//Group G is generated by
//c2c3c8c9(1 5)(3 8)
//c1c5(1 5 8 2 3)(4 7 6)
//c4c6c7c9(6 7)
//(4 6 7)


4.S3*D5
MatrixGroup(11, Integer Ring) of order 2^2 * 3 * 5
Generators:

    c2c3c8c9(1 5)(3 8)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  0  1  1  0  0  0  0  1  1]
    [ 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  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  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]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [-1  0  0  0  0  0  0  0  0  0 -1]

    c1c5(1 5 8 2 3)(4 7 6)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  0  1  0  0  1  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  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  0  0  0 -1  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  0  0  0  0  0  0  0  0  1]

    c4c6c7c9(6 7)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  0  0  0  1  0  1  1  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  1  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  0  0  0  0  0 -1  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [-1  0  0  0  0  0  0  0  0  0 -1]
    
    (4 6 7)
    [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 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 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 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
{@
    Mod: ( 0  1  0  0  0  0  0 -1  0  0  0),
    Mod: (0 0 0 0 0 0 0 1 0 0 0),
    Mod: ( 0  1  0  0  0 -1  0  0  0  0  0),
    Mod: (0 0 0 0 0 0 0 0 1 0 0),
    Mod: ( 0  1  0  0  0  0  0  0 -1  0  0),
    Mod: (0 0 0 0 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1  1  0  0  0  0]
[ 1 -1  0  0  0  0]
[ 0  0 -1  0  0  1]
[ 0  0  0 -1  1  0]
[ 0  0  0  1 -1  0]
[ 0  0  1  0  0 -1]
Stabilizer Group Name:
D5
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  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  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [ 0  0  0  0  0  1  0  0  0  0  0]
    [-1  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  0  0]
    [ 0  0  0  0  1  0  0  0  0  0  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  0  1  1  0  0  0  0  1  1]
    [ 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  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  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]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [-1  0  0  0  0  0  0  0  0  0 -1]
2
{@
    Mod: (0 0 1 0 0 0 0 0 0 0 0),
    Mod: ( 0  1  0  0  0  0 -1  0  0  0  0),
    Mod: ( 0  1  0  0 -1  0  0  0  0  0  0),
    Mod: (0 0 0 0 1 0 0 0 0 0 0),
    Mod: (0 0 0 0 0 0 0 0 0 1 0),
    Mod: ( 0  1  0 -1  0  0  0  0  0  0  0),
    Mod: ( 0  1  0  0  0  0  0  0  0 -1  0),
    Mod: (0 0 0 1 0 0 0 0 0 0 0),
    Mod: ( 0  1 -1  0  0  0  0  0  0  0  0),
    Mod: (0 0 0 0 0 0 1 0 0 0 0)
@}
Intersection Matrix:
[-1  0  0  0  0  0  0  0  1  0]
[ 0 -1  0  0  0  0  0  0  0  1]
[ 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  1  0  0  0]
[ 0  0  0  0  0 -1  0  1  0  0]
[ 0  0  0  0  1  0 -1  0  0  0]
[ 0  0  0  0  0  1  0 -1  0  0]
[ 1  0  0  0  0  0  0  0 -1  0]
[ 0  1  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]
    [ 2  1  0  0  0  1  0  1  1  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  1  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  0  0  0  0  0 -1  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [ 0  0  0  0  0  0  0  0  0  1  0]
    [-1  0  0  0  0  0  0  0  0  0 -1]

    [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 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 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 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]
3
{@
    Mod: (0 0 0 0 0 0 0 0 0 0 1),
    Mod: ( 0  1  0  0  0  0  0  0  0  0 -1)
@}
Intersection Matrix:
[-1  1]
[ 1 -1]
Stabilizer Group Name:
D15
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 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]
    [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 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]
    [ 4  1  1  1  1  1  1  1  1  1  0]
    [-1  0  0  0  0  0  0  0  0 -1  0]
    [-1  0  0  0 -1  0  0  0  0  0  0]
    [-1  0  0 -1  0  0  0  0  0  0  0]
    [-1  0  0  0  0  0  0 -1  0  0  0]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [-1  0  0  0  0 -1  0  0  0  0  0]
    [-1  0  0  0  0  0  0  0 -1  0  0]
    [-1  0 -1  0  0  0  0  0  0  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  0  0  1  0  0  1  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  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  0  0  0 -1  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  0  0  0  0  0  0  0  0  1]