the 25 isometry classes of irreducible [19,13,4]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 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 0 0
1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 9216
and is strongly generated by the following 10 elements:
(
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 1 
0 0 0 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 
1 0 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 1 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 0 0 1 
0 1 1 0 1 0 
1 0 1 1 0 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
0 0 0 1 0 0 
, 
1 0 0 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 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
1 0 1 1 0 0 
0 1 1 0 0 1 
, 
1 0 1 0 1 0 
0 1 1 0 1 0 
0 0 0 0 1 0 
0 0 0 1 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, 6)(12, 15)(13, 16)(14, 17), 
(5, 16)(6, 13)(12, 17)(14, 15), 
(5, 15)(6, 12)(13, 17)(14, 16), 
(4, 9)(5, 12)(10, 11)(13, 14), 
(4, 10)(5, 13)(9, 11)(12, 14), 
(4, 16, 11, 15)(5, 14)(6, 9, 17, 10)(12, 13), 
(3, 8)(4, 6, 5, 9, 15, 12)(10, 17, 13)(11, 16, 14)(18, 19), 
(2, 3)(6, 17)(7, 18)(9, 10)(12, 13), 
(2, 8)(4, 13, 9, 12)(5, 11, 14, 10)(6, 15, 16, 17)(7, 19), 
(1, 13)(2, 14)(3, 5)(8, 12)
orbits: { 1, 13, 16, 6, 17, 14, 5, 12, 4, 11, 15, 10, 9, 2, 3, 8 }, { 7, 18, 19 }

code no       2:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 9216
and is strongly generated by the following 9 elements:
(
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 1 0 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 0 0 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 1 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 1 1 1 0 
0 1 1 1 0 0 
0 0 0 0 0 1 
, 
1 0 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 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 1 1 1 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 0 0 0 1 0 
1 1 0 1 0 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 0 1 0 0 0 
1 1 1 1 1 0 
0 0 0 0 1 0 
1 0 1 0 0 1 
, 
0 1 1 0 1 0 
1 0 1 0 1 0 
1 1 0 0 1 0 
1 1 0 1 0 0 
1 1 1 1 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 15)(11, 14)(12, 17)(13, 16), 
(5, 14)(11, 15)(12, 16)(13, 17), 
(5, 17)(11, 16)(12, 15)(13, 14), 
(4, 13, 17)(5, 14, 10)(8, 12, 16)(9, 11, 15), 
(4, 5)(8, 11)(9, 12)(10, 13), 
(4, 16)(8, 17)(9, 14)(10, 15), 
(3, 7)(4, 11, 8, 5)(6, 18)(9, 12, 10, 13)(14, 15), 
(2, 7)(4, 15, 9, 17)(6, 19)(8, 16, 10, 14)(11, 13), 
(1, 15, 12, 2, 14, 13)(3, 17, 5, 7, 16, 11)(4, 8)(9, 10)
orbits: { 1, 13, 16, 17, 14, 4, 10, 11, 12, 8, 7, 5, 9, 3, 15, 2 }, { 6, 18, 19 }

code no       3:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 2304
and is strongly generated by the following 9 elements:
(
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 1 0 
0 1 1 0 0 1 
, 
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 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 0 1 0 
0 1 1 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 0 1 1 0 0 
0 1 1 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
0 1 1 1 0 0 
1 0 1 0 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
0 1 1 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
0 1 1 1 0 0 
1 0 1 1 0 0 
0 0 0 1 0 0 
1 0 1 0 1 0 
1 0 0 0 0 0 
1 1 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(6, 19)(17, 18), 
(6, 18)(17, 19), 
(4, 9)(5, 12)(8, 10)(11, 13), 
(4, 13)(5, 10)(8, 12)(9, 11), 
(4, 8)(5, 11)(9, 10)(12, 13), 
(3, 7)(4, 10, 8, 9)(5, 12, 11, 13)(6, 17)(14, 15), 
(2, 7)(4, 11)(5, 10)(6, 18)(8, 12)(9, 13)(14, 16), 
(1, 7)(2, 3)(4, 5, 10, 13)(8, 11, 9, 12), 
(1, 5, 10)(2, 11, 9)(3, 13, 8, 7, 12, 4)(6, 17)(14, 15)
orbits: { 1, 7, 10, 3, 2, 8, 5, 9, 4, 12, 13, 11 }, { 6, 19, 18, 17 }, { 14, 15, 16 }

