the 15 isometry classes of irreducible [23,11,7]_2 codes are:

code no       1:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0
1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 40320
and is strongly generated by the following 11 elements:
(
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 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 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 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 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 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 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 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
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 0 1 0 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 1 0 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 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 0 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 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 0 
0 1 0 1 1 0 0 1 1 0 1 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
0 1 0 1 1 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 1 0 1 0 1 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 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
1 1 0 0 0 1 0 1 0 1 1 0 
0 1 0 1 1 0 0 1 1 0 1 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 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 1 0 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
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 1 1 0 1 0 1 0 0 1 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 1 0 1 1 1 0 0 1 0 
0 1 0 1 1 0 0 1 1 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 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
0 1 1 0 1 0 1 0 0 1 1 0 
0 0 1 0 1 1 0 1 1 1 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 0 0 0 0 0 1 
, 
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 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 1 1 1 0 0 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 0 0 0 0 0 0 1 0 0 0 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 1 1 0 1 0 1 0 0 1 1 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
0 1 0 1 1 0 0 1 1 0 1 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
1 1 0 0 0 1 0 1 0 1 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
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 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 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(12, 13), 
(4, 10)(5, 18)(6, 16)(7, 19)(8, 20)(9, 11)(12, 13)(14, 17)(15, 21), 
(4, 9)(5, 7)(6, 8)(10, 11)(14, 15)(16, 20)(17, 21)(18, 19), 
(4, 17)(5, 16)(6, 18)(7, 20)(8, 19)(9, 21)(10, 14)(11, 15)(12, 13), 
(4, 16)(5, 17)(6, 10)(7, 21)(8, 11)(9, 20)(12, 13)(14, 18)(15, 19), 
(3, 22, 23)(4, 20, 21)(6, 8, 7)(9, 19, 10)(11, 15, 16)(12, 13)(14, 18, 17), 
(2, 22, 3)(4, 17, 10)(5, 9, 8)(6, 11, 19)(7, 18, 21)(12, 13)(15, 20, 16), 
(2, 15, 17, 6, 20)(3, 10, 16, 14, 5)(4, 23, 18, 9, 19)(7, 11, 21, 22, 8), 
(1, 3, 2)(4, 9, 17)(5, 8, 10)(6, 15, 16)(7, 18, 14)(11, 20, 19)(12, 13), 
(1, 16, 19, 21, 10)(2, 8, 17, 18, 9)(3, 11, 15, 7, 20)(4, 5, 14, 6, 22), 
(1, 9, 4, 18, 23)(2, 17, 14, 3, 7)(5, 11, 8, 10, 20)(6, 21, 22, 16, 15)
orbits: { 1, 2, 10, 23, 3, 20, 9, 7, 4, 11, 14, 6, 19, 17, 8, 21, 22, 18, 5, 16, 15 }, { 12, 13 }

code no       2:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0
0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 1920
and is strongly generated by the following 7 elements:
(
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 0 1 0 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 1 0 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 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 0 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 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 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 1 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 0 
0 1 0 1 1 0 0 1 1 0 1 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 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 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 0 0 0 0 0 1 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 1 1 1 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 
1 0 0 0 1 1 1 0 1 0 1 0 
1 0 0 1 1 0 1 1 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 1 0 0 0 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 0 0 1 1 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 1 0 0 1 1 1 1 0 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 0 0 1 1 0 
0 1 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
0 0 1 1 0 1 1 1 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 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 1 0 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 0 1 
, 
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 0 0 0 0 1 0 
0 1 1 0 1 0 1 0 0 1 1 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 0 1 0 1 1 0 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 0 
0 0 0 0 0 0 1 0 0 0 0 0 
0 1 0 1 1 0 0 1 1 0 1 0 
1 0 0 0 0 0 0 0 0 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):
(4, 9)(5, 7)(6, 8)(10, 11)(14, 15)(16, 20)(17, 21)(18, 19), 
(4, 11)(5, 19)(6, 20)(7, 18)(8, 16)(9, 10)(14, 21)(15, 17), 
(4, 17)(5, 16)(6, 18)(7, 20)(8, 19)(9, 21)(10, 14)(11, 15), 
(4, 8)(5, 15)(6, 9)(7, 14)(10, 20)(11, 16)(17, 19)(18, 21), 
(3, 22)(4, 21, 20, 5)(6, 15, 11, 18)(7, 9, 17, 16)(8, 14, 10, 19)(12, 23), 
(2, 3, 22)(4, 8, 16)(5, 10, 7)(6, 14, 19)(9, 21, 15)(17, 20, 18), 
(1, 11, 3, 8)(2, 16, 22, 4)(5, 17)(6, 7, 9, 18)(10, 14, 20, 21)(15, 19)
orbits: { 1, 8, 6, 16, 19, 4, 3, 20, 18, 9, 5, 11, 17, 2, 10, 14, 15, 22, 7, 21 }, { 12, 23 }, { 13 }

