the 12 isometry classes of irreducible [21,8,8]_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
1 1 1 1 1 1 1 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 0 0 1 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
1 0 1 0 1 0 1 1 0 1 1 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 1 0 0
1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 1
the automorphism group has order 144
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 0 0 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 
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 1 0 0 0 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 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 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 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 
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 
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 
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 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 1 0 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 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 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 
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 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 1 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 0 0 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 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 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 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 
1 0 1 0 1 0 1 1 0 1 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 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 0 0 0 1 1 1 0 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 
)
acting on the columns of the generator matrix as follows (in order):
(13, 14), 
(5, 10, 18)(6, 16, 19)(7, 8, 11)(9, 17, 15)(12, 20, 21), 
(3, 4)(7, 15)(8, 17)(9, 11)(10, 18)(12, 20)(16, 19), 
(2, 6)(3, 11)(4, 9)(7, 8)(13, 14)(15, 17)(16, 19), 
(2, 19)(3, 8)(4, 15)(6, 16)(7, 11)(9, 17), 
(2, 3, 4)(5, 10, 18)(6, 8, 17)(7, 9, 19)(11, 15, 16)(13, 14)
orbits: { 1 }, { 2, 6, 19, 4, 16, 17, 9, 3, 15, 8, 11, 7 }, { 5, 18, 10 }, { 12, 21, 20 }, { 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
1 1 1 1 1 1 1 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 0 0 1 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
1 0 1 0 1 0 1 1 0 1 1 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 1 0 0
1 0 0 1 1 0 1 1 1 0 0 1 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 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 
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 
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 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 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 0 0 0 0 0 1 
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 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 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 
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 
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 
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 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 0 0 
0 0 0 1 0 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 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 
1 0 1 0 1 0 1 1 0 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 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 1 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 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 0 1 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 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):
(8, 9)(10, 16)(11, 17)(12, 20)(13, 21)(18, 19), 
(8, 19)(9, 18)(10, 17)(11, 16)(12, 13)(20, 21), 
(5, 6)(7, 15)(8, 10)(9, 16)(11, 19)(12, 20)(17, 18), 
(3, 4)(7, 15)(8, 17)(9, 11)(10, 18)(12, 20)(16, 19), 
(3, 5, 4, 6)(7, 15)(8, 16, 18, 11)(9, 10, 19, 17)(12, 20), 
(2, 15, 7)(3, 18, 11)(4, 9, 10)(5, 19, 16)(6, 8, 17)
orbits: { 1 }, { 2, 7, 15 }, { 3, 4, 6, 11, 5, 10, 17, 16, 19, 9, 18, 8 }, { 12, 20, 13, 21 }, { 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
1 1 1 1 1 1 1 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 0 0 1 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
1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 0 0 1 0 0 0
1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0
1 0 1 1 0 1 0 1 0 0 1 1 0 0 0 0 0 0 0 0 1
the automorphism group has order 768
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 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 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 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 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 1 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 1 0 0 0 0 0 0 0 0 
1 1 0 0 1 1 0 1 1 0 1 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 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 0 1 1 0 1 1 1 0 0 1 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 1 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 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 
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 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 0 0 0 0 0 0 0 0 0 0 
1 0 1 1 0 1 0 1 0 0 1 1 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 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 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 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 
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 1 0 0 1 1 0 1 1 0 1 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 
1 0 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 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 
1 0 1 1 0 1 0 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 1 0 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 1 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 0 1 1 0 1 1 1 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 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 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 0 0 1 1 1 0 1 0 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 0 0 0 1 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 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 
1 1 1 1 1 1 1 1 1 1 1 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(13, 14), 
(5, 9)(6, 16)(7, 10)(8, 15)(11, 20)(12, 17)(18, 19), 
(3, 4)(5, 10)(6, 16)(7, 9)(8, 15)(11, 17)(12, 20), 
(3, 19)(4, 18)(5, 20)(7, 17)(9, 12)(10, 11)(13, 14), 
(3, 5, 12)(4, 20, 10)(6, 16, 21)(7, 9, 18)(11, 19, 17), 
(2, 6)(3, 9)(4, 11)(7, 17)(8, 15)(10, 18)(12, 19), 
(2, 16, 6, 21)(3, 11, 4, 9)(5, 20)(8, 15)(10, 18, 12, 19), 
(2, 10, 3)(4, 16, 9)(5, 17, 20)(6, 11, 19)(12, 18, 21)(13, 14)
orbits: { 1 }, { 2, 6, 21, 3, 16, 19, 18, 4, 12, 9, 10, 11, 17, 20, 5, 7 }, { 8, 15 }, { 13, 14 }

