 0 1 0 0 1 2 1 1 1 0 1 1 2 -1 0 1 0 1 0 0 1 1 1 0 1 0]
[ 2 1 1 0 1 2 1 0 2 1 0 0 1 0 2 1 1 1 0 1 1 1 1 0 -1 2 1 0 0 0 0 1 1 0 1 1]
[ 0 0 1 2 1 0 1 1 0 0 2 1 0 1 0 1 1 0 2 1 1 0 1 1 2 -1 0 2 1 1 1 1 1 1 0 0]
[ 0 0 2 1 1 1 1 1 1 0 1 1 0 1 0 2 0 1 2 0 1 1 1 0 1 0 -1 2 0 0 2 1 1 1 1 0]
[ 2 1 0 0 1 1 0 0 1 1 0 0 2 1 1 0 1 1 0 1 1 1 0 1 0 2 2 -1 1 1 0 1 0 1 1 2]
[ 1 0 2 0 1 2 0 0 1 1 1 1 0 1 1 1 1 1 1 0 2 0 1 0 0 1 0 1 -1 1 1 0 2 0 2 1]
[ 1 1 1 1 1 1 2 1 2 0 0 0 1 0 1 2 0 1 1 1 0 2 1 0 0 1 0 1 1 -1 1 2 0 1 0 0]
[ 2 1 0 1 1 1 1 0 1 1 1 0 1 0 2 0 2 0 0 2 1 0 1 1 0 1 2 0 1 1 -1 1 1 0 0 1]
[ 0 1 1 0 0 1 0 1 0 2 1 2 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 0 2 1 -1 2 0 2 1]
[ 1 1 0 1 1 0 1 1 1 0 0 0 2 1 0 1 0 1 1 1 0 2 0 1 1 1 1 0 2 0 1 2 -1 2 0 1]
[ 1 1 1 1 1 2 1 0 1 1 1 1 0 0 2 1 2 0 0 1 1 0 2 0 0 1 1 1 0 1 0 0 2 -1 1 0]
[ 1 1 0 2 1 0 2 1 1 0 1 0 1 0 1 1 1 0 1 2 0 1 1 1 1 0 1 1 2 0 0 2 0 1 -1 0]
[ 0 1 1 2 1 1 2 1 1 0 1 1 0 0 1 2 1 0 1 1 0 1 2 0 1 0 0 2 1 0 1 1 1 0 0 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 7 3 3 2 0 3 2 2 3]
[-3 -1 -2 -1 0 -1 -1 -1 -1]
[-3 -2 -1 -1 0 -1 -1 -1 -1]
[-2 -1 -1 -1 0 -1 0 0 -1]
[ 0 0 0 0 1 0 0 0 0]
[-3 -1 -1 -1 0 -1 -1 -1 -2]
[-2 -1 -1 0 0 -1 0 -1 -1]
[-2 -1 -1 0 0 -1 -1 0 -1]
[-3 -1 -1 -1 0 -2 -1 -1 -1]
14
{@
Mod: ( 4 -2 -2 -1 -1 -1 -1 -2 -1),
Mod: ( 2 -1 0 -1 0 -1 0 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -1 -2 -2 -2),
Mod: ( 2 -1 -1 -1 -1 0 0 -1 0),
Mod: ( 2 0 0 -1 -1 -1 0 -1 -1),
Mod: ( 5 -1 -1 -2 -2 -2 -2 -2 -2),
Mod: ( 2 0 -1 -1 -1 -1 0 -1 0),
Mod: ( 5 -2 -2 -2 -1 -1 -2 -2 -2),
Mod: ( 2 0 0 -1 0 -1 -1 -1 -1),
Mod: ( 5 -2 -1 -2 -1 -2 -2 -2 -2),
Mod: ( 1 0 0 0 0 -1 0 -1 0),