code no       3:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 288
and is strongly generated by the following 7 elements:
(
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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 1 1 0 1 0 1 0 0 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
0 1 0 1 1 0 0 1 1 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 0 
0 1 0 1 1 0 0 1 1 0 1 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 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 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 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
0 0 1 1 0 1 1 1 0 0 1 0 
0 0 1 0 1 1 0 1 1 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 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 0 0 0 0 0 0 0 1 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 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 0 0 0 0 0 0 0 1 0 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 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 1 0 1 1 0 0 1 1 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 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 1 1 0 0 0 1 1 1 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 1 0 0 1 1 1 1 0 0 0 1 
, 
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 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
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 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 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):
(5, 6, 14)(7, 17, 20)(8, 16, 11)(9, 18, 19)(10, 21, 15)(12, 22, 23), 
(4, 21)(5, 20)(6, 19)(7, 16)(8, 18)(9, 17)(10, 15)(11, 14), 
(4, 17)(5, 16)(6, 18)(7, 20)(8, 19)(9, 21)(10, 14)(11, 15), 
(4, 7)(5, 9)(6, 15)(8, 14)(10, 19)(11, 18)(16, 21)(17, 20), 
(4, 10)(5, 18)(6, 16)(7, 19)(8, 20)(9, 11)(14, 17)(15, 21), 
(2, 3)(4, 21, 5, 20)(6, 11, 14, 19)(7, 15, 9, 8)(10, 16, 18, 17)(12, 22), 
(1, 2, 3)(4, 17, 9)(5, 10, 8)(6, 16, 15)(7, 14, 18)(11, 19, 20)
orbits: { 1, 3, 2 }, { 4, 21, 17, 7, 10, 20, 9, 16, 15, 14, 18, 19, 8, 5, 11, 6 }, { 12, 23, 22 }, { 13 }

code no       4:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0
0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 0 1 1 1 1 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 0 1 0 0 0 0 0 0 0 0 0 1 0
1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 1920
and is strongly generated by the following 8 elements:
(
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 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 0 0 0 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 0 0 0 0 0 0 0 1 0 0 
0 0 1 1 1 0 1 0 1 0 0 1 
0 0 1 1 0 1 1 1 0 0 1 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 1 0 1 0 1 0 0 1 1 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 1 1 1 0 1 0 1 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 0 0 1 1 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 
1 0 0 0 1 1 1 0 1 0 1 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 1 0 0 1 1 1 1 0 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
1 0 1 0 0 1 1 0 0 1 0 1 
0 1 1 0 1 0 1 0 0 1 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 1 1 0 1 0 1 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 0 1 0 0 0 0 
0 1 0 0 1 1 1 1 0 0 0 1 
0 0 1 1 0 1 1 1 0 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
, 
1 0 0 0 0 0 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 1 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 1 1 0 1 0 1 0 0 1 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 0 1 0 0 1 1 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 1 0 1 0 1 1 0 1 1 0 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 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 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 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
0 0 0 1 0 0 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 1 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 1 1 0 0 0 1 1 1 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 1 0 1 1 1 0 0 1 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
1 0 1 0 0 1 1 0 0 1 0 1 
0 0 0 0 0 0 0 0 0 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 1 0 1 1 1 0 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 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 1 1 1 0 1 0 1 0 0 1 
0 0 0 1 0 0 0 0 0 0 0 0 
0 1 1 0 1 0 1 0 0 1 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 
)
acting on the columns of the generator matrix as follows (in order):
(4, 15)(5, 9)(6, 8)(7, 14)(11, 22)(12, 18)(19, 21)(20, 23), 
(3, 20)(4, 18)(5, 16)(7, 14)(8, 17)(10, 19)(11, 15)(12, 22), 
(2, 20)(5, 19)(6, 17)(7, 14)(9, 18)(10, 15)(11, 16)(12, 21), 
(2, 23)(3, 20)(4, 19)(5, 22)(9, 21)(10, 18)(11, 15)(12, 16), 
(2, 15, 23, 11)(3, 21, 20, 9)(4, 22, 19, 5)(7, 14)(8, 17)(10, 12, 18, 16), 
(1, 5)(2, 17)(3, 18)(4, 19)(6, 16)(8, 9)(10, 11)(15, 20), 
(1, 4)(2, 11)(3, 8)(5, 19)(6, 15)(9, 18)(10, 17)(16, 20), 
(1, 18, 4, 9, 23)(2, 12, 6, 20, 10)(3, 16, 21, 17, 19)(5, 22, 8, 11, 15)
orbits: { 1, 5, 4, 23, 9, 16, 19, 22, 15, 18, 20, 2, 21, 8, 11, 12, 6, 3, 10, 17 }, { 7, 14 }, { 13 }