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

code no       5:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 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
1 1 1 1 0 0 0 1 1 1 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 1 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
1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0
1 1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 0 0 0 1
the automorphism group has order 24
and is strongly generated by the following 3 elements:
(
1 0 0 0 0 0 0 0 0 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 
1 0 0 1 1 0 1 1 1 0 0 1 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 1 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 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 0 0 0 0 0 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 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 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 1 1 0 1 1 0 1 0 0 
1 1 1 1 1 1 1 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 
1 0 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 0 1 1 0 1 1 1 0 0 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, 9)(6, 16)(7, 10)(8, 15)(11, 20)(12, 17)(18, 19), 
(3, 19)(4, 18)(5, 20)(7, 17)(9, 12)(10, 11), 
(2, 6)(3, 9)(4, 11)(7, 17)(8, 15)(10, 18)(12, 19)
orbits: { 1 }, { 2, 6, 16 }, { 3, 19, 9, 18, 12, 5, 4, 10, 17, 20, 11, 7 }, { 8, 15 }, { 13 }, { 14 }, { 21 }

code no       6:
================
1 1 1 1 1 1 1 1 1 1 1 1 1 1 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
1 1 1 1 0 0 0 1 1 1 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 1 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
1 0 0 1 1 0 1 1 1 0 0 1 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 1 0
0 1 1 1 1 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 1
the automorphism group has order 128
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 0 0 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 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 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 
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 0 0 1 1 0 1 1 1 0 0 1 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 
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 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 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 
1 0 0 1 1 1 0 1 0 1 0 0 1 
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 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 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 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 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 0 0 0 0 0 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 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 
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 
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 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 
, 
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 0 
1 0 0 1 1 0 1 1 1 0 0 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 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 
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 
0 1 1 1 1 0 0 1 0 0 0 1 1 
0 1 0 0 0 0 0 0 0 0 0 0 0 
1 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 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 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 
1 0 0 1 1 1 0 1 0 1 0 0 1 
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 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 1 0 0 0 1 1 1 0 0 0 
, 
0 1 1 1 1 0 0 1 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 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 0 0 1 
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 0 0 0 0 0 1 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
1 1 1 1 0 0 0 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 
1 0 1 0 1 0 1 1 0 1 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 15)(6, 7)(8, 16)(9, 10)(12, 19)(13, 20), 
(5, 16)(6, 10)(7, 9)(8, 15)(12, 20)(13, 19), 
(2, 17)(3, 18)(5, 16)(6, 7)(8, 15)(9, 10), 
(2, 18)(3, 17)(5, 16)(8, 15)(12, 13)(19, 20), 
(2, 12)(3, 19)(5, 7)(6, 8)(9, 15)(10, 16)(11, 21)(13, 17)(18, 20), 
(1, 14)(2, 7, 18, 6)(3, 10, 17, 9)(5, 20, 8, 12)(13, 15, 19, 16), 
(1, 11, 14, 21)(2, 12, 8, 9, 3, 19, 15, 6)(5, 7, 17, 20, 16, 10, 18, 13)
orbits: { 1, 14, 21, 11 }, { 2, 17, 18, 12, 6, 3, 13, 10, 7, 20, 19, 8, 15, 9, 16, 5 }, { 4 }

