the 7 isometry classes of irreducible [25,12,8]_2 codes are:

code no       1:
================
1 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 1 1 1 1 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 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 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 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 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 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 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 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 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 1 0 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 887040
and is strongly generated by the following 12 elements:
(
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 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 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 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 
1 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 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 
0 0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 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 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 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 
1 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 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 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 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 0 1 0 0 0 0 0 0 
1 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 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 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 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 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 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 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 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
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 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 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 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 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 0 
0 0 1 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 1 0 0 0 0 0 0 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 0 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 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 1 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 
, 
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 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 0 0 0 1 0 1 0 1 1 0 
1 0 0 1 1 0 1 1 1 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 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
1 1 0 1 1 0 0 0 0 1 1 1 0 
1 0 1 0 1 0 1 1 0 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 1 0 0 0 0 0 0 0 0 0 0 0 
1 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 0 0 0 0 0 1 0 0 0 0 0 
1 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 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 1 1 1 1 1 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 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 
1 0 0 1 0 1 1 0 1 1 1 0 0 
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 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 1 1 0 1 0 1 0 0 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 0 1 
, 
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 0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 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 0 1 0 
1 0 0 1 1 0 1 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 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 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 1 0 1 1 0 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 1 0 0 0 0 0 0 
1 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 1 1 1 0 0 0 1 1 1 0 0 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 1 1 0 0 0 1 0 1 0 1 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 0 1 1 0 1 0 1 0 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(13, 14), 
(6, 15, 7)(8, 12, 19)(9, 21, 11)(10, 22, 18)(13, 14)(16, 20, 17)(23, 25, 24), 
(5, 21)(6, 22)(7, 12)(8, 18)(9, 11)(10, 17)(13, 14)(15, 20)(16, 19), 
(5, 22)(6, 21)(7, 20)(8, 17)(9, 19)(10, 18)(11, 16)(12, 15)(13, 14), 
(5, 10)(6, 8)(7, 9)(11, 12)(15, 16)(17, 21)(18, 22)(19, 20), 
(5, 20)(6, 12)(7, 22)(8, 11)(9, 18)(10, 19)(13, 14)(15, 21)(16, 17), 
(4, 23, 24)(5, 22, 6)(7, 16, 18)(8, 15, 11)(9, 10, 12)(13, 14)(17, 20, 19), 
(4, 10, 21, 19, 15)(5, 9, 24, 6, 16)(7, 8, 17, 23, 20)(11, 18, 12, 22, 25), 
(3, 4, 23)(5, 16, 8)(6, 19, 17)(9, 18, 22)(10, 21, 11)(12, 20, 15), 
(3, 9, 23, 11)(4, 16, 24, 19)(5, 12, 6, 15)(7, 21, 20, 22)(8, 18)(10, 17), 
(2, 3, 4)(5, 15, 6)(8, 18, 12)(9, 19, 20)(10, 11, 21)(13, 14)(16, 17, 22), 
(2, 25)(3, 19, 20, 23, 11, 12)(4, 16, 7)(5, 17, 22, 8, 21, 18)(6, 10)(9, 15, 24)
orbits: { 1 }, { 2, 4, 25, 24, 15, 3, 19, 7, 23, 22, 9, 16, 6, 20, 12, 21, 8, 5, 11, 10, 18, 17 }, { 13, 14 }

code no       2:
================
1 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 1 1 1 1 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 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 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 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 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 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 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 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 1 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 0 0 1 1 1 1 0 0 0 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 8 elements:
(