code no       4:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 192
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 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 1 
, 
1 0 0 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 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
1 1 0 1 0 0 
1 0 1 1 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 0 0 1 0 1 
, 
1 1 1 0 0 0 
1 0 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 1 1 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 7)(4, 8)(6, 17)(12, 13)(14, 15), 
(3, 4)(7, 8)(12, 14)(13, 15)(18, 19), 
(2, 3)(8, 9)(11, 12)(15, 16)(17, 18), 
(2, 8)(3, 9)(6, 19)(11, 15)(12, 16), 
(1, 2, 7)(4, 10, 9)(6, 18, 17)(11, 12, 13)(14, 16, 15), 
(1, 8)(2, 4)(3, 10)(7, 9)
orbits: { 1, 7, 8, 3, 2, 9, 4, 10 }, { 5 }, { 6, 17, 19, 18 }, { 11, 12, 15, 13, 14, 16 }

code no       5:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 128
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
0 1 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
0 0 0 0 1 0 
1 1 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 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
0 0 0 1 0 0 
1 1 0 1 0 0 
0 1 1 1 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 1 1 0 0 
0 1 1 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 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(12, 13)(14, 15), 
(4, 9)(5, 13)(6, 17)(8, 10)(11, 12)(14, 15)(16, 18), 
(4, 10)(5, 13)(6, 18)(8, 9)(11, 12)(16, 17), 
(3, 7)(4, 8)(6, 16)(12, 13)(14, 15), 
(1, 2)(5, 11)(6, 16)(9, 10), 
(1, 8, 2, 4)(3, 9, 7, 10)(6, 16)(12, 13)(14, 15), 
(1, 9)(2, 10)(3, 4)(7, 8)
orbits: { 1, 2, 4, 9, 8, 10, 3, 7 }, { 5, 11, 13, 12 }, { 6, 17, 18, 16 }, { 14, 15 }, { 19 }

code no       6:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 96
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
0 1 1 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 0 1 1 0 0 
0 0 1 0 0 0 
0 1 1 0 1 0 
0 0 0 0 0 1 
, 
0 0 1 0 0 0 
1 1 1 0 0 0 
1 0 0 0 0 0 
1 0 1 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
0 0 0 1 0 0 
1 1 0 1 0 0 
1 0 1 1 0 0 
1 0 0 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
0 1 1 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(12, 13)(14, 15), 
(4, 9)(5, 13)(8, 10)(11, 12)(14, 15)(18, 19), 
(3, 4)(5, 11)(7, 8)(12, 15)(13, 14)(17, 18), 
(3, 4, 9)(5, 15, 12, 11, 14, 13)(7, 8, 10)(17, 18, 19), 
(1, 3)(2, 7)(4, 9)(5, 11)(8, 10)(12, 13)(14, 15), 
(1, 4)(2, 8)(3, 9)(7, 10), 
(1, 7)(2, 3)(4, 10)(5, 11)(8, 9)(12, 13)(14, 15)
orbits: { 1, 3, 4, 7, 9, 2, 10, 8 }, { 5, 11, 13, 12, 14, 15 }, { 6 }, { 16 }, { 17, 18, 19 }

code no       7:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 5 elements:
(
1 0 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 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 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 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 0 1 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 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 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5)(8, 11)(9, 12)(10, 13)(18, 19), 
(3, 4)(7, 8)(12, 14)(13, 15)(17, 18), 
(3, 7)(4, 8)(5, 11)(6, 16), 
(3, 8, 5, 7, 4, 11)(6, 16)(9, 14, 12)(10, 15, 13)(17, 18, 19), 
(1, 2)(6, 16)(9, 10)(12, 13)(14, 15)
orbits: { 1, 2 }, { 3, 4, 7, 11, 5, 8 }, { 6, 16 }, { 9, 12, 10, 14, 13, 15 }, { 17, 18, 19 }

