//Group G is generated by
//c1c2c5c6(1 5)(2 6)(3 4)
//c1c2c3c4c5c6(1 2)(3 5)
//(3 5 6)
//c1c4(1 4 2)


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

    c1c2c5c6(1 5)(2 6)(3 4)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  1  1  0  0  1  1  0  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  1  0  0  0  0  0  0]
    [-1  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  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]

    c1c2c3c4c5c6(1 2)(3 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  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]
    [-1  0  0  0  0 -1  0  0  0  0  0]
    [-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  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 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 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 0]
    [0 0 0 0 0 0 0 0 0 0 1]
    
    c1c4(1 4 2)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  1  0  1  0  0  0  0  0]
    [-1  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  1  0  0  0  0  0  0]
    [-1  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  0]
    [ 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  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  1  0 -1  0  0  0  0  0  0  0),
    (0 0 0 1 0 0 0 0 0 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:
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 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 0]
    [0 0 0 0 0 0 0 0 0 0 1]