code no       5:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0
1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0
1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 1920
and is strongly generated by the following 8 elements:
(
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 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 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 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 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 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
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 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 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 1 0 1 1 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 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 0 0 0 0 0 0 0 0 1 0 
1 0 1 1 0 1 1 1 0 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 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 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 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 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 0 1 1 0 0 1 1 0 1 0 
1 1 0 1 0 1 1 0 1 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 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
1 1 0 1 1 0 0 1 1 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 1 0 1 1 1 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 0 1 0 1 1 0 1 1 1 0 0 
1 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 1 0 1 0 0 1 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 1 1 0 0 1 1 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 1 0 1 1 1 0 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 1 0 1 0 0 1 1 0 
0 1 0 0 0 0 0 0 0 0 0 0 
1 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 1 1 1 0 0 0 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 
1 1 0 1 1 0 0 1 1 0 1 0 
1 1 1 1 1 1 1 1 1 1 1 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
1 0 1 1 0 1 1 1 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 0 1 0 0 0 0 0 0 0 0 0 
1 1 0 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 1 0 0 0 0 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):
(12, 13), 
(4, 5)(6, 14)(7, 9)(8, 15)(10, 18)(11, 19)(16, 17)(20, 21), 
(4, 11)(5, 19)(6, 20)(7, 18)(8, 16)(9, 10)(12, 13)(14, 21)(15, 17), 
(4, 15)(5, 8)(6, 7)(9, 14)(10, 21)(11, 17)(16, 19)(18, 20), 
(4, 21)(5, 20)(6, 19)(7, 16)(8, 18)(9, 17)(10, 15)(11, 14), 
(3, 23, 22)(4, 15, 9)(5, 18, 17)(6, 19, 11)(7, 20, 10)(8, 16, 21)(12, 13), 
(2, 3, 22)(4, 19, 18)(5, 14, 8)(6, 10, 20)(7, 16, 17)(11, 15, 21)(12, 13), 
(2, 4, 19)(3, 5, 11)(6, 23, 21)(7, 16, 9)(10, 18, 15)(14, 22, 20)
orbits: { 1 }, { 2, 22, 19, 23, 3, 14, 11, 5, 16, 6, 4, 21, 9, 20, 17, 8, 7, 15, 18, 10 }, { 12, 13 }

code no       6:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0
1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0
1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 96
and is strongly generated by the following 6 elements:
(
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 0 1 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 1 1 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 1 0 1 0 1 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 0 0 0 0 1 
, 
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 0 1 0 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 1 0 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 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 0 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 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 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 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 0 1 1 0 0 1 1 0 1 0 
1 1 0 1 0 1 1 0 1 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 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 0 0 1 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 1 0 1 1 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 0 
0 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 1 0 1 0 0 1 1 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 0 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 1 0 1 1 0 1 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 1 0 0 0 0 
1 1 0 0 1 1 1 1 0 0 0 1 
, 
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 1 1 0 1 0 1 0 0 1 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 1 0 1 1 0 1 1 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 
1 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 0 1 1 0 1 1 1 0 0 1 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):
(4, 16)(5, 17)(6, 10)(7, 21)(8, 11)(9, 20)(14, 18)(15, 19), 
(4, 9)(5, 7)(6, 8)(10, 11)(14, 15)(16, 20)(17, 21)(18, 19), 
(4, 15)(5, 8)(6, 7)(9, 14)(10, 21)(11, 17)(16, 19)(18, 20), 
(4, 5)(6, 14)(7, 9)(8, 15)(10, 18)(11, 19)(16, 17)(20, 21), 
(3, 22)(5, 21)(6, 10)(7, 17)(8, 11)(12, 23)(14, 15)(18, 19), 
(2, 22, 3)(4, 7, 15)(5, 16, 18)(8, 21, 17)(9, 10, 20)(11, 14, 19)
orbits: { 1 }, { 2, 3, 22 }, { 4, 16, 9, 15, 5, 20, 19, 17, 14, 7, 8, 21, 18, 10, 11, 6 }, { 12, 23 }, { 13 }

code no       7:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
1 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0
1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 96
and is strongly generated by the following 6 elements:
(
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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 1 0 1 1 1 0 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 0 1 1 1 0 1 0 1 0 0 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 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 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 0 1 1 0 0 1 1 0 1 0 
1 1 0 1 0 1 1 0 1 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 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 0 0 1 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 1 0 1 1 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 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 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 1 0 1 1 1 0 0 1 0 
1 1 0 1 1 0 0 1 1 0 1 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 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 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 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 1 1 0 0 1 1 0 1 0 
1 0 1 1 0 1 1 1 0 0 1 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 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 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 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 0 1 0 1 1 0 1 1 1 0 0 
1 1 0 1 0 1 1 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 1 0 0 0 
1 0 1 1 0 1 1 1 0 0 1 0 
1 1 0 0 1 1 1 1 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 6, 14)(7, 17, 20)(8, 16, 11)(9, 18, 19)(10, 21, 15)(12, 22, 23), 
(4, 15)(5, 8)(6, 7)(9, 14)(10, 21)(11, 17)(16, 19)(18, 20), 
(4, 5)(6, 14)(7, 9)(8, 15)(10, 18)(11, 19)(16, 17)(20, 21), 
(4, 17)(5, 16)(6, 18)(7, 20)(8, 19)(9, 21)(10, 14)(11, 15), 
(4, 18)(5, 10)(6, 17)(7, 11)(8, 21)(9, 19)(14, 16)(15, 20), 
(2, 3)(4, 5)(7, 18)(8, 17)(9, 10)(11, 19)(12, 22)(15, 16)
orbits: { 1 }, { 2, 3 }, { 4, 15, 5, 17, 18, 21, 8, 11, 20, 16, 14, 10, 7, 6, 9, 19 }, { 12, 23, 22 }, { 13 }