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 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 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 1 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
1 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 
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 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 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 
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 
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 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 
1 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 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 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 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 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 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
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 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 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 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 0 1 0 1 0 1 1 0 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 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 1 0 0 0 1 0 1 0 1 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 0 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 0 0 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 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 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 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
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 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 1 1 0 1 0 1 0 0 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 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 0 1 0 1 1 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 1 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 0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 0 1 1 0 1 0 1 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 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):
(8, 9)(10, 16)(11, 17)(12, 20)(13, 25)(18, 19)(21, 22)(23, 24), 
(5, 20)(6, 12)(7, 22)(8, 11)(9, 18)(10, 19)(15, 21)(16, 17), 
(5, 6)(7, 15)(8, 10)(9, 16)(11, 19)(12, 20)(17, 18)(21, 22), 
(5, 10)(6, 8)(7, 9)(11, 12)(15, 16)(17, 21)(18, 22)(19, 20), 
(5, 16)(6, 9)(7, 8)(10, 15)(11, 22)(12, 18)(17, 20)(19, 21), 
(4, 23, 24)(5, 22, 6)(7, 16, 18)(8, 15, 11)(9, 10, 12)(17, 20, 19), 
(3, 9, 23, 11)(4, 16, 24, 19)(5, 12, 6, 15)(7, 21, 20, 22)(8, 18)(10, 17), 
(2, 21, 17, 16, 15)(3, 7, 5, 20, 22)(4, 11, 9, 18, 8)(6, 19, 23, 10, 12)
orbits: { 1 }, { 2, 15, 21, 7, 16, 10, 8, 6, 22, 17, 19, 9, 18, 3, 5, 4, 23, 11, 12, 20, 24 }, { 13, 25 }, { 14 }

code no       3:
================
1 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 1 1 1 1 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 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
1 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 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 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 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 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
1 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 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 1 1 1 0 1 0 1 0 0 1 0 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 
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 0 
0 0 0 0 1 0 0 0 0 0 0 0 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 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 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 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 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 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 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
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 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 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 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 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
0 0 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 0 0 0 1 1 1 0 1 0 1 0 
1 1 0 0 1 1 0 1 1 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 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 0 0 0 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 0 1 1 0 1 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 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 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 
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 1 1 0 1 0 1 0 0 1 1 0 
1 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 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 
1 1 0 0 1 1 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 0 0 0 0 1 0 0 
1 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 
0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
1 0 1 1 0 1 0 1 0 0 1 1 0 
1 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 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 0 0 1 1 0 1 1 1 0 0 1 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 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 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 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 0 1 0 1 1 0 0 1 1 0 1 0 
1 0 1 1 0 1 0 1 0 0 1 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 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 
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 0 0 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 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7, 15)(8, 18, 21)(9, 17, 12)(10, 19, 20)(11, 22, 16)(13, 24, 25), 
