the 21 isometry classes of irreducible [23,18,3]_2 codes are:

code no       1:
================
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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 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 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0
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 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 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 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 168
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
0 0 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 1 1 0 0 
0 0 0 1 0 
0 1 0 0 1 
, 
1 0 0 0 0 
1 0 1 0 0 
0 1 1 0 0 
0 0 0 1 0 
1 0 1 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
0 0 0 0 1 
, 
1 1 0 0 0 
1 0 1 0 0 
1 1 1 0 0 
0 0 0 1 0 
0 1 1 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 10)(5, 20)(8, 9)(14, 17)(15, 16)(18, 19), 
(3, 9)(5, 19)(8, 10)(14, 16)(15, 17)(18, 20), 
(2, 10, 8)(3, 7, 9)(5, 19, 22)(12, 17, 15)(13, 16, 14)(18, 20, 21), 
(2, 7)(3, 8)(12, 13)(14, 15)(19, 20)(21, 22), 
(1, 10, 3, 8, 2, 9, 7)(5, 20, 19, 22, 18, 21, 23)(11, 17, 14, 15, 12, 16, 13)
orbits: { 1, 7, 3, 2, 9, 10, 8 }, { 4 }, { 5, 20, 19, 22, 23, 18, 21 }, { 6 }, { 11, 13, 14, 12, 16, 17, 15 }

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

code no       3:
================
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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 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 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0
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 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 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 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 384
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 1 1 0 0 
0 0 0 1 0 
0 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
0 0 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 1 0 
0 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
1 0 1 0 0 
1 1 1 0 0 
0 0 0 1 0 
0 0 1 0 1 
, 
1 0 0 0 0 
0 0 1 1 0 
0 1 0 1 0 
1 0 0 1 0 
0 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 18)(6, 23)(19, 20)(21, 22), 
(4, 11)(5, 18)(12, 13)(14, 15)(16, 17)(19, 20)(21, 22), 
(3, 9)(5, 19)(8, 10)(14, 16)(15, 17)(18, 20), 
(3, 10)(5, 20)(8, 9)(14, 17)(15, 16)(18, 19), 
(3, 17)(5, 18)(6, 22)(8, 16)(9, 15)(10, 14)(19, 20)(21, 23), 
(2, 9, 8)(3, 7, 10)(5, 20, 21)(12, 16, 15)(13, 17, 14)(18, 19, 22), 
(2, 15, 7, 14)(3, 13, 8, 12)(4, 11)(5, 6, 18, 23)(16, 17)
orbits: { 1 }, { 2, 8, 14, 10, 9, 16, 13, 15, 17, 7, 3, 12 }, { 4, 11 }, { 5, 18, 19, 20, 21, 23, 22, 6 }

code no       4:
================
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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 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 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0
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 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 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 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 21504
and is strongly generated by the following 11 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 0 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
0 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 1 0 1 0 
0 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
0 0 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 1 0 0 
0 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 0 1 0 
1 0 1 0 0 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 1 1 1 1 
1 0 0 0 1 
1 0 0 1 0 
, 
1 0 0 0 0 
1 1 1 1 0 
0 1 1 0 0 
0 1 0 1 0 
1 0 1 1 1 
, 
0 0 1 1 0 
1 1 1 1 0 
1 1 1 0 0 
0 1 0 1 0 
0 0 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 22)(6, 19)(18, 21)(20, 23), 
(5, 23)(6, 18)(19, 21)(20, 22), 
(5, 19)(6, 22)(18, 20)(21, 23), 
(4, 12)(5, 19)(11, 13)(14, 16)(15, 17)(18, 20), 
(4, 11)(5, 18)(12, 13)(14, 15)(16, 17)(19, 20), 
(3, 10)(5, 20)(8, 9)(14, 17)(15, 16)(18, 19), 
(3, 8)(5, 18)(9, 10)(14, 15)(16, 17)(19, 20), 
(3, 11)(4, 8)(9, 13)(10, 12), 
(3, 23)(4, 18)(5, 11)(6, 8)(9, 21)(10, 22)(12, 20)(13, 19)(14, 17)(15, 16), 
(2, 17)(3, 13, 11, 9)(4, 10, 8, 12)(5, 22)(7, 16)(18, 21), 
(1, 15, 14)(2, 16, 17)(3, 10)(4, 9, 11, 13, 8, 12)(5, 18, 21)(6, 20, 19)
orbits: { 1, 14, 16, 15, 17, 7, 2 }, { 3, 10, 8, 11, 23, 9, 12, 22, 4, 6, 13, 5, 20, 21, 18, 19 }

