//Group G is generated by
//c1c2c3c4c5c6(2 6)(4 5)
//(3 4 5)
//c1c6(1 2 6)


5.C3:S3
MatrixGroup(11, Integer Ring) of order 2 * 3^2
Generators:

    c1c2c3c4c5c6(2 6)(4 5)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 3  1  1  1  1  1  1  1  0  0  0]
    [-1  0 -1  0  0  0  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  0  0  0  0  0 -1  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]
    [ 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]

    (3 4 5)
    [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 1 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 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]
    
    c1c6(1 2 6)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  1  1  0  0  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  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]
    [-1  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]
1
{@
    ( 0  1  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 1 0 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 0 1 0 0 0 0 0)
@}
Intersection Matrix:
[-1  0  1  0  0  0]
[ 0 -1  0  1  0  0]
[ 1  0 -1  0  0  0]
[ 0  1  0 -1  0  0]
[ 0  0  0  0 -1  1]
[ 0  0  0  0  1 -1]
Stabilizer Group Name:
C3
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  1  1  0  0  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  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]
    [-1  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]
2
{@
    ( 0  1  0  0  0  0  0 -1  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 1 0 0 0 0 0 0 0 0),
    ( 0  1  0 -1  0  0  0  0  0  0  0),
    (0 0 0 0 0 0 0 1 0 0 0)
@}
Intersection Matrix:
[-1  0  0  0  0  1]
[ 0 -1  0  1  0  0]
[ 0  0 -1  0  1  0]
[ 0  1  0 -1  0  0]
[ 0  0  1  0 -1  0]
[ 1  0  0  0  0 -1]
Stabilizer Group Name:
C3
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 0 1 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 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]