code no       8:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 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 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
1 0 1 1 0 0 
1 0 0 1 1 0 
1 0 0 1 0 1 
, 
1 0 1 1 0 0 
0 1 1 1 0 0 
0 0 0 1 0 0 
1 0 0 0 0 0 
1 0 1 0 1 0 
1 0 0 1 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 1 1 0 0 
0 1 0 0 0 0 
1 1 0 0 1 0 
1 0 0 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 12)(6, 16)(8, 10)(11, 13), 
(3, 9, 4)(5, 12, 14)(6, 16, 17)(7, 10, 8)(11, 13, 15), 
(1, 4, 3, 9)(2, 8, 7, 10)(5, 12)(6, 18, 16, 17)(11, 13), 
(1, 8)(2, 4)(3, 10)(5, 11)(6, 17)(7, 9)(12, 13)(14, 15)(16, 18)
orbits: { 1, 9, 8, 4, 3, 7, 10, 2 }, { 5, 12, 14, 11, 13, 15 }, { 6, 16, 17, 18 }, { 19 }

code no       9:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 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 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
1 0 1 1 0 0 
1 0 0 1 1 0 
1 0 0 1 0 1 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 0 1 1 0 0 
1 1 0 0 1 0 
1 0 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 12)(6, 16)(8, 10)(11, 13), 
(3, 9, 4)(5, 12, 14)(6, 16, 17)(7, 10, 8)(11, 13, 15), 
(1, 2)(3, 7)(4, 8)(5, 11)(9, 10)(12, 13)(14, 15), 
(1, 7)(2, 3)(4, 9)(5, 11)(6, 16)(8, 10)(12, 13)(17, 18)
orbits: { 1, 2, 7, 3, 8, 4, 10, 9 }, { 5, 12, 14, 11, 13, 15 }, { 6, 16, 17, 18 }, { 19 }

code no      10:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 144
and is strongly generated by the following 6 elements:
(
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 1 
0 0 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
1 1 0 1 0 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 0 1 0 0 0 
1 1 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6)(11, 15)(12, 16)(13, 17)(14, 18), 
(4, 10)(5, 13)(6, 17)(8, 9)(11, 12)(15, 16), 
(4, 8)(5, 11)(6, 15)(9, 10)(12, 13)(16, 17), 
(4, 15)(5, 11)(6, 8)(9, 17)(10, 16)(12, 13)(14, 19), 
(3, 7)(9, 10)(12, 13)(16, 17), 
(2, 7, 3)(8, 10, 9)(11, 13, 12)(15, 17, 16)
orbits: { 1 }, { 2, 3, 7 }, { 4, 10, 8, 15, 9, 16, 6, 11, 17, 12, 5, 13 }, { 14, 18, 19 }

code no      11:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 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 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 1 0 0 
1 1 1 0 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 7)(4, 8)(5, 11)(6, 15), 
(3, 8)(4, 7)(5, 15)(6, 11)(12, 17)(13, 18)(14, 16), 
(1, 2)(3, 7)(5, 11)(12, 13)(17, 18)
orbits: { 1, 2 }, { 3, 7, 8, 4 }, { 5, 11, 15, 6 }, { 9 }, { 10 }, { 12, 17, 13, 18 }, { 14, 16 }, { 19 }

code no      12:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 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 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 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 1 0 
0 0 0 0 0 1 
, 
0 0 0 1 0 0 
1 1 0 1 0 0 
1 0 1 1 0 0 
0 0 0 0 1 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):
(4, 5)(8, 11)(9, 12)(10, 13)(17, 18), 
(2, 3)(8, 9)(11, 12)(15, 16), 
(1, 5, 4)(2, 11, 8)(3, 12, 9)(7, 13, 10)(17, 18, 19)
orbits: { 1, 4, 5 }, { 2, 3, 8, 9, 11, 12 }, { 6 }, { 7, 10, 13 }, { 14 }, { 15, 16 }, { 17, 18, 19 }