code no       8:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
1 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0
1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 0 1 0 1 0 0 1 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 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 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 0 1 0 1 1 0 1 1 1 0 0 
1 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 0 1 1 0 1 1 1 0 0 1 0 
1 0 1 1 1 0 1 0 1 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 1 0 1 0 0 1 1 0 
1 0 0 0 1 1 1 0 1 0 1 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 1 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 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 1 0 0 
1 1 0 0 1 1 1 1 0 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 0 1 0 1 0 0 1 1 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 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
1 1 1 1 1 1 1 1 1 1 1 1 
1 1 0 1 0 1 1 0 1 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 1 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 1 1 1 0 1 0 1 0 0 1 
1 1 1 0 1 0 1 0 0 1 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 0 1 1 0 1 1 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 10, 15)(5, 16, 9)(6, 17, 8)(7, 14, 18)(11, 20, 19)(12, 22, 23), 
(3, 21)(4, 20)(6, 8)(9, 16)(10, 11)(12, 22)(14, 18)(15, 19), 
(2, 3, 21)(4, 20, 5)(6, 17, 8)(7, 18, 14)(9, 15, 11)(10, 19, 16), 
(1, 13)(2, 17)(3, 6, 21, 8)(4, 10, 20, 11)(7, 23)(9, 19, 16, 15)(12, 14, 22, 18)
orbits: { 1, 13 }, { 2, 21, 17, 3, 6, 8 }, { 4, 15, 20, 5, 11, 10, 19, 9, 16 }, { 7, 18, 14, 23, 22, 12 }

code no       9:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0
1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0
1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0
1 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 960
and is strongly generated by the following 9 elements:
(
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 0 1 0 0 0 0 0 0 0 0 0 
1 0 0 1 0 1 0 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 
1 1 0 0 0 1 0 1 0 1 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 1 0 0 0 1 1 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 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 0 
0 0 1 0 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 1 0 0 0 1 1 0 1 
1 0 0 1 0 1 0 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 
1 1 0 0 0 1 0 1 0 1 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 0 0 0 0 1 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 0 1 0 0 0 0 0 0 0 0 0 
1 0 1 1 0 0 0 0 1 1 1 0 
1 1 0 0 0 1 0 1 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 
1 0 1 0 0 1 1 0 0 1 0 1 
1 1 0 0 1 0 0 0 1 1 0 1 
0 0 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 0 1 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 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
1 1 0 0 0 1 0 1 0 1 1 0 
1 0 1 1 0 0 0 0 1 1 1 0 
1 0 0 1 0 1 0 1 1 0 0 1 
1 1 0 0 1 0 0 0 1 1 0 1 
1 0 1 0 0 1 1 0 0 1 0 1 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 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 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 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 1 0 0 0 0 1 1 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 1 0 1 0 1 1 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 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 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 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 1 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 0 1 0 1 0 1 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 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 1 0 0 0 0 1 1 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
1 1 0 0 0 1 0 1 0 1 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 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 0 0 0 0 0 0 0 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 1 1 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 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 
1 0 1 1 0 0 0 0 1 1 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 0 
1 1 0 0 1 0 0 0 1 1 0 1 
1 0 0 1 0 1 0 1 1 0 0 1 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 0 0 1 1 0 1 1 0 1 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 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 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 21)(5, 12)(6, 19)(7, 18)(8, 11)(9, 23)(14, 20)(15, 22), 
(4, 18)(5, 11)(6, 23)(7, 21)(8, 12)(9, 19)(14, 22)(15, 20), 
(4, 20)(5, 19)(6, 12)(7, 22)(8, 23)(9, 11)(14, 21)(15, 18), 
(4, 19)(5, 20)(6, 21)(7, 23)(8, 22)(9, 18)(11, 15)(12, 14), 
(3, 16, 10)(4, 20, 8)(5, 11, 6)(7, 9, 18)(12, 22, 21)(14, 15, 19), 
(2, 16)(3, 10)(4, 5)(6, 7)(8, 14)(9, 15)(11, 19)(18, 20), 
(2, 8)(3, 6)(4, 20)(5, 18)(7, 10)(9, 19)(11, 15)(14, 16), 
(2, 10)(3, 16)(4, 15)(5, 9)(6, 14)(7, 8)(11, 20)(18, 19), 
(2, 8, 4, 20, 23)(3, 14, 5, 19, 21)(6, 9, 11, 12, 10)(7, 15, 18, 22, 16)
orbits: { 1 }, { 2, 16, 8, 10, 23, 3, 14, 22, 11, 12, 20, 7, 9, 6, 21, 19, 15, 18, 5, 4 }, { 13 }, { 17 }