Mod: ( 4 -1 -1 -1 -2 -1 -1 -2 -2),
Mod: ( 2 0 -1 -1 0 -1 -1 -1 0),
Mod: ( 2 -1 0 -1 0 -1 -1 -1 0),
Mod: ( 5 -2 -2 -2 -2 -1 -2 -2 -1),
Mod: ( 2 0 0 -1 -1 -1 -1 -1 0),
Mod: ( 4 -2 -1 -1 -1 -1 -1 -2 -2),
Mod: ( 4 -1 -2 -1 -1 -2 -1 -2 -1),
Mod: ( 5 -2 -2 -2 -2 -1 -1 -2 -2),
Mod: ( 2 -1 0 -1 0 0 -1 -1 -1),
Mod: ( 2 0 0 -1 -1 0 -1 -1 -1),
Mod: ( 2 -1 -1 -1 0 -1 0 -1 0),
Mod: ( 1 0 0 0 -1 0 0 -1 0),
Mod: ( 2 0 -1 -1 -1 0 -1 -1 0),
Mod: ( 2 -1 0 -1 -1 0 -1 -1 0),
Mod: ( 5 -1 -2 -2 -1 -2 -2 -2 -2),
Mod: ( 1 -1 0 0 0 0 0 -1 0),
Mod: ( 2 -1 0 -1 -1 0 0 -1 -1),
Mod: ( 5 -1 -2 -2 -2 -2 -2 -2 -1),
Mod: ( 5 -2 -1 -2 -2 -1 -2 -2 -2),
Mod: ( 4 -1 -1 -1 -1 -2 -1 -2 -2),
Mod: ( 5 -1 -2 -2 -2 -2 -1 -2 -2),
Mod: ( 2 -1 -1 -1 0 0 -1 -1 0),
Mod: ( 5 -2 -2 -2 -1 -2 -2 -2 -1),
Mod: ( 4 -1 -2 -1 -2 -1 -1 -2 -1),
Mod: ( 5 -2 -2 -2 -1 -2 -1 -2 -2)
@}
Intersection Matrix:
[-1 1 1 0 2 2 1 0 2 1 1 1 1 1 0 2 0 0 0 1 2 0 1 1 1 1 0 1 1 1 1 1 0 0 0 0]
[ 1 -1 2 1 0 1 1 1 0 0 0 1 1 0 2 1 0 1 1 0 1 0 1 2 1 1 0 0 2 1 0 1 1 1 2 0]
[ 1 2 -1 1 1 0 1 0 1 1 2 0 1 2 0 1 1 1 0 1 0 2 1 0 1 0 2 1 0 0 1 0 1 1 0 1]
[ 0 1 1 -1 1 2 0 1 2 2 1 1 1 1 0 1 1 1 0 1 1 0 0 0 0 2 0 0 1 1 2 1 0 1 0 1]
[ 2 0 1 1 -1 0 0 2 0 1 0 0 1 1 2 0 1 1 1 1 0 1 0 1 1 1 1 0 1 1 0 0 2 2 1 1]
[ 2 1 0 2 0 -1 1 1 0 0 1 0 1 1 1 0 1 1 1 1 0 2 1 1 1 0 2 1 0 0 0 0 2 1 1 1]
[ 1 1 1 0 0 1 -1 2 1 2 0 1 0 1 1 0 2 0 1 2 1 0 0 0 1 1 1 1 0 2 1 0 1 1 0 1]
[ 0 1 0 1 2 1 2 -1 1 0 2 1 1 1 0 2 0 1 0 0 1 1 2 1 1 0 1 1 1 0 1 1 0 0 1 0]
[ 2 0 1 2 0 0 1 1 -1 0 0 1 0 0 2 0 1 1 2 0 0 1 1 1 1 0 1 1 1 1 0 1 1 1 2 1]
[ 1 0 1 2 1 0 2 0 0 -1 1 1 1 0 1 1 0 1 1 0 1 1 2 2 1 0 1 1 1 0 0 1 1 0 2 0]
[ 1 0 2 1 0 1 0 2 0 1 -1 1 0 0 2 0 1 0 2 1 1 0 0 1 1 1 0 1 1 2 0 1 1 1 1 1]