code no       7:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 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
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 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
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0
0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0
1 1 0 0 0 1 1 1 0 1 0 1 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 1
the automorphism group has order 1152
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 
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 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 
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 
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 0 0 0 0 0 0 0 1 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 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 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 
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 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 0 0 
0 0 0 0 0 1 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 0 0 0 0 0 
1 1 0 0 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 1 0 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 
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 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 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 0 1 0 1 1 0 1 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 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 
1 1 0 0 0 1 1 1 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 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 1 0 0 0 
1 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 1 0 0 0 0 0 0 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 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 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 
, 
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 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 0 0 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 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 0 0 0 0 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):
(13, 21), 
(5, 6)(7, 14)(8, 15)(9, 10)(11, 17)(16, 18), 
(3, 4)(7, 14)(8, 11)(9, 16)(10, 18)(12, 19)(15, 17), 
(2, 6, 5)(3, 15, 11, 4, 17, 8)(7, 10, 9, 14, 18, 16)(12, 19), 
(2, 3)(5, 17)(6, 11)(7, 18)(8, 15)(12, 20)(14, 16), 
(1, 2, 5, 6)(3, 18, 7, 15)(4, 10, 14, 17)(8, 9, 11, 16), 
(1, 14)(2, 7)(3, 6)(4, 5)(8, 18)(9, 17)(10, 16)(11, 15)
orbits: { 1, 6, 14, 5, 2, 11, 3, 7, 9, 16, 10, 17, 4, 8, 15, 18 }, { 12, 19, 20 }, { 13, 21 }

code no       8:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 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
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 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
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0
0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0
1 1 0 0 0 1 1 1 0 1 0 1 0 0 0 0 0 0 0 1 0
0 1 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1
the automorphism group has order 2304
and is strongly generated by the following 6 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 1 0 1 1 1 0 0 1 1 0 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 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 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 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 0 0 1 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 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 
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 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 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 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 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 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 1 0 0 0 0 0 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 
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 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 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 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 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 0 0 0 0 0 0 1 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 0 1 
, 
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 
0 0 0 0 0 0 0 0 1 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 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 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 1 
)
acting on the columns of the generator matrix as follows (in order):
(13, 21), 
(5, 10, 18)(6, 15, 17)(7, 8, 16)(9, 11, 14)(12, 19, 20), 
(5, 17, 9)(6, 18, 8)(7, 11, 15)(10, 14, 16)(12, 20, 19), 
(3, 4)(5, 14, 6, 7)(8, 16, 15, 18)(9, 11, 10, 17)(12, 19), 
(2, 4, 3)(6, 14, 7)(9, 15, 10)(12, 19, 20)(16, 18, 17), 
(1, 10)(2, 15)(3, 8)(4, 9)(5, 17)(6, 18)(7, 11)(14, 16)
orbits: { 1, 10, 5, 16, 11, 15, 18, 9, 7, 17, 8, 14, 6, 2, 4, 3 }, { 12, 20, 19 }, { 13, 21 }

code no       9:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 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
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 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
1 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 0 1 0 0 0
0 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 0 0
1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 0 0 0 0 1 0
1 1 0 0 0 1 1 1 0 1 0 1 1 0 0 0 0 0 0 0 1
the automorphism group has order 1536
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 
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 
1 0 0 1 1 0 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 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 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 1 0 1 0 1 1 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 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 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 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 1 0 0 0 0 0 
1 1 1 1 0 0 0 1 1 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 0 0 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 1 
, 
1 0 0 0 0 0 0 0 0 0 0 0 0 
0 1 0 0 0 0 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 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 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 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 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 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 
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 
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 
1 0 0 1 1 0 1 1 1 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 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 0 1 1 0 1 1 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 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 
1 1 1 1 1 1 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 0 0 0 1 
, 
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 1 0 1 0 1 1 0 1 1 0 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 
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 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 1 0 0 0 0 0 0 0 
1 0 0 0 0 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 1 0 1 1 1 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, 20)(17, 18), 
(8, 10)(9, 15)(11, 17)(12, 13)(16, 18)(19, 20), 
(5, 7)(6, 14)(8, 9)(10, 15)(11, 18)(16, 17), 
(5, 14)(6, 7)(8, 10)(9, 15)(11, 16)(17, 18), 
(3, 4)(5, 6)(8, 18)(9, 17)(10, 11)(13, 20)(15, 16), 
(2, 4)(5, 16)(6, 17)(7, 18)(8, 10)(11, 14)(12, 19), 
(1, 11)(2, 16)(3, 17)(4, 18)(5, 15)(6, 10)(7, 9)(8, 14)(12, 19)(13, 20)
orbits: { 1, 11, 16, 17, 18, 10, 14, 15, 5, 2, 9, 6, 3, 8, 7, 4 }, { 12, 19, 13, 20 }, { 21 }