code no      13:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 36
and is strongly generated by the following 4 elements:
(
1 0 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 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 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 1 0 
0 0 0 0 0 1 
, 
0 1 1 0 1 0 
1 0 1 0 1 0 
1 1 0 0 1 0 
0 0 0 1 0 0 
1 1 1 0 0 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5)(8, 11)(9, 12)(10, 13)(17, 18), 
(3, 7)(4, 8)(5, 11)(6, 15), 
(2, 3)(8, 9)(11, 12)(15, 16), 
(1, 13)(2, 12)(3, 11)(5, 7)(17, 19)
orbits: { 1, 13, 10 }, { 2, 3, 12, 7, 11, 9, 5, 8, 4 }, { 6, 15, 16 }, { 14 }, { 17, 18, 19 }

code no      14:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 192
and is strongly generated by the following 7 elements:
(
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 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 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 1 0 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 0 0 1 
0 0 0 1 0 0 
0 0 0 0 1 0 
0 0 1 0 0 0 
, 
0 0 0 1 0 0 
1 1 0 1 0 0 
1 0 1 1 0 0 
1 0 0 0 0 0 
0 0 0 0 1 0 
1 0 0 1 0 1 
, 
1 1 0 0 1 0 
0 0 0 0 1 0 
0 1 0 0 1 1 
1 1 0 1 0 0 
1 0 0 0 0 0 
0 1 1 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(6, 15)(16, 17)(18, 19), 
(4, 8)(5, 11)(6, 15)(9, 10)(12, 13), 
(4, 5)(6, 15)(8, 11)(9, 12)(10, 13)(16, 19)(17, 18), 
(3, 7)(4, 8)(5, 11)(6, 15), 
(3, 6)(7, 15)(9, 16)(10, 17)(12, 18)(13, 19), 
(1, 4)(2, 8)(3, 9)(6, 16)(7, 10)(15, 17), 
(1, 5, 2, 11)(3, 18, 7, 19)(4, 8)(6, 12, 15, 13)(9, 17)(10, 16)
orbits: { 1, 4, 11, 8, 5, 2 }, { 3, 7, 6, 9, 19, 15, 10, 18, 16, 13, 12, 17 }, { 14 }

code no      15:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 16
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 1 1 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 1 0 1 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 0 1 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 8)(5, 11)(6, 15)(9, 10)(12, 13), 
(1, 8)(2, 4)(3, 10)(6, 17)(7, 9)(15, 16), 
(1, 7)(2, 3)(4, 9)(5, 11)(8, 10)(12, 13)(16, 17)(18, 19)
orbits: { 1, 8, 7, 4, 10, 9, 2, 3 }, { 5, 11 }, { 6, 15, 17, 16 }, { 12, 13 }, { 14 }, { 18, 19 }

code no      16:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 32
and is strongly generated by the following 5 elements:
(
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 1 0 
1 0 0 1 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 0 0 1 0 0 
1 0 0 1 0 1 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 0 1 0 0 0 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 1 1 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 1 0 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(6, 16)(15, 17)(18, 19), 
(3, 7)(9, 10)(12, 13), 
(2, 4)(3, 6, 7, 16)(9, 15, 10, 17)(11, 14)(12, 18, 13, 19), 
(1, 2)(4, 8)(6, 15)(12, 13)(16, 17), 
(1, 8)(2, 4)(3, 10)(6, 17)(7, 9)(15, 16)
orbits: { 1, 2, 8, 4 }, { 3, 7, 16, 10, 6, 9, 17, 15 }, { 5 }, { 11, 14 }, { 12, 13, 19, 18 }

code no      17:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 16
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 1 1 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 1 0 1 0 1 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
0 1 1 1 0 0 
1 0 1 1 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 7)(4, 8)(5, 11)(6, 15), 
(1, 8)(2, 4)(3, 10)(6, 17)(7, 9)(15, 16), 
(1, 2)(5, 11)(9, 10)(16, 17), 
(1, 10)(2, 9)(3, 4)(5, 11)(7, 8)(16, 17)(18, 19)
orbits: { 1, 8, 2, 10, 4, 7, 9, 3 }, { 5, 11 }, { 6, 15, 17, 16 }, { 12 }, { 13 }, { 14 }, { 18, 19 }