[ 1 1 0 1 0 0 1 1 1 1 1 -1 2 2 1 1 0 1 0 1 0 2 0 1 1 1 1 0 1 0 0 0 2 2 0 1]
[ 1 1 1 1 1 1 0 1 0 1 0 2 -1 0 1 0 2 0 2 1 1 0 1 0 1 0 1 2 0 2 1 1 0 0 1 1]
[ 1 0 2 1 1 1 1 1 0 0 0 2 0 -1 1 0 1 1 2 0 1 0 1 1 0 1 0 1 1 1 1 2 0 0 2 1]
[ 0 2 0 0 2 1 1 0 2 1 2 1 1 1 -1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 2 1 0 0 0 1]
[ 2 1 1 1 0 0 0 2 0 1 0 1 0 0 1 -1 2 1 2 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 2]
[ 0 0 1 1 1 1 2 0 1 0 1 0 2 1 1 2 -1 1 0 0 1 1 1 2 1 1 0 0 2 0 0 1 1 1 1 0]
[ 0 1 1 1 1 1 0 1 1 1 0 1 0 1 1 1 1 -1 1 2 2 0 1 1 2 0 1 2 0 2 0 0 1 0 0 0]
[ 0 1 0 0 1 1 1 0 2 1 2 0 2 2 0 2 0 1 -1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 0 0]
[ 1 0 1 1 1 1 2 0 0 0 1 1 1 0 1 1 0 2 1 -1 0 1 1 1 0 1 0 0 2 0 1 2 0 1 2 1]
[ 2 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 2 1 0 -1 2 0 0 0 1 1 0 1 0 1 1 1 2 1 2]
[ 0 0 2 0 1 2 0 1 1 1 0 2 0 0 1 1 1 0 1 1 2 -1 1 1 1 1 0 1 1 2 1 1 0 0 1 0]
[ 1 1 1 0 0 1 0 2 1 2 0 0 1 1 1 0 1 1 1 1 0 1 -1 0 0 2 0 0 1 1 1 1 1 2 0 2]
[ 1 2 0 0 1 1 0 1 1 2 1 1 0 1 0 0 2 1 1 1 0 1 0 -1 0 1 1 1 0 1 2 1 0 1 0 2]
[ 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 2 1 0 0 1 0 0 -1 2 0 0 1 0 2 2 0 1 1 2]
[ 1 1 0 2 1 0 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 2 1 2 -1 2 2 0 1 0 0 1 0 1 0]
[ 0 0 2 0 1 2 1 1 1 1 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 2 -1 0 2 1 1 2 0 1 1 1]
[ 1 0 1 0 0 1 1 1 1 1 1 0 2 1 1 1 0 2 0 0 0 1 0 1 0 2 0 -1 2 0 1 1 1 2 1 1]
[ 1 2 0 1 1 0 0 1 1 1 1 1 0 1 0 0 2 0 1 2 1 1 1 0 1 0 2 2 -1 1 1 0 1 0 0 1]
[ 1 1 0 1 1 0 2 0 1 0 2 0 2 1 0 1 0 2 0 0 0 2 1 1 0 1 1 0 1 -1 1 1 1 1 1 1]