(5, 10)(6, 8)(7, 9)(11, 12)(15, 16)(17, 21)(18, 22)(19, 20), 
(5, 22)(6, 21)(7, 20)(8, 17)(9, 19)(10, 18)(11, 16)(12, 15), 
(5, 9)(6, 16)(7, 10)(8, 15)(11, 21)(12, 17)(18, 20)(19, 22), 
(5, 11)(6, 19)(7, 17)(8, 20)(9, 21)(10, 12)(15, 18)(16, 22), 
(4, 23)(5, 21)(7, 9)(10, 17)(11, 12)(13, 24)(15, 19)(16, 20), 
(3, 23, 4)(5, 12, 17)(6, 15, 10)(7, 18, 22)(8, 21, 20)(11, 16, 19), 
(2, 12, 11, 6, 8)(3, 17, 7, 18, 15)(4, 9, 10, 20, 22)(5, 21, 16, 19, 23)
orbits: { 1 }, { 2, 8, 21, 6, 17, 15, 20, 18, 11, 9, 5, 16, 19, 10, 12, 7, 3, 22, 4, 23 }, { 13, 25, 24 }, { 14 }

code no       4:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 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 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 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 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 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 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 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 1 1 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 20401920
and is strongly generated by the following 11 elements:
(
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 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 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 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 1 0 0 1 0 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 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 
0 0 0 0 0 0 1 0 0 0 0 0 0 
1 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 0 0 1 0 1 1 0 1 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 1 0 1 1 1 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 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 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 
1 1 0 0 0 1 1 1 0 1 0 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 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 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 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 
, 
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 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 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 1 1 0 1 0 1 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 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 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 
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 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
1 1 0 0 0 1 1 1 0 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 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 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 1 1 1 1 1 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 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 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
1 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 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 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 1 1 1 0 0 0 1 0 1 1 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
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 
1 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 
1 0 1 0 1 0 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 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 
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 0 0 1 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 0 1 1 1 0 0 0 1 0 1 1 0 
1 1 0 0 1 1 0 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 0 1 0 0 0 
1 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 1 0 1 1 1 0 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 
0 1 0 0 0 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 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 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 
1 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 1 0 1 1 1 0 0 1 1 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 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 1 0 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 0 0 0 0 0 0 
0 0 0 1 1 1 1 1 0 0 1 1 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 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
0 1 1 1 0 0 1 0 0 1 1 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
0 1 1 1 0 0 1 0 0 1 1 1 0 
1 1 0 0 1 1 0 1 1 0 1 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 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
1 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 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 1 1 1 1 1 0 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 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(13, 25), 
(6, 14, 7)(8, 21, 11)(9, 19, 18)(10, 12, 16)(15, 20, 17)(22, 24, 23), 
(5, 20)(6, 21)(7, 12)(8, 18)(9, 16)(10, 11)(14, 19)(15, 17), 
(5, 16)(6, 17)(7, 11)(8, 19)(9, 20)(10, 12)(14, 18)(15, 21), 
(5, 21)(6, 20)(7, 19)(8, 11)(9, 17)(10, 18)(12, 14)(15, 16), 
(5, 12)(6, 19)(7, 20)(8, 17)(9, 11)(10, 16)(14, 21)(15, 18), 
(4, 22, 23)(5, 21, 6)(7, 9, 11)(8, 12, 15)(10, 14, 17)(16, 18, 19), 
(4, 8, 15, 10, 9)(5, 20, 22, 19, 14)(6, 18, 16, 7, 23)(11, 24, 17, 21, 12), 
(3, 9, 21, 10, 19)(4, 15, 6, 11, 12)(5, 18, 14, 22, 16)(7, 23, 17, 20, 8), 
(2, 15, 22, 5, 7)(3, 18, 10, 17, 9)(4, 24, 12, 11, 14)(6, 20, 21, 16, 19), 
(1, 19, 4, 6, 16, 2, 24)(3, 9, 12, 21, 20, 18, 5)(7, 8, 22, 11, 17, 14, 15)
orbits: { 1, 24, 22, 11, 4, 2, 23, 20, 14, 15, 8, 21, 10, 7, 9, 12, 6, 19, 16, 5, 17, 18, 3 }, { 13, 25 }

code no       5:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 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 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 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 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 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 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 0 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0