code no      10:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0
1 1 0 1 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0
1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 20160
and is strongly generated by the following 9 elements:
(
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 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 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 0 0 0 1 0 1 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 
1 0 1 0 1 0 0 0 1 1 1 0 
1 0 0 1 1 0 1 1 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 1 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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 0 1 0 1 1 0 1 0 1 0 
1 1 0 1 0 0 0 0 1 1 0 1 
1 0 0 0 1 1 0 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 
1 1 0 0 0 1 0 1 0 1 1 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 0 0 0 0 1 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 0 1 0 0 0 0 0 0 0 0 0 
1 1 0 1 0 0 0 0 1 1 0 1 
1 0 1 0 0 1 1 0 0 1 0 1 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 0 1 0 0 0 1 1 1 0 
1 1 0 0 0 1 0 1 0 1 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 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
1 0 0 0 1 1 0 1 1 0 0 1 
1 1 0 0 0 1 0 1 0 1 1 0 
1 0 0 1 0 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 1 0 0 0 0 1 1 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 1 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 0 1 0 0 0 0 0 0 0 0 0 
1 0 1 0 1 0 0 0 1 1 1 0 
1 1 0 0 0 1 0 1 0 1 1 0 
1 0 0 0 1 1 0 1 1 0 0 1 
1 1 0 1 0 0 0 0 1 1 0 1 
1 0 1 0 0 1 1 0 0 1 0 1 
1 0 0 1 0 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 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 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 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 0 1 0 1 1 0 1 0 1 0 
1 0 1 0 1 0 0 0 1 1 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 0 1 1 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
1 1 0 0 0 1 0 1 0 1 1 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 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 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 
1 0 0 0 1 1 0 1 1 0 0 1 
1 1 1 0 0 0 1 1 1 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 0 1 0 1 1 0 1 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 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 0 1 0 1 0 0 0 1 1 1 0 
0 1 0 0 0 0 0 0 0 0 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 
1 1 0 0 1 0 1 0 0 0 1 1 
0 0 0 0 0 0 0 1 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 0 1 0 0 0 0 1 1 0 1 
0 0 0 0 0 0 0 0 0 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 1 0 1 0 0 0 1 1 1 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 0 0 0 1 0 1 0 1 1 0 
1 0 0 0 1 1 0 1 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 14, 6)(7, 21, 18)(8, 11, 12)(9, 17, 19)(10, 23, 16)(15, 22, 20), 
(4, 11)(5, 17)(6, 22)(7, 20)(8, 12)(9, 18)(14, 21)(15, 19), 
(4, 22)(5, 21)(6, 11)(7, 19)(8, 18)(9, 12)(14, 17)(15, 20), 
(4, 12)(5, 20)(6, 18)(7, 17)(8, 11)(9, 22)(14, 19)(15, 21), 
(4, 19)(5, 18)(6, 20)(7, 22)(8, 21)(9, 17)(11, 15)(12, 14), 
(3, 16, 10)(4, 11, 6)(5, 19, 8)(7, 9, 17)(12, 21, 20)(14, 15, 18), 
(3, 22, 18)(4, 16, 8)(5, 7, 10)(11, 14, 20)(12, 17, 15)(19, 21, 23), 
(2, 11)(3, 17)(4, 6)(5, 7)(8, 15)(9, 14)(10, 19)(16, 18), 
(2, 18, 11, 14, 10, 7, 23)(3, 21, 17, 20, 12, 15, 8)(4, 19, 9, 5, 22, 6, 16)
orbits: { 1 }, { 2, 11, 23, 8, 4, 6, 15, 20, 18, 10, 21, 7, 12, 19, 16, 22, 14, 17, 5, 9, 3 }, { 13 }

code no      11:
================
1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0
0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 80640
and is strongly generated by the following 9 elements:
(
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 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 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 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 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 0 1 0 
1 0 1 0 1 1 1 1 0 0 0 1 
, 
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 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 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 0 0 1 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 1 0 1 1 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 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 1 0 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 1 1 0 0 1 1 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 1 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 1 1 0 0 1 1 0 1 0 
1 1 0 1 0 1 1 1 0 0 1 0 
1 1 1 1 1 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 0 0 0 0 0 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 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 0 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 0 1 0 1 1 1 0 0 1 0 
0 0 1 0 1 1 0 1 1 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 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 0 0 1 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
1 1 0 1 0 1 1 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 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 1 1 1 0 0 0 1 0 1 1 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 0 0 0 1 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 0 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 1 0 1 0 1 1 1 0 0 1 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 1 1 1 1 1 0 0 1 1 0 
0 0 1 0 1 1 0 1 1 1 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 1 0 0 0 
0 1 1 1 0 0 0 1 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
0 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 1 1 1 0 0 1 1 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 1 0 1 1 1 0 0 1 0 
1 0 0 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 0 0 0 1 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):
(12, 23), 
(7, 8)(9, 14)(10, 15)(11, 18)(16, 17)(19, 20)(21, 22), 
(4, 18)(5, 11)(6, 20)(7, 15)(8, 17)(9, 16)(10, 14)(13, 19), 
(4, 16)(5, 15)(6, 17)(7, 11)(8, 20)(9, 18)(10, 13)(14, 19), 
(4, 14)(5, 8)(6, 7)(9, 13)(10, 18)(11, 17)(15, 20)(16, 19), 
(4, 5)(6, 13)(7, 9)(8, 14)(10, 17)(11, 18)(15, 16)(19, 20), 
(3, 21, 22)(5, 20, 19)(6, 16, 17)(7, 13, 8)(9, 11, 15)(10, 18, 14), 
(2, 18, 3, 13)(4, 15, 20, 16)(5, 8, 19, 14)(6, 22, 11, 21)(7, 17)(9, 10), 
(1, 9, 16)(2, 13, 19)(3, 20, 6)(4, 14, 17)(7, 21, 15)(8, 10, 18)
orbits: { 1, 16, 17, 9, 4, 19, 15, 6, 20, 8, 11, 10, 7, 14, 18, 13, 5, 21, 3, 22, 2 }, { 12, 23 }