[ 1 0 1 2 0 0 1 1 0 0 0 0 1 1 2 1 0 0 1 1 1 1 1 2 2 0 1 1 1 1 -1 0 2 1 1 0]
[ 1 1 0 1 0 0 0 1 1 1 1 0 1 2 1 1 1 0 0 2 1 1 1 1 2 0 2 1 0 1 0 -1 2 1 0 0]
[ 0 1 1 0 2 2 1 0 1 1 1 2 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 2 2 -1 0 1 1]
[ 0 1 1 1 2 1 1 0 1 0 1 2 0 0 0 1 1 0 1 1 2 0 2 1 1 0 1 2 0 1 1 1 0 -1 1 0]
[ 0 2 0 0 1 1 0 1 2 2 1 0 1 2 0 1 1 0 0 2 1 1 0 0 1 1 1 1 0 1 1 0 1 1 -1 1]
[ 0 0 1 1 1 1 1 0 1 0 1 1 1 1 1 2 0 0 0 1 2 0 2 2 2 0 1 1 1 1 0 0 1 0 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[10 3 3 3 3 6 3 3 3]
[-3 -1 0 -1 -1 -2 -1 -1 -1]
[-3 0 -1 -1 -1 -2 -1 -1 -1]
[-3 -1 -1 0 -1 -2 -1 -1 -1]
[-3 -1 -1 -1 -1 -2 -1 -1 0]
[-6 -2 -2 -2 -2 -3 -2 -2 -2]
[-3 -1 -1 -1 -1 -2 0 -1 -1]
[-3 -1 -1 -1 -1 -2 -1 0 -1]
[-3 -1 -1 -1 0 -2 -1 -1 -1]
15
{@
Mod: ( 3 -2 -1 -1 -1 -1 -1 -1 0),
Mod: (0 0 0 0 1 0 0 0 0),
Mod: ( 2 -1 0 0 0 -1 -1 -1 -1),
Mod: ( 3 -1 -1 -1 0 -1 -1 -1 -2),
Mod: ( 3 -1 -1 -1 -2 -1 -1 -1 0),
Mod: ( 1 0 0 -1 -1 0 0 0 0),
Mod: ( 3 -1 0 -1 -1 -2 -1 -1 -1),
Mod: ( 1 -1 0 -1 0 0 0 0 0),
Mod: ( 4 -1 -1 -2 -2 -1 -1 -1 -2),
Mod: ( 2 0 0 0 -1 -1 -1 -1 -1),
Mod: ( 2 0 -1 0 -1 -1 -1 -1 0),
Mod: ( 5 -2 -2 -1 -2 -1 -2 -2 -2),
Mod: ( 4 -1 -2 -2 -1 -2 -1 -1 -1),
Mod: ( 4 -2 -1 -2 -1 -1 -1 -1 -2),
Mod: ( 6 -2 -2 -2 -3 -2 -2 -2 -2),
Mod: ( 3 -1 -1 -1 -1 0 -1 -1 -2),
Mod: ( 3 0 -2 -1 -1 -1 -1 -1 -1),
Mod: ( 6 -3 -2 -2 -2 -2 -2 -2 -2),
Mod: ( 2 -1 -1 0 0 -1 -1 -1 0),
Mod: ( 2 -1 0 0 -1 0 -1 -1 -1),
Mod: ( 3 -1 -2 -1 0 -1 -1 -1 -1),
Mod: (0 0 0 0 0 1 0 0 0),
Mod: ( 3 -1 -1 -1 -1 -2 -1 -1 0),
Mod: ( 3 -2 0 -1 -1 -1 -1 -1 -1),
Mod: ( 5 -1 -2 -1 -2 -2 -2 -2 -2),
Mod: (0 1 0 0 0 0 0 0 0),
Mod: ( 3 -1 0 -1 -2 -1 -1 -1 -1),
Mod: ( 4 -1 -1 -2 -1 -2 -1 -1 -2),