code no      18:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 0 1 0 
1 1 0 1 0 0 
1 1 0 0 0 1 
, 
0 0 1 0 0 0 
1 1 1 0 0 0 
1 0 0 0 0 0 
0 0 0 1 0 0 
1 0 1 0 1 0 
0 0 0 0 0 1 
, 
1 1 0 1 0 0 
0 1 1 1 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
0 1 1 0 1 0 
0 0 1 1 0 1 
, 
1 0 1 1 0 0 
0 0 0 1 0 0 
1 1 0 1 0 0 
0 1 1 0 1 0 
0 1 0 0 0 0 
0 0 1 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 8)(5, 11)(6, 15)(9, 10)(12, 13), 
(3, 7)(4, 11)(5, 8)(6, 15)(9, 12)(10, 13)(16, 18)(17, 19), 
(1, 3)(2, 7)(5, 12)(11, 13)(16, 17), 
(1, 8)(2, 10)(3, 4)(5, 13)(6, 17)(7, 9)(15, 16), 
(1, 13, 4, 2, 5, 9)(3, 12, 10, 7, 11, 8)(6, 19, 16, 15, 18, 17)
orbits: { 1, 3, 8, 9, 7, 4, 5, 11, 10, 12, 2, 13 }, { 6, 15, 17, 16, 19, 18 }, { 14 }

code no      19:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 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 1 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 0 0 1 0 1 
, 
0 0 0 1 0 0 
1 0 1 1 0 0 
1 1 0 1 0 0 
1 0 0 0 0 0 
0 0 0 0 1 0 
1 0 0 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(2, 3)(6, 16)(8, 9)(11, 12)(15, 17)(18, 19), 
(1, 4)(2, 9)(3, 8)(6, 16)(7, 10)(11, 12)(15, 17)
orbits: { 1, 4 }, { 2, 3, 9, 8 }, { 5 }, { 6, 16 }, { 7, 10 }, { 11, 12 }, { 13 }, { 14 }, { 15, 17 }, { 18, 19 }

code no      20:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 1152
and is strongly generated by the following 9 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
1 1 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 1 0 0 
1 1 1 0 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 0 0 1 
0 0 0 0 1 0 
1 1 0 1 0 0 
0 0 1 0 0 0 
, 
0 1 1 1 0 0 
1 0 1 1 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 0 0 1 0 1 
0 1 1 0 1 0 
, 
1 0 1 1 0 0 
0 1 1 1 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 1 0 1 0 1 
0 1 1 0 1 0 
, 
0 1 0 0 1 1 
1 0 0 0 1 1 
0 0 0 0 0 1 
0 1 1 0 1 0 
1 1 0 0 1 0 
0 1 0 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(6, 14)(12, 13)(15, 16), 
(4, 8)(6, 14)(9, 10)(17, 18), 
(4, 11)(5, 8)(9, 13)(10, 12)(15, 18)(16, 17), 
(3, 4)(5, 14)(6, 11)(7, 8)(12, 16)(13, 15), 
(3, 8)(4, 7)(5, 14)(6, 11)(12, 15)(13, 16), 
(3, 6, 7, 14)(4, 11, 8, 5)(9, 18)(10, 17)(12, 15)(13, 16), 
(1, 10)(2, 9)(5, 15)(6, 13)(11, 16)(12, 14), 
(1, 9)(2, 10)(5, 16)(6, 13)(11, 15)(12, 14), 
(1, 12, 8, 17, 2, 13, 4, 18)(3, 9, 16, 6)(5, 11)(7, 10, 15, 14)
orbits: { 1, 10, 9, 18, 12, 17, 2, 7, 13, 3, 15, 4, 16, 14, 8, 6, 5, 11 }, { 19 }

code no      21:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 32
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
1 0 1 1 0 0 
0 1 1 1 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
1 0 1 0 1 0 
1 0 0 1 0 1 
, 
0 1 1 1 0 0 
1 0 1 1 0 0 
1 1 0 1 0 0 
1 1 1 0 0 0 
1 0 1 0 1 0 
0 1 0 1 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 1 1 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 1 0 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(6, 14)(12, 13)(15, 16), 
(3, 4)(5, 14)(6, 11)(7, 8)(12, 16)(13, 15)(18, 19), 
(1, 9)(2, 10)(3, 4)(5, 12)(6, 15)(7, 8)(11, 13)(14, 16), 
(1, 10)(2, 9)(3, 8)(4, 7)(5, 12)(6, 16)(11, 13)(14, 15), 
(1, 8)(2, 4)(3, 10)(6, 16)(7, 9)(14, 15)
orbits: { 1, 9, 10, 8, 2, 7, 3, 4 }, { 5, 11, 14, 12, 6, 13, 16, 15 }, { 17 }, { 18, 19 }

