//Group G is generated by
//c2c6(1 4)(2 6)(3 5)
//c2c5(1 5 2)(3 4 6)
//c1c3c5c6(1 6)(2 4)(3 5)


3.D6
MatrixGroup(11, Integer Ring) of order 2^2 * 3
Generators:

    c2c6(1 4)(2 6)(3 5)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  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 -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  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]

    c2c5(1 5 2)(3 4 6)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  1  1  0  0  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  1  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]
    [ 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]
    
    c1c3c5c6(1 6)(2 4)(3 5)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 2  1  1  0  1  0  1  1  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]
    [-1  0  0  0  0  0 -1  0  0  0  0]
    [ 0  0  0  1  0  0  0  0  0  0  0]
    [-1  0  0  0 -1  0  0  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 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 -1  0  0  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 -1  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 0 0 0 0 0 1 0 0 0 0),
    ( 0  1 -1  0  0  0  0  0  0  0  0)
@}
Intersection Matrix:
[-1  0  0  0  0  0  0  0  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  0  1  0]
[ 0  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  1  0  0  0  0]
[ 0  1  0  0  0  0 -1  0  0  0  0  0]
[ 0  0  0  0  0  1  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]
[ 0  0  1  0  0  0  0  0  0  0 -1  0]
[ 1  0  0  0  0  0  0  0  0  0  0 -1]
Stabilizer Group Name:
C1
MatrixGroup(11, Integer Ring) of order 1