//Group G is generated by
//(1 4)(3 7)(5 6)
//c2c3(1 6)
//c5c6(1 3)(4 7)
//c1c3c4c5(1 6 3)(4 7 5)
//c1c3c4c7(1 6 3)(4 5 7)


9.S3wrC2
MatrixGroup(11, Integer Ring) of order 2^3 * 3^2
Generators:

    (1 4)(3 7)(5 6)
    [1 0 0 0 0 0 0 0 0 0 0]
    [0 1 0 0 0 0 0 0 0 0 0]
    [0 0 0 0 0 1 0 0 0 0 0]
    [0 0 0 1 0 0 0 0 0 0 0]
    [0 0 0 0 0 0 0 0 1 0 0]
    [0 0 1 0 0 0 0 0 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 1 0 0 0 0 0 0]
    [0 0 0 0 0 0 0 0 0 1 0]
    [0 0 0 0 0 0 0 0 0 0 1]

    c2c3(1 6)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  1  0  0  0  0  0  0]
    [ 0  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]
    [ 0  0  0  0  0  1  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  0  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  0  1]

    c5c6(1 3)(4 7)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  0  1  1  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  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    c1c3c4c5(1 6 3)(4 7 5)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  1  0  0  1  0  1  1  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [-1  0 -1  0  0  0  0  0  0  0  0]
    [-1  0  0  0  0  0  0  0 -1  0  0]
    [-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  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
    
    c1c3c4c7(1 6 3)(4 5 7)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  1  0  0  1  1  1  0  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [-1  0 -1  0  0  0  0  0  0  0  0]
    [-1  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]
    [-1  0  0  0  0 -1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
1
{@
    (0 0 0 1 0 0 0 0 0 0 0),
    ( 0  1  0 -1  0  0  0  0  0  0  0)
@}
Intersection Matrix:
[-1  1]
[ 1 -1]
Stabilizer Group Name:
S3^2
MatrixGroup(11, Integer Ring)
Generators:
    [1 0 0 0 0 0 0 0 0 0 0]
    [0 1 0 0 0 0 0 0 0 0 0]
    [0 0 0 0 0 1 0 0 0 0 0]
    [0 0 0 1 0 0 0 0 0 0 0]
    [0 0 0 0 0 0 0 0 1 0 0]
    [0 0 1 0 0 0 0 0 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 1 0 0 0 0 0 0]
    [0 0 0 0 0 0 0 0 0 1 0]
    [0 0 0 0 0 0 0 0 0 0 1]

    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  0  1  1  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  0  0  0  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  1  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  1  0  0  1  0  1  1  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [-1  0 -1  0  0  0  0  0  0  0  0]
    [-1  0  0  0  0  0  0  0 -1  0  0]
    [-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  0  0  0  1  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  1  0  0  1  1  1  0  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [-1  0 -1  0  0  0  0  0  0  0  0]
    [-1  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]
    [-1  0  0  0  0 -1  0  0  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]
2
{@
    (0 0 1 0 0 0 0 0 0 0 0),
    ( 0  1  0  0  0  0 -1  0  0  0  0),
    (0 0 0 0 0 0 0 1 0 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 0 0 0 1 0 0 0 0 0 0),
    ( 0  1  0  0  0  0  0 -1  0  0  0),
    (0 0 0 0 0 1 0 0 0 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 -1  0  0  0  0  0  0  0  0),
    (0 0 0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-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 -1  0  0  0  1  0  0  0  0  0]
[ 0  0  0 -1  0  1  0  0  0  0  0  0]
[ 0  0  0  0 -1  0  0  1  0  0  0  0]
[ 0  0  0  1  0 -1  0  0  0  0  0  0]
[ 0  0  1  0  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  0  0  0 -1  1  0  0]
[ 0  0  0  0  0  0  0  0  1 -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]
Stabilizer Group Name:
S3
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  1  0  0  1  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  0  1  0  0  0  0  0  0]
    [-1  0  0  0  0  0  0  0 -1  0  0]
    [-1  0  0  0  0 -1  0  0  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  0  0  0  0  1  0]
    [ 0  0  0  0  0  0  0  0  0  0  1]

    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  0  0  0  0  1  0  0]
    [ 0  0  1  0  0  0  0  0  0  0  0]
    [-1  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  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  1  0  0  0]
    [-1  0  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  0  1]