Mod: ( 3 -1 -2 -1 -1 0 -1 -1 -1),
Mod: ( 5 -2 -2 -1 -1 -2 -2 -2 -2),
Mod: ( 1 0 0 -1 0 -1 0 0 0),
Mod: ( 3 0 -1 -1 -1 -1 -1 -1 -2),
Mod: ( 4 -1 -2 -2 -2 -1 -1 -1 -1),
Mod: ( 2 -1 -1 0 -1 0 -1 -1 0),
Mod: ( 6 -2 -2 -2 -2 -3 -2 -2 -2),
Mod: ( 4 -2 -2 -2 -1 -1 -1 -1 -1)
@}
Intersection Matrix:
[-1 1 1 2 0 1 1 0 2 2 1 1 1 1 1 2 2 0 0 1 1 1 0 0 2 2 1 2 1 1 1 3 1 0 1 0]
[ 1 -1 0 0 2 1 1 0 2 1 1 2 1 1 3 1 1 2 0 1 0 0 1 1 2 0 2 1 1 1 0 1 2 1 2 1]
[ 1 0 -1 0 2 2 0 1 2 0 1 1 2 1 2 1 2 1 0 0 1 1 1 0 1 1 1 1 2 0 1 1 3 1 1 2]
[ 2 0 0 -1 3 2 1 1 1 1 2 1 1 0 2 0 1 1 1 1 0 1 2 1 1 1 2 0 1 0 1 0 2 2 1 1]
[ 0 2 2 3 -1 0 1 1 1 1 0 1 1 2 0 2 1 1 1 1 2 1 0 1 1 1 0 2 1 2 1 2 0 0 1 1]
[ 1 1 2 2 0 -1 1 0 0 1 1 2 1 1 1 1 1 2 2 1 2 0 1 1 2 0 0 1 1 3 0 1 0 1 2 1]
[ 1 1 0 1 1 1 -1 1 1 0 1 2 1 1 1 2 2 1 1 1 2 2 0 0 1 1 0 0 3 1 0 1 2 2 0 2]
[ 0 0 1 1 1 0 1 -1 1 2 2 2 1 0 2 1 2 1 1 1 1 0 1 0 3 1 1 1 1 2 0 2 1 1 2 0]
[ 2 2 2 1 1 0 1 1 -1 1 2 1 1 0 0 0 1 1 3 1 2 1 2 1 1 1 0 0 1 2 1 0 0 2 1 1]
[ 2 1 0 1 1 1 0 2 1 -1 0 1 2 2 1 1 1 2 1 0 2 1 1 1 0 0 0 1 2 1 1 0 2 1 1 3]
[ 1 1 1 2 0 1 1 2 2 0 -1 1 1 3 1 2 0 2 0 1 1 1 0 2 0 0 1 2 1 1 1 1 1 0 1 2]
[ 1 2 1 1 1 2 2 2 1 1 1 -1 2 1 0 0 1 0 1 0 1 1 2 1 0 2 1 2 0 0 3 1 1 0 1 1]
[ 1 1 2 1 1 1 1 1 1 2 1 2 -1 1 1 2 0 1 1 3 0 2 0 2 1 1 2 0 1 1 0 1 0 2 0 0]
[ 1 1 1 0 2 1 1 0 0 2 3 1 1 -1 1 0 2 0 2 1 1 1 2 0 2 2 1 0 1 1 1 1 1 2 1 0]
[ 1 3 2 2 0 1 1 2 0 1 1 0 1 1 -1 1 1 0 2 1 2 2 1 1 0 2 0 1 1 1 2 1 0 1 0 1]
[ 2 1 1 0 2 1 2 1 0 1 2 0 2 0 1 -1 1 1 2 0 1 0 3 1 1 1 1 1 0 1 2 0 1 1 2 1]
[ 2 1 2 1 1 1 2 2 1 1 0 1 0 2 1 1 -1 2 1 2 0 1 1 3 0 0 2 1 0 1 1 0 0 1 1 1]
[ 0 2 1 1 1 2 1 1 1 2 2 0 1 0 0 1 2 -1 1 1 1 2 1 0 1 3 1 1 1 0 2 2 1 1 0 0]