0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 887040
and is strongly generated by the following 9 elements:
(
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 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 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 1 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 1 1 0 1 0 1 1 1 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 
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 1 1 1 0 0 1 1 0 1 0 
1 1 0 0 0 1 1 1 0 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 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 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 1 1 1 1 1 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 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 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
0 0 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 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
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 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 
1 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 
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 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
1 0 1 0 1 0 1 1 0 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 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 1 1 1 1 0 0 1 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 1 1 0 1 0 1 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 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 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 
0 0 0 0 0 0 0 0 0 0 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 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
1 0 1 1 1 0 0 0 1 0 1 1 0 
1 1 1 1 0 0 0 1 1 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 
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 1 0 0 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 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 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 0 0 0 1 0 0 0 0 
1 1 0 0 1 1 0 1 1 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 0 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 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
1 0 1 1 1 0 0 0 1 0 1 1 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
1 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 
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 0 0 0 0 0 0 1 
, 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 1 0 1 1 1 0 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 0 
0 0 0 0 0 0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 0 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 0 0 0 0 
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 
1 0 1 0 1 0 1 1 0 1 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(8, 9)(10, 15)(11, 16)(12, 19)(13, 24)(17, 18)(20, 21)(22, 23), 
(5, 21)(6, 20)(7, 19)(8, 11)(9, 17)(10, 18)(12, 14)(15, 16), 
(5, 9)(6, 15)(7, 10)(8, 14)(11, 12)(16, 20)(17, 21)(18, 19), 
(5, 8)(6, 10)(7, 15)(9, 14)(11, 21)(12, 17)(16, 19)(18, 20), 
(4, 23, 22)(5, 12, 16)(6, 7, 15)(8, 11, 18)(9, 21, 19)(14, 17, 20), 
(3, 8, 20, 15, 12)(4, 10, 6, 16, 19)(5, 17, 14, 23, 11)(7, 22, 18, 21, 9), 
(3, 4)(5, 12, 6, 19)(7, 21, 14, 20)(8, 9, 10, 15)(11, 17, 18, 16)(22, 23), 
(2, 22, 23, 4, 3)(5, 11, 17, 9, 18)(6, 14, 8, 10, 19)(7, 12, 16, 21, 15), 
(1, 16, 20)(2, 17, 12, 4, 11, 21)(3, 18, 19)(5, 9)(6, 15, 14, 10, 7, 8)(22, 23)
orbits: { 1, 20, 21, 6, 16, 18, 17, 8, 14, 5, 11, 9, 7, 15, 10, 12, 19, 22, 3, 2, 23, 4 }, { 13, 24 }, { 25 }

code no       6:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 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 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 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 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 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 0 0 1 1 1 1 1 0 0 1 1 0 0 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 0 0 1 0 0
1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0
0 0 1 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 120960
and is strongly generated by the following 7 elements:
(
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 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 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 1 1 0 1 0 1 1 1 0 0 1 0 
0 1 0 1 1 1 0 0 1 1 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 0 
1 0 0 1 0 1 1 0 1 1 1 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 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 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 
1 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 
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 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
1 0 1 0 1 0 1 1 0 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 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 0 
1 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 0 0 0 0 1 0 0 0 
0 1 0 1 1 1 0 0 1 1 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 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 
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 
0 0 1 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 1 1 1 1 0 0 1 1 0 
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 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 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 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 
0 0 0 1 1 1 1 1 0 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 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 1 1 1 0 0 0 1 1 1 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