code no      12:
================
1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0
1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0
0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 5760
and is strongly generated by the following 8 elements:
(
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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 0 1 0 1 1 1 0 0 1 0 
1 0 1 1 1 0 0 1 1 0 1 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
0 0 1 1 1 0 1 0 1 0 0 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 0 1 1 1 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 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 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 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 1 1 1 0 1 0 1 0 
1 0 0 1 1 0 1 1 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 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 1 1 1 0 1 0 1 0 
1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
0 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 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 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 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 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 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 0 1 1 1 0 0 1 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 0 
0 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 1 1 1 1 0 0 1 1 0 
1 1 0 1 0 1 1 1 0 0 1 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 
1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 1 1 1 0 0 0 1 
, 
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 1 1 1 1 0 0 1 1 0 
0 0 0 0 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 1 1 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 0 0 0 1 1 1 0 1 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 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
, 
0 0 0 1 0 0 0 0 0 0 0 0 
0 0 1 0 1 1 0 1 1 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 1 0 0 0 0 
0 0 1 1 1 1 1 0 0 1 1 0 
1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 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):
(5, 6, 13)(7, 15, 18)(8, 16, 20)(9, 10, 19)(11, 14, 17)(12, 22, 23), 
(4, 6)(5, 13)(7, 14)(8, 9)(10, 15)(11, 19)(16, 17)(18, 20), 
(4, 9)(5, 7)(6, 8)(10, 19)(11, 15)(13, 14)(16, 18)(17, 20), 
(4, 19)(5, 20)(6, 11)(7, 17)(8, 15)(9, 10)(13, 18)(14, 16), 
(4, 13)(5, 6)(7, 8)(9, 14)(10, 16)(11, 20)(15, 17)(18, 19), 
(3, 21)(4, 15, 7, 18)(5, 14, 9, 6)(8, 17, 13, 19)(10, 11, 20, 16)(12, 22), 
(2, 21, 3)(4, 14, 11)(5, 15, 6)(7, 10, 9)(8, 13, 19)(16, 18, 20), 
(1, 7, 4)(2, 19, 17)(3, 16, 11)(5, 10, 8)(6, 14, 21)(9, 13, 20)
orbits: { 1, 4, 6, 9, 19, 13, 18, 11, 7, 5, 8, 15, 21, 10, 14, 20, 2, 17, 16, 3 }, { 12, 23, 22 }