[ 0 0 0 1 1 2 1 1 3 1 0 1 1 2 2 2 1 1 -1 1 0 1 0 1 1 1 2 2 1 0 1 2 2 0 1 1]
[ 1 1 0 1 1 1 1 1 1 0 1 0 3 1 1 0 2 1 1 -1 2 0 2 0 1 1 0 2 1 1 2 1 2 0 2 2]
[ 1 0 1 0 2 2 2 1 2 2 1 1 0 1 2 1 0 1 0 2 -1 1 1 2 1 1 3 1 0 0 1 1 1 1 1 0]
[ 1 0 1 1 1 0 2 0 1 1 1 1 2 1 2 0 1 2 1 0 1 -1 2 1 2 0 1 2 0 2 1 1 1 0 3 1]
[ 0 1 1 2 0 1 0 1 2 1 0 2 0 2 1 3 1 1 0 2 1 2 -1 1 1 1 1 1 2 1 0 2 1 1 0 1]
[ 0 1 0 1 1 1 0 0 1 1 2 1 2 0 1 1 3 0 1 0 2 1 1 -1 2 2 0 1 2 1 1 2 2 1 1 1]
[ 2 2 1 1 1 2 1 3 1 0 0 0 1 2 0 1 0 1 1 1 1 2 1 2 -1 1 1 1 1 0 2 0 1 1 0 2]
[ 2 0 1 1 1 0 1 1 1 0 0 2 1 2 2 1 0 3 1 1 1 0 1 2 1 -1 1 1 1 2 0 0 1 1 2 2]
[ 1 2 1 2 0 0 0 1 0 0 1 1 2 1 0 1 2 1 2 0 3 1 1 0 1 1 -1 1 2 2 1 1 1 1 1 2]
[ 2 1 1 0 2 1 0 1 0 1 2 2 0 0 1 1 1 1 2 2 1 2 1 1 1 1 1 -1 2 1 0 0 1 3 0 1]
[ 1 1 2 1 1 1 3 1 1 2 1 0 1 1 1 0 0 1 1 1 0 0 2 2 1 1 2 2 -1 1 2 1 0 0 2 0]
[ 1 1 0 0 2 3 1 2 2 1 1 0 1 1 1 1 1 0 0 1 0 2 1 1 0 2 2 1 1 -1 2 1 2 1 0 1]
[ 1 0 1 1 1 0 0 0 1 1 1 3 0 1 2 2 1 2 1 2 1 1 0 1 2 0 1 0 2 2 -1 1 1 2 1 1]
[ 3 1 1 0 2 1 1 2 0 0 1 1 1 1 1 0 0 2 2 1 1 1 2 2 0 0 1 0 1 1 1 -1 1 2 1 2]
[ 1 2 3 2 0 0 2 1 0 2 1 1 0 1 0 1 0 1 2 2 1 1 1 2 1 1 1 1 0 2 1 1 -1 1 1 0]
[ 0 1 1 2 0 1 2 1 2 1 0 0 2 2 1 1 1 1 0 0 1 0 1 1 1 1 1 3 0 1 2 2 1 -1 2 1]
[ 1 2 1 1 1 2 0 2 1 1 1 1 0 1 0 2 1 0 1 2 1 3 0 1 0 2 1 0 2 0 1 1 1 2 -1 1]
[ 0 1 2 1 1 1 2 0 1 3 2 1 0 0 1 1 1 0 1 2 0 1 1 1 2 2 2 1 0 1 1 2 0 1 1 -1]
Stabilizer Group Name:
C2
MatrixGroup(9, Integer Ring)
Generators:
[ 7 3 3 2 3 0 2 2 3]
[-3 -1 -1 -1 -1 0 -1 -1 -2]
[-3 -1 -1 -1 -2 0 -1 -1 -1]
[-2 -1 -1 -1 -1 0 0 0 -1]
[-3 -1 -2 -1 -1 0 -1 -1 -1]
[ 0 0 0 0 0 1 0 0 0]
[-2 -1 -1 0 -1 0 0 -1 -1]
[-2 -1 -1 0 -1 0 -1 0 -1]
[-3 -2 -1 -1 -1 0 -1 -1 -1]