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

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

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

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

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

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

code no      11:
================
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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 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 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0
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 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 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
1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
0 0 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 384
and is strongly generated by the following 9 elements:
(
1 0 0 0 0 
0 1 0 0 0 
1 1 1 0 0 
1 1 0 1 0 
1 1 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 0 1 1 1 
1 0 0 0 1 
1 0 0 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 0 1 0 
1 1 1 0 0 
1 1 1 1 1 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 1 1 
1 1 0 0 1 
1 1 0 1 0 
, 
1 0 0 0 0 
0 0 1 1 0 
0 0 1 0 0 
0 1 1 0 0 
0 0 0 0 1 
, 
1 0 0 0 0 
1 1 0 0 0 
0 0 1 0 0 
1 0 0 1 0 
0 0 0 0 1 
, 
0 1 1 1 0 
1 0 1 1 0 
1 1 0 1 0 
1 1 1 0 0 
1 1 1 1 1 
, 
0 1 0 0 0 
1 0 0 0 0 
1 1 1 0 0 
1 1 0 1 0 
1 1 0 0 1 
, 
0 0 1 1 0 
0 1 1 1 0 
1 0 0 1 0 
0 0 1 0 0 
1 0 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 10)(4, 13)(5, 19)(6, 21)(8, 9)(11, 12)(17, 18)(22, 23), 
(3, 22)(4, 17)(5, 11)(6, 9)(8, 21)(10, 23)(12, 19)(13, 18), 
(3, 13)(4, 10)(5, 6)(8, 12)(9, 11)(17, 23)(18, 22)(19, 21), 
(3, 6)(4, 19)(5, 13)(8, 23)(9, 22)(10, 21)(11, 18)(12, 17), 
(2, 14)(4, 9)(7, 15)(10, 11)(18, 21)(19, 22), 
(2, 7)(4, 11)(9, 10)(14, 15)(18, 19)(21, 22), 
(1, 16)(2, 15)(3, 13)(4, 10)(5, 6)(19, 21), 
(1, 2)(3, 10)(4, 13)(5, 19)(6, 21)(15, 16), 
(1, 15, 14)(2, 7, 16)(3, 4, 11)(5, 21, 22)(6, 19, 18)(9, 13, 10)
orbits: { 1, 16, 2, 14, 15, 7 }, { 3, 10, 22, 13, 6, 11, 23, 4, 21, 9, 18, 19, 5, 12, 17, 8 }, { 20 }

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

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

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

code no      15:
================
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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 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 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 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 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 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 0 0 0 0 0 0
0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 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 1 0 1 0 0 0 0 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 0 0 0 0 1 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 1 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 768
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 0 1 
0 0 0 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 1 0 0 1 
1 0 0 1 0 
1 1 1 0 0 
, 
1 0 0 0 0 
1 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 0 0 0 1 
, 
1 0 0 0 0 
0 0 1 0 1 
0 1 0 0 1 
0 1 1 1 1 
1 0 0 0 1 
, 
1 0 0 0 0 
1 0 0 0 1 
1 1 0 1 0 
1 0 1 0 1 
1 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 16)(6, 23)(17, 18)(19, 20)(21, 22), 
(4, 5)(11, 16)(12, 17)(13, 18)(14, 19)(15, 20), 
(4, 11)(5, 16)(12, 13)(14, 15)(17, 18)(19, 20), 
(3, 18, 8, 17)(4, 11)(5, 9, 16, 10)(12, 13)(14, 21, 15, 22)(19, 20), 
(2, 7)(5, 16)(9, 10)(12, 13)(19, 20), 
(2, 20, 7, 19)(3, 18, 8, 17)(4, 6, 11, 23)(5, 16)(21, 22), 
(2, 16)(3, 12, 8, 13)(4, 19, 11, 20)(5, 7)(6, 15)(9, 22, 10, 21)(14, 23)
orbits: { 1 }, { 2, 7, 19, 16, 20, 5, 14, 4, 11, 9, 15, 10, 22, 23, 6, 21 }, { 3, 17, 13, 18, 12, 8 }

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

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

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

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

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

code no      21:
================
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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
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 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 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 0 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 0 0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 1 0 0 0 0 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 0 0 0 0 1 0 0 0 0 0
1 1 1 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 0 0 0 0 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 0 0 0 0 1 0 0
1 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 2688
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 1 1 1 0 
1 1 1 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
1 0 0 0 1 
1 0 0 1 0 
, 
1 0 0 0 0 
0 1 0 0 0 
0 1 0 1 1 
0 1 1 0 1 
0 0 0 0 1 
, 
1 0 0 0 0 
0 1 0 0 0 
0 1 1 0 1 
1 0 0 0 1 
1 1 0 1 1 
, 
1 0 0 0 0 
0 0 0 0 1 
0 1 1 0 1 
0 0 0 1 0 
0 1 0 0 0 
, 
0 0 0 0 1 
0 0 0 1 1 
1 1 0 0 0 
1 1 1 1 0 
1 0 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 14)(5, 19)(10, 13)(11, 12)(15, 18)(16, 17), 
(4, 15)(5, 10)(11, 16)(12, 17)(13, 19)(14, 18), 
(3, 21)(4, 18)(8, 22)(9, 20)(10, 19)(11, 17), 
(3, 14, 18)(4, 21, 15)(5, 10, 22)(8, 13, 19)(9, 12, 17)(11, 20, 16), 
(2, 5)(3, 18)(6, 12)(7, 15)(8, 19)(11, 20), 
(1, 5)(2, 17, 13, 20)(3, 14, 4, 7)(6, 10, 16, 8)(9, 22)(11, 19)(12, 23)(18, 21)
orbits: { 1, 5, 19, 10, 22, 2, 13, 8, 11, 6, 9, 20, 17, 16, 12, 23 }, { 3, 21, 18, 7, 4, 15, 14 }