code no      13:
================
1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0
0 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0
0 1 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 5760
and is strongly generated by the following 10 elements:
(
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 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 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 1 1 1 1 0 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 
0 1 1 1 0 1 0 1 1 0 0 1 
1 1 0 1 0 1 1 1 0 0 1 0 
1 0 0 1 1 0 1 1 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 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 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 0 1 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
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 0 0 1 0 0 0 
1 1 0 1 1 0 1 0 1 0 0 1 
1 0 0 0 1 1 1 0 1 0 1 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 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 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 1 0 1 1 0 1 0 0 
0 0 0 0 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 0 1 0 0 0 0 
0 1 0 0 1 1 1 1 0 0 0 1 
1 1 0 1 0 1 1 1 0 0 1 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 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 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 1 1 0 1 0 1 0 0 1 
0 0 0 0 0 0 0 0 1 0 0 0 
0 1 0 1 0 1 1 0 1 1 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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 0 1 1 1 0 0 1 1 0 1 0 
1 1 0 1 0 1 1 1 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 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 1 1 0 1 0 1 0 0 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
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 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 1 0 1 0 1 1 1 0 0 1 0 
1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 1 1 0 0 1 1 0 1 0 
1 1 0 1 0 1 1 1 0 0 1 0 
1 1 1 1 1 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 0 0 0 0 0 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
0 1 1 1 0 1 0 1 1 0 0 1 
0 0 0 0 0 0 0 0 0 0 0 1 
1 1 0 1 1 0 1 0 1 0 0 1 
0 1 0 1 0 1 1 0 1 1 0 0 
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 0 0 0 0 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 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 1 0 0 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 1 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 1 0 0 0 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 1 0 0 1 1 1 1 0 0 0 1 
, 
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 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 1 0 1 1 0 1 1 1 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 0 1 1 1 0 1 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 
)
acting on the columns of the generator matrix as follows (in order):
(7, 21)(8, 12)(9, 23)(10, 18)(11, 15)(14, 22)(16, 20)(17, 19), 
(7, 16)(8, 17)(9, 10)(11, 22)(12, 19)(14, 15)(18, 23)(20, 21), 
(7, 15)(8, 10)(9, 17)(11, 21)(12, 18)(14, 16)(19, 23)(20, 22), 
(7, 19)(8, 20)(9, 11)(10, 22)(12, 16)(14, 18)(15, 23)(17, 21), 
(5, 6, 13)(7, 10, 20)(8, 17, 18)(9, 15, 11)(12, 21, 22)(14, 16, 19), 
(4, 17)(5, 10)(6, 16)(7, 19)(8, 18)(9, 20)(11, 14)(13, 15), 
(4, 16)(5, 15)(6, 17)(7, 11)(8, 20)(9, 18)(10, 13)(14, 19), 
(4, 18, 17, 8, 23)(5, 19, 15, 14, 12)(6, 11, 10, 9, 22)(7, 21, 13, 20, 16), 
(2, 3)(4, 17, 20, 9)(5, 10, 19, 7)(6, 15, 18, 14)(8, 13, 16, 11)(12, 21), 
(1, 3, 2)(4, 6, 5)(7, 18, 17)(8, 11, 16)(9, 20, 15)(10, 14, 19)
orbits: { 1, 2, 3 }, { 4, 17, 16, 23, 9, 5, 19, 8, 21, 6, 18, 20, 7, 14, 12, 13, 11, 15, 10, 22 }

code no      14:
================
1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0
0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0
0 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0
1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 40320
and is strongly generated by the following 8 elements:
(
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 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 0 0 0 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 0 0 0 0 0 0 0 1 0 0 
1 1 0 1 1 0 1 0 1 0 0 1 
1 1 0 1 0 1 1 1 0 0 1 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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 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 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 0 1 0 1 1 1 1 0 0 0 1 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 1 0 1 1 1 0 0 1 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 1 1 0 0 0 1 0 1 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 0 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 0 0 1 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 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 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 1 0 1 1 0 1 0 1 0 0 1 
, 
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 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 0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 1 0 0 0 0 
0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
0 1 0 1 1 1 0 1 0 1 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
1 1 0 1 1 0 1 0 1 0 0 1 
1 1 0 1 0 1 1 1 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 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 1 0 1 1 1 0 1 0 1 0 1 
1 0 1 0 1 1 1 1 0 0 0 1 
0 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 1 1 0 0 0 1 0 1 1 0 
0 0 1 0 0 0 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 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 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 0 0 1 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 0 1 0 1 1 1 1 0 0 0 1 
, 
1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 1 0 0 0 0 0 
1 1 0 1 0 1 1 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 
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 1 1 1 0 0 0 1 0 1 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 1 
, 
1 1 0 0 1 0 0 1 0 0 1 1 
0 1 0 1 1 1 0 1 0 1 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 
1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 1 1 1 0 0 0 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 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 0 0 0 0 0 0 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 14)(5, 9)(6, 8)(7, 13)(11, 21)(12, 17)(18, 20)(19, 22), 
(4, 13, 5)(7, 14, 9)(10, 18, 20)(11, 21, 15)(12, 16, 17)(19, 23, 22), 
(3, 19)(4, 15)(5, 17)(6, 8)(7, 16)(9, 11)(10, 18)(12, 21), 
(3, 21, 15, 11)(4, 22, 12, 5)(6, 8)(7, 23, 13, 16)(9, 17, 19, 14)(18, 20), 
(2, 20, 10, 18)(3, 11, 15, 21)(4, 22, 9, 17)(5, 19, 14, 12)(6, 8)(7, 13), 
(2, 19)(4, 18)(6, 8)(9, 10)(11, 15)(12, 20)(13, 16)(14, 17), 
(1, 14)(2, 13)(3, 18)(4, 7)(5, 17)(9, 11)(10, 19)(15, 16), 
(1, 11, 16, 21, 20, 18, 23)(2, 17, 13, 3, 4, 14, 22)(5, 9, 12, 10, 19, 7, 15)
orbits: { 1, 14, 23, 4, 7, 19, 17, 18, 5, 15, 3, 13, 9, 16, 22, 2, 10, 12, 20, 21, 11 }, { 6, 8 }

