//Group G is generated by
//(1 3)(2 4)(5 6)
//c1c3(1 5 2 4 3 6)


15.S5
MatrixGroup(11, Integer Ring) of order 2^3 * 3 * 5
Generators:

    (1 3)(2 4)(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 1 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 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 1 0]
    [0 0 0 0 0 0 0 0 0 0 1]
    
    c1c3(1 5 2 4 3 6)
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  0  1  1  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  0  0  0  0 -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]
    [ 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:
D5
MatrixGroup(11, Integer Ring)
Generators:
    [ 1  0  0  0  0  0  0  0  0  0  0]
    [ 1  1  0  0  0  0  1  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]
    [ 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  0  0  0  0 -1  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  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]
    [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 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 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 0]
    [0 0 0 0 0 0 0 0 0 0 1]