code no      10:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 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
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 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 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 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 1 0
0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 0 1
the automorphism group has order 432
and is strongly generated by the following 6 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 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 
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 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 0 0 0 0 0 0 1 0 0 0 
0 0 0 0 0 0 0 1 0 0 0 0 0 
1 0 1 0 0 1 1 1 1 0 0 0 1 
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 
, 
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 1 0 0 0 0 0 0 0 
1 1 0 0 0 1 1 1 0 1 0 1 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 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 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 1 0 1 0 1 1 0 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 0 0 0 0 0 0 1 0 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 0 
1 0 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 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 
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 0 0 0 0 0 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 
, 
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 
1 0 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 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 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 0 0 0 
0 0 0 0 1 0 0 0 0 0 0 0 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 
1 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 
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 1 0 1 1 0 1 0 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 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 
1 0 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 1 0 1 0 1 1 1 0 0 1 0 
1 1 0 0 1 1 0 1 1 0 1 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 10)(6, 8)(7, 9)(11, 19)(12, 16)(14, 15)(17, 18), 
(5, 6, 7)(8, 10, 9)(11, 19, 20)(12, 21, 16)(13, 17, 18), 
(2, 5, 10)(3, 8, 6)(4, 11, 19)(12, 14, 17)(15, 16, 18), 
(1, 9, 7)(2, 5, 10)(4, 18, 17)(11, 15, 12)(14, 19, 16), 
(1, 3, 9, 8, 7, 6)(2, 5, 10)(4, 18, 15, 12, 14, 19)(11, 17, 16)(13, 20), 
(1, 10)(2, 3, 7, 9, 8, 5)(4, 17, 20, 15, 11, 21)(12, 18)(13, 14, 16)
orbits: { 1, 7, 6, 10, 9, 8, 3, 5, 2 }, { 4, 19, 17, 21, 11, 14, 18, 13, 12, 20, 16, 15 }

code no      11:
================
1 1 1 1 1 1 1 0 0 0 0 0 0 1 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
1 1 0 0 1 1 0 1 1 0 1 0 0 0 0 1 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 1 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 0 0 0
1 1 0 0 0 1 1 1 0 1 0 1 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 1 0
0 0 0 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 1
the automorphism group has order 144
and is strongly generated by the following 4 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 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 
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 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 0 1 1 1 0 1 0 1 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 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 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 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 
1 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 1 1 1 0 0 0 1 1 1 0 0 0 
0 0 0 0 0 0 0 0 0 0 1 0 0 
0 0 1 0 0 0 0 0 0 0 0 0 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 1 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 0 1 
, 
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 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 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 
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 0 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 1 0 0 0 0 0 0 0 0 
1 0 1 0 0 1 1 1 1 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 10)(6, 8)(7, 9)(11, 19)(12, 16)(14, 15)(17, 18), 
(2, 10)(3, 6)(4, 19)(7, 9)(12, 15)(14, 18)(16, 17), 
(2, 17)(3, 6)(4, 15)(5, 11)(7, 9)(10, 16)(12, 19), 
(1, 3, 7, 6, 9, 8)(2, 19, 5, 12, 10, 18)(4, 15, 14)(11, 16, 17)(13, 20)
orbits: { 1, 8, 6, 9, 3, 7 }, { 2, 10, 17, 18, 5, 16, 12, 14, 11, 19, 15, 4 }, { 13, 20 }, { 21 }

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