code no      15:
================
1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0
0 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0
0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0
0 0 1 1 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0
0 1 0 0 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0
1 1 1 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 887040
and is strongly generated by the following 14 elements:
(
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 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 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 0 0 0 0 1 0 0 
1 0 0 1 1 0 1 1 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 1 0 0 0 
0 1 0 1 1 1 1 0 0 1 0 1 
, 
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 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 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 0 0 0 0 0 0 1 1 1 1 1 
0 0 0 0 0 0 0 0 0 0 0 1 
1 1 1 1 0 1 1 1 0 1 1 1 
0 1 0 0 0 1 1 1 1 0 1 1 
0 0 1 1 0 0 1 1 1 1 0 1 
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 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 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 0 1 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
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 1 1 1 1 0 1 1 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 1 0 1 1 1 0 1 1 1 
, 
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 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 0 1 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
0 1 0 1 1 1 1 0 0 1 0 1 
0 1 0 0 0 1 1 1 1 0 1 1 
1 1 0 0 1 0 1 0 0 0 1 1 
0 0 0 0 0 0 0 0 0 0 0 1 
1 0 0 1 0 1 1 0 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 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 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
0 1 1 1 1 0 1 1 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 0 0 0 1 1 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 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 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 0 1 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
0 1 0 0 0 1 1 1 1 0 1 1 
0 0 1 1 0 0 1 1 1 1 0 1 
1 0 0 1 0 1 1 0 1 0 0 1 
, 
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 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 0 1 0 0 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 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 1 0 1 1 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 
1 0 0 1 0 1 1 0 1 0 0 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 0 0 0 1 1 1 0 0 0 
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 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 1 1 1 1 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 1 0 1 0 0 1 
, 
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 0 1 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 1 1 1 0 1 1 1 
1 0 0 1 0 1 1 0 1 0 0 1 
1 0 0 0 0 0 0 1 1 1 1 1 
0 1 1 1 1 0 1 1 0 0 1 0 
1 0 0 1 1 0 1 1 0 1 0 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 
1 1 1 0 0 0 1 1 1 0 0 0 
1 1 0 0 1 0 1 0 0 0 1 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 0 0 1 
0 1 0 1 1 1 1 0 0 1 0 1 
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 1 0 0 0 0 0 
0 0 1 1 0 0 1 1 1 1 0 1 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 
1 1 0 0 1 0 1 0 0 0 1 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 
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 0 1 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 0 0 0 1 0 0 0 0 
1 0 0 1 0 1 1 0 1 0 0 1 
0 1 0 0 0 1 1 1 1 0 1 1 
0 0 1 1 0 0 1 1 1 1 0 1 
1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 1 1 1 1 0 1 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 
1 0 0 1 1 0 1 1 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 1 0 0 
1 1 1 1 1 1 0 0 0 0 0 0 
0 0 1 1 0 0 1 1 1 1 0 1 
0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 
1 1 0 0 1 0 1 0 0 0 1 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 1 1 1 0 1 1 1 
0 0 1 0 0 0 0 0 0 0 0 0 
0 1 1 1 1 0 1 1 0 0 1 0 
1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 0 0 0 0 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 1 1 1 1 0 1 1 
0 0 0 0 1 0 0 0 0 0 0 0 
0 1 0 1 1 1 1 0 0 1 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 1 1 1 1 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 
0 1 0 0 0 0 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 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 
0 0 1 1 0 0 1 1 1 1 0 1 
0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 0 1 1 1 0 1 1 1 
1 0 0 1 0 1 1 0 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(7, 10)(8, 15)(9, 11)(12, 18)(14, 16)(17, 20)(19, 22)(21, 23), 
(7, 23)(8, 12)(9, 22)(10, 21)(11, 19)(14, 17)(15, 18)(16, 20), 
(7, 14)(8, 9)(10, 16)(11, 15)(12, 22)(17, 23)(18, 19)(20, 21), 
(7, 18)(8, 21)(9, 20)(10, 12)(11, 17)(14, 19)(15, 23)(16, 22), 
(6, 13)(7, 11)(8, 16)(9, 15)(10, 14)(17, 22)(18, 21), 
(5, 13)(8, 14)(10, 21)(11, 19)(12, 17)(15, 20)(16, 18), 
(4, 7)(5, 8)(6, 9)(10, 15)(12, 17)(13, 14)(20, 21), 
(4, 8, 6, 14)(5, 7, 13, 9)(10, 11, 15, 16)(12, 17)(18, 20, 19, 21), 
(4, 18, 22)(5, 21, 17)(6, 20, 12, 13, 19, 23)(7, 16)(8, 10, 14, 11, 9, 15), 
(3, 17)(4, 18)(6, 10)(8, 19)(9, 13)(11, 20)(14, 15), 
(3, 5, 6, 4)(7, 20, 17, 8)(9, 12, 16, 21)(10, 15, 22, 19)(11, 14), 
(2, 21)(3, 16, 17, 20, 12, 11)(4, 18, 13, 8, 19, 9)(5, 14, 15)(6, 10, 7), 
(2, 17, 22)(4, 8, 16)(5, 10, 14)(6, 19, 13)(7, 21, 9)(11, 15, 18), 
(2, 5, 10, 6, 4, 8, 17, 12, 20, 23)(3, 7)(9, 16, 18, 22, 11, 14, 21, 13, 15, 19)
orbits: { 1 }, { 2, 21, 22, 23, 10, 20, 8, 18, 19, 5, 16, 7, 14, 9, 12, 17, 15, 6, 11, 4, 13, 3 }