code no      22:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0
1 1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 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 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
1 0 1 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 1 1 0 0 
0 0 0 1 0 0 
0 1 1 1 0 0 
0 1 0 0 0 0 
0 1 1 0 1 0 
0 0 1 1 0 1 
, 
1 1 0 0 1 0 
1 0 1 0 1 0 
0 1 1 0 1 0 
1 1 0 1 0 0 
0 1 0 0 0 0 
1 0 0 0 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 10)(5, 12)(6, 14)(8, 9)(11, 13)(15, 16)(17, 18), 
(3, 7)(4, 5)(8, 11)(9, 13)(10, 12)(15, 17)(16, 18), 
(1, 9)(2, 4)(3, 10)(5, 13)(6, 16)(7, 8)(14, 15)(17, 18), 
(1, 13, 3, 11)(2, 5, 7, 12)(4, 10, 9, 8)(6, 17)(14, 18)
orbits: { 1, 9, 11, 8, 13, 10, 3, 7, 5, 4, 12, 2 }, { 6, 14, 16, 17, 15, 18 }, { 19 }

code no      23:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 1 0 0 0 0 0 0 0 0 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 1 0 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 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 0 0 1 
0 0 0 0 1 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 
1 1 0 1 0 0 
1 1 1 0 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
1 0 1 1 0 0 
1 0 0 1 0 1 
1 0 0 1 1 0 
1 1 0 1 0 0 
0 0 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6)(11, 14)(12, 15)(13, 16), 
(3, 5, 4, 6)(7, 11, 8, 14)(9, 17)(10, 18)(12, 13, 16, 15), 
(3, 8)(4, 7)(5, 11)(6, 14)(12, 13)(15, 16), 
(2, 17, 9)(3, 14, 12, 8, 5, 16)(4, 6, 15, 7, 11, 13)(10, 18, 19)
orbits: { 1 }, { 2, 9, 17 }, { 3, 6, 8, 16, 5, 4, 14, 11, 12, 13, 15, 7 }, { 10, 18, 19 }

code no      24:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 16
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 0 0 1 
1 1 0 0 1 0 
1 1 0 1 0 0 
0 0 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 0 1 
0 0 1 0 0 0 
0 0 0 1 0 0 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 1 0 1 0 0 
1 1 1 0 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 6)(4, 11)(5, 8)(7, 14)(9, 18)(10, 17)(12, 16), 
(3, 5)(4, 6)(7, 11)(8, 14)(9, 17)(10, 18)(13, 15), 
(1, 2)(3, 8)(4, 7)(6, 14)(9, 10)(12, 13)(15, 16)
orbits: { 1, 2 }, { 3, 6, 5, 8, 4, 14, 11, 7 }, { 9, 18, 17, 10 }, { 12, 16, 13, 15 }, { 19 }

code no      25:
================
1 1 1 0 0 0 1 0 0 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 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 6
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 
0 0 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 1 0 0 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 1 0 1 0 0 
1 1 1 0 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
, 
0 0 0 0 1 0 
0 1 0 0 0 0 
1 0 0 0 1 1 
1 0 0 1 1 0 
1 0 0 0 0 0 
1 0 1 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(2, 5)(4, 6)(7, 12)(8, 17)(9, 15)(10, 18)(13, 14)(16, 19), 
(1, 2)(3, 8)(4, 7)(6, 14)(9, 10)(12, 13)(15, 16)(18, 19), 
(1, 5)(3, 17)(4, 13)(6, 12)(7, 14)(9, 19)(10, 16)(15, 18)
orbits: { 1, 2, 5 }, { 3, 8, 17 }, { 4, 6, 7, 13, 14, 12 }, { 9, 15, 10, 19, 16, 18 }, { 11 }