1 0 1 0 1 0 1 1 0 1 1 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 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 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 
1 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 0 0 0 1 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 1 1 1 1 1 0 0 1 1 0 
1 0 0 1 0 1 1 0 1 1 1 0 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 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 0 1 
, 
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 
0 0 0 0 0 0 0 0 0 1 0 0 0 
1 0 0 1 0 1 1 0 1 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 0 0 0 0 0 
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 
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 1 1 1 1 1 0 0 1 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(6, 7, 14)(8, 16, 19)(9, 17, 21)(10, 11, 20)(12, 15, 18)(13, 23, 24), 
(5, 8)(6, 10)(7, 15)(9, 14)(11, 21)(12, 17)(16, 19)(18, 20), 
(5, 12, 15)(6, 21, 8)(7, 19, 10)(9, 14, 20)(11, 16, 17)(13, 24, 23), 
(4, 22)(5, 9, 8, 14)(6, 17, 10, 12)(7, 21, 15, 11)(13, 23)(16, 18, 19, 20), 
(3, 4, 22)(5, 17, 11)(6, 15, 8)(7, 19, 12)(9, 18, 20)(10, 21, 16), 
(2, 17, 22, 8)(3, 20, 4, 7)(5, 6, 18, 9)(10, 16)(11, 15, 19, 12)(14, 21), 
(1, 16, 12, 15, 20, 21, 7)(2, 17, 14, 9, 5, 6, 19)(3, 18, 4, 22, 11, 8, 10)
orbits: { 1, 7, 6, 15, 10, 11, 12, 4, 21, 14, 8, 5, 20, 19, 17, 16, 22, 18, 3, 9, 2 }, { 13, 24, 23 }, { 25 }

code no       7:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
1 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 0 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 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 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 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 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 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 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 1 0
0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 138240
and is strongly generated by the following 9 elements:
(
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 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 0 0 0 0 0 1 0 0 0 0 0 0 
0 0 1 1 1 0 1 0 1 1 0 0 1 
0 1 1 0 1 1 0 1 0 1 0 0 1 
1 0 1 0 0 1 1 1 1 0 0 0 1 
0 1 0 1 1 1 0 0 1 1 0 1 0 
1 0 0 1 0 1 1 0 1 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 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 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 0 0 0 0 0 0 0 0 0 0 1 
1 0 1 0 0 1 1 1 1 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 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 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 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 
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 0 1 1 0 1 1 0 0 
1 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 0 0 0 0 1 0 0 0 
0 1 1 0 1 1 0 1 0 1 0 0 1 
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 
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 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 1 1 0 1 1 0 1 0 1 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 0 0 1 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 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 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 0 
0 0 0 0 1 0 0 0 0 0 0 0 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 0 
0 1 0 1 1 1 0 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 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 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 
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 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
0 0 1 1 1 0 1 0 1 1 0 0 1 
1 0 1 0 0 1 1 1 1 0 0 0 1 
1 0 1 0 1 0 1 1 0 1 1 0 0 
1 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 
1 1 0 0 0 1 1 1 0 1 0 1 0 
1 1 1 1 1 1 1 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 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 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 0 1 0 0 0 0 0 0 0 
1 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 0 0 1 1 0 1 1 0 1 0 0 
1 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 
0 1 1 0 1 0 1 1 1 0 0 1 0 
1 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 
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 
1 1 0 0 0 1 1 1 0 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 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 0 0 
0 0 0 0 0 0 1 0 0 0 0 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
0 1 1 0 1 1 0 1 0 1 0 0 1 
1 0 0 1 0 1 1 0 1 1 1 0 0 
0 0 0 0 0 0 0 0 0 1 0 0 0 
, 
0 1 0 1 1 1 0 0 1 1 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 1 0 
1 1 0 0 0 1 1 1 0 1 0 1 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 
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 1 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 0 0 0 0 0 0 
1 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 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(8, 24)(9, 23)(10, 22)(11, 21)(12, 18)(13, 15)(16, 20)(17, 19), 
(8, 13)(9, 22)(10, 23)(11, 12)(15, 24)(16, 19)(17, 20)(18, 21), 
(8, 17)(9, 18)(10, 11)(12, 23)(13, 20)(15, 16)(19, 24)(21, 22), 
(8, 23)(9, 24)(10, 13)(11, 20)(12, 17)(15, 22)(16, 21)(18, 19), 
(6, 7, 14)(8, 11, 21)(9, 18, 19)(10, 16, 12)(13, 22, 23)(15, 17, 20), 
(5, 20, 11, 10, 13)(6, 19, 17, 8, 24)(7, 21, 18, 9, 22)(12, 16, 15, 23, 14), 
(3, 4)(7, 14)(8, 11)(9, 16)(10, 18)(12, 19)(13, 22)(15, 17), 
(2, 4, 3)(5, 8, 23, 11, 19, 7, 9, 24, 18, 12, 6, 15, 22, 17, 20)(10, 13, 16, 21, 14), 
(1, 9, 21)(2, 8, 12)(3, 15, 20)(4, 10, 19)(5, 14, 6)(11, 17, 16)
orbits: { 1, 21, 11, 18, 22, 16, 7, 9, 12, 10, 20, 8, 23, 19, 24, 15, 13, 17, 6, 14, 4, 5, 2, 3 }, { 25 }