the 15 isometry classes of irreducible [13,5,5]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 0 1 0 1 0 1 0 0 0 0 1 0
0 1 0 1 0 1 1 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
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 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 1 0 
1 1 1 1 1 1 1 1 
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 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 1 0 
1 1 1 1 1 1 1 1 
, 
0 1 0 0 0 0 0 0 
1 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 1 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 0 1 0 
1 1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(8, 9), 
(3, 5)(4, 6)(8, 9)(10, 11), 
(1, 2)(3, 4)(5, 6)(8, 9)(12, 13)
orbits: { 1, 2 }, { 3, 5, 4, 6 }, { 7 }, { 8, 9 }, { 10, 11 }, { 12, 13 }

code no       2:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 0 1 0 1 0 1 0 0 0 0 1 0
1 1 0 1 0 1 1 0 0 0 0 0 1
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
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 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 1 0 
1 1 1 1 1 1 1 1 
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 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 1 0 
1 1 1 1 1 1 1 1 
, 
1 1 1 1 0 0 0 0 
0 1 0 0 0 0 0 0 
1 1 0 1 0 1 1 0 
1 0 1 0 1 0 1 0 
0 0 1 0 0 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(8, 9), 
(3, 5)(4, 6)(8, 9)(10, 11), 
(1, 11, 10)(3, 5, 13)(4, 6, 12)
orbits: { 1, 10, 11 }, { 2 }, { 3, 5, 13 }, { 4, 6, 12 }, { 7 }, { 8, 9 }

code no       3:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 0 1 0 1 0 1 0 0 0 0 1 0
0 1 1 0 1 0 0 1 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 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 1 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 1 0 0 0 0 0 
0 0 0 0 0 0 1 0 
0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 1 0 0 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 0 
0 1 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 0 0 0 1 0 
0 0 0 1 0 0 0 0 
0 0 0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(4, 6)(10, 11), 
(2, 5)(4, 7)(10, 12), 
(1, 5, 2, 3)(4, 7, 6, 8)(10, 12, 11, 13)
orbits: { 1, 3, 5, 2 }, { 4, 6, 7, 8 }, { 9 }, { 10, 11, 12, 13 }

code no       4:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 0 1 0 1 0 1 0 0 0 0 1 0
1 1 1 0 1 0 0 1 0 0 0 0 1
the automorphism group has order 6
and is strongly generated by the following 2 elements:
(
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 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 1 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 1 0 0 0 0 0 
0 0 0 0 0 0 1 0 
0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 5)(4, 6)(10, 11), 
(2, 5)(4, 7)(10, 12)
orbits: { 1 }, { 2, 5, 3 }, { 4, 6, 7 }, { 8 }, { 9 }, { 10, 11, 12 }, { 13 }

code no       5:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 0 1 0 1 0 1 0 0 0 0 1 0
0 1 0 1 1 0 0 1 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
0 1 0 1 1 0 0 1 
1 0 1 0 1 0 1 0 
0 0 0 0 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 1 0 0 0 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 1 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 1 
0 0 0 0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 13)(2, 12)(3, 8)(4, 7)(9, 11), 
(1, 2)(3, 4)(7, 8)(12, 13)
orbits: { 1, 13, 2, 12 }, { 3, 8, 4, 7 }, { 5 }, { 6 }, { 9, 11 }, { 10 }

code no       6:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 0 1 0 1 0 1 0 0 0 0 1 0
1 1 0 1 1 0 0 1 0 0 0 0 1
the automorphism group has order 2
and is strongly generated by the following 1 elements:
(
1 1 0 0 1 1 0 0 
0 1 0 0 0 0 0 0 
1 1 0 1 1 0 0 1 
1 0 1 0 1 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 1 
0 0 0 0 0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(1, 11)(3, 13)(4, 12)(5, 6)(7, 8)(9, 10)
orbits: { 1, 11 }, { 2 }, { 3, 13 }, { 4, 12 }, { 5, 6 }, { 7, 8 }, { 9, 10 }

code no       7:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 0 1 0 1 0 1 0 0 0 0 1 0
0 1 1 1 1 0 0 1 0 0 0 0 1
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
1 1 1 1 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 1 0 0 
0 1 1 1 1 0 0 1 
1 0 1 0 1 0 1 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 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 0 
0 0 0 0 0 0 0 1 
, 
1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 
0 1 1 1 1 0 0 1 
1 1 1 1 1 1 1 1 
0 0 0 0 1 0 0 0 
0 1 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 
1 0 1 0 1 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 10)(7, 13)(8, 12), 
(2, 3)(6, 7)(11, 12), 
(2, 6)(3, 13)(4, 9)(7, 10)(8, 12)
orbits: { 1 }, { 2, 3, 6, 10, 13, 7 }, { 4, 9 }, { 5 }, { 8, 12, 11 }

code no       8:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 1 1 0 1 0 1 0 0 0 0 1 0
1 0 1 1 0 1 1 0 0 0 0 0 1
the automorphism group has order 4
and is strongly generated by the following 2 elements:
(
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 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 1 0 
1 1 1 1 1 1 1 1 
, 
1 1 1 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 
1 0 1 1 0 1 1 0 
0 0 0 0 0 1 0 0 
1 1 0 0 1 1 0 0 
1 1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(8, 9), 
(1, 10)(5, 13)(7, 11)(8, 9)
orbits: { 1, 10 }, { 2 }, { 3 }, { 4 }, { 5, 13 }, { 6 }, { 7, 11 }, { 8, 9 }, { 12 }

code no       9:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 1 1 0 1 0 1 0 0 0 0 1 0
1 1 0 1 0 1 0 1 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 4 elements:
(
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 1 0 0 0 0 
1 1 1 0 1 0 1 0 
1 1 0 1 0 1 0 1 
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 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 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 1 0 
0 0 0 0 0 0 0 1 
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
1 1 0 1 0 1 0 1 
1 1 1 0 1 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 1 
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 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 1 0 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 12)(6, 13)(9, 11), 
(3, 5)(4, 6)(10, 11), 
(3, 13)(4, 12)(5, 6)(7, 8)(9, 10), 
(1, 2)
orbits: { 1, 2 }, { 3, 5, 13, 12, 6, 4 }, { 7, 8 }, { 9, 11, 10 }

code no      10:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 1 1 0 1 0 1 0 0 0 0 1 0
1 0 1 1 0 1 0 1 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
1 1 1 1 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 
1 0 1 1 0 1 0 1 
0 0 0 0 0 1 0 0 
1 1 1 1 1 1 1 1 
1 1 0 0 1 1 0 0 
, 
1 0 1 1 0 1 0 1 
0 1 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 
0 0 0 0 0 0 1 0 
1 1 1 1 0 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 1 0 0 0 0 
1 1 0 0 1 1 0 0 
, 
0 0 1 0 0 0 0 0 
1 1 1 0 1 0 1 0 
1 0 0 0 0 0 0 0 
1 0 1 1 0 1 0 1 
0 0 0 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 1 
)
acting on the columns of the generator matrix as follows (in order):
(1, 10)(3, 4)(5, 13)(7, 9)(8, 11), 
(1, 13)(3, 9)(4, 7)(5, 10)(8, 11), 
(1, 3)(2, 12)(4, 13)(5, 7)(9, 10)
orbits: { 1, 10, 13, 3, 5, 9, 4, 7 }, { 2, 12 }, { 6 }, { 8, 11 }

code no      11:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
0 0 1 1 1 0 1 0 0 0 0 1 0
1 0 1 0 1 1 1 0 0 0 0 0 1
the automorphism group has order 8
and is strongly generated by the following 3 elements:
(
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 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 1 0 
1 1 1 1 1 1 1 1 
, 
0 0 1 0 0 0 0 0 
0 0 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 1 0 0 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 1 0 0 
1 1 1 1 1 1 1 1 
, 
0 0 0 0 0 0 1 0 
1 1 0 0 1 1 0 0 
0 0 0 0 0 1 0 0 
0 0 1 1 1 0 1 0 
1 0 1 0 1 1 1 0 
0 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(8, 9), 
(1, 3)(2, 4)(6, 7)(8, 9)(11, 12), 
(1, 7)(2, 11)(3, 6)(4, 12)(5, 13)
orbits: { 1, 3, 7, 6 }, { 2, 4, 11, 12 }, { 5, 13 }, { 8, 9 }, { 10 }

code no      12:
================
1 1 1 1 1 1 1 1 1 0 0 0 0
1 1 1 1 0 0 0 0 0 1 0 0 0
1 1 0 0 1 1 0 0 0 0 1 0 0
1 0 1 1 1 0 1 0 0 0 0 1 0
1 0 1 0 1 1 0 1 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
1 1 0 0 1 1 0 0 
0 0 0 0 0 1 0 0 
1 1 1 1 0 0 0 0 
0 0 0 1 0 0 0 0 
1 0 1 1 1 0 1 0 
1 0 1 0 1 1 0 1 
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 
0 0 0 1 0 0 0 0 
1 1 0 0 1 1 0 0 
0 0 0 0 0 1 0 0 
1 0 1 0 1 1 0 1 
1 0 1 1 1 0 1 0 
, 
0 0 0 0 0 1 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 
1 1 1 1 1 1 1 1 
0 0 0 0 1 0 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 
, 
1 1 1 1 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 1 0 0 0 
1 0 1 1 1 0 1 0 
1 1 0 0 1 1 0 0 
1 1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 11)(4, 6)(5, 10)(7, 12)(8, 13), 
(3, 10)(5, 11)(7, 13)(8, 12), 
(1, 6)(3, 8)(4, 9)(10, 12), 
(1, 10)(3, 4)(6, 12)(7, 11)(8, 9)
orbits: { 1, 6, 10, 4, 12, 5, 3, 9, 7, 8, 11, 13 }, { 2 }

code no      13:
================
1 1 1 1 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 0 1 0 0 0
1 0 1 0 1 0 1 0 0 0 1 0 0
0 1 0 1 0 1 1 0 0 0 0 1 0
0 0 1 1 1 1 1 1 0 0 0 0 1
the automorphism group has order 96
and is strongly generated by the following 4 elements:
(
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 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 1 0 
0 0 1 1 1 1 1 1 
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 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 1 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 1 0 0 0 0 0 
1 0 1 0 1 0 1 0 
0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 
1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 1 
, 
0 0 1 0 0 0 0 0 
1 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 1 0 1 0 1 0 
0 0 0 0 1 0 0 0 
1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(8, 13), 
(3, 5)(4, 6)(9, 10), 
(2, 5)(4, 11)(7, 9), 
(1, 2, 4, 3)(5, 6, 12, 11)(7, 10)
orbits: { 1, 3, 5, 4, 2, 11, 6, 12 }, { 7, 9, 10 }, { 8, 13 }

code no      14:
================
1 1 1 1 0 0 0 0 1 0 0 0 0
1 1 0 0 1 1 0 0 0 1 0 0 0
1 0 1 0 1 0 1 0 0 0 1 0 0
1 0 0 1 1 0 0 1 0 0 0 1 0
1 1 0 0 0 1 1 1 0 0 0 0 1
the automorphism group has order 12
and is strongly generated by the following 3 elements:
(
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 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 1 
0 0 0 0 0 0 1 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 1 0 0 0 0 
0 0 0 0 1 0 0 0 
1 0 1 0 1 0 1 0 
1 1 0 0 1 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 1 0 
1 1 0 0 1 1 0 0 
0 0 0 0 0 0 0 1 
1 0 0 0 0 0 0 0 
1 0 1 0 1 0 1 0 
0 1 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 4)(7, 8)(11, 12), 
(2, 3)(6, 11)(7, 10), 
(1, 5)(2, 7)(3, 10)(4, 8)(6, 11)(9, 13)
orbits: { 1, 5 }, { 2, 3, 7, 4, 10, 8 }, { 6, 11, 12 }, { 9, 13 }

code no      15:
================
1 1 1 1 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 0 1 0 0 0
0 1 1 0 1 1 0 1 0 0 1 0 0
0 1 0 1 1 0 1 1 0 0 0 1 0
1 0 1 1 0 1 1 1 0 0 0 0 1
the automorphism group has order 576
and is strongly generated by the following 8 elements:
(
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 1 0 0 0 0 
0 0 0 0 0 1 0 0 
0 0 0 0 1 0 0 0 
1 0 0 0 1 1 1 0 
0 1 1 0 1 1 0 1 
, 
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 1 0 0 0 0 
0 0 0 0 0 0 1 0 
1 0 0 0 1 1 1 0 
0 0 0 0 1 0 0 0 
0 1 0 1 1 0 1 1 
, 
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 1 0 0 0 0 
1 0 1 1 0 1 1 1 
0 1 0 1 1 0 1 1 
0 1 1 0 1 1 0 1 
1 0 0 0 1 1 1 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 
1 1 1 1 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 1 0 0 
1 0 0 0 1 1 1 0 
0 1 1 0 1 1 0 1 
, 
1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 
1 1 1 1 0 0 0 0 
0 0 0 0 1 0 0 0 
0 0 0 0 0 0 1 0 
1 0 0 0 1 1 1 0 
0 1 0 1 1 0 1 1 
, 
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 1 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 1 
, 
1 0 0 0 0 0 0 0 
1 1 1 1 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 1 1 0 
0 0 0 0 0 0 1 0 
0 0 0 0 1 0 0 0 
0 1 1 0 1 1 0 1 
, 
1 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 
1 0 1 1 0 1 1 1 
0 1 1 0 1 1 0 1 
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 0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6)(7, 10)(8, 11)(12, 13), 
(5, 7)(6, 10)(8, 12)(11, 13), 
(5, 13)(6, 12)(7, 11)(8, 10), 
(4, 9)(7, 10)(8, 11), 
(3, 9, 4)(6, 10, 7)(8, 11, 12), 
(2, 5)(3, 6)(4, 7)(9, 10), 
(2, 4, 3, 9)(5, 7, 6, 10)(8, 11), 
(2, 7, 13, 3, 5, 8)(4, 6, 12, 9, 10, 11)
orbits: { 1 }, { 2, 5, 9, 8, 6, 7, 13, 10, 3, 4, 12, 11 }