the 16 isometry classes of irreducible [21,15,4]_2 codes are:

code no       1:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
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 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 3072
and is strongly generated by the following 9 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 1 0 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 1 1 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 0 1 1 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 0 0 1 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 1 1 1 0 0 
1 1 1 1 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 0 0 0 1 0 
0 1 1 0 0 1 
, 
0 1 1 1 0 0 
0 0 0 1 0 0 
1 1 0 1 0 0 
0 1 0 0 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 1 0 0 1 0 
1 0 1 0 1 0 
0 1 1 0 1 0 
0 0 1 1 1 0 
0 0 0 1 0 0 
0 1 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(12, 13)(14, 15)(16, 17), 
(5, 15)(11, 14)(12, 17)(13, 16), 
(5, 17)(11, 16)(12, 15)(13, 14), 
(4, 10)(5, 15, 13, 16)(6, 20)(8, 9)(11, 14, 12, 17)(18, 19), 
(4, 8)(5, 15, 11, 14)(6, 18)(9, 10)(12, 17, 13, 16)(19, 20), 
(3, 7)(4, 9, 8, 10)(5, 14, 12, 17)(6, 19, 18, 20)(11, 15, 13, 16), 
(2, 7)(4, 8, 9, 10)(6, 18, 19, 20)(11, 13)(14, 15, 16, 17), 
(1, 10)(2, 4)(3, 8)(5, 12)(6, 19)(7, 9)(15, 17), 
(1, 15, 8, 13, 3, 17, 10, 11)(2, 16, 4, 5, 7, 14, 9, 12)(6, 18, 19, 20)
orbits: { 1, 10, 11, 4, 9, 8, 17, 5, 14, 16, 15, 13, 2, 7, 3, 12 }, { 6, 20, 18, 19 }, { 21 }

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

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

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

code no       5:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
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 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 720
and is strongly generated by the following 6 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 1 1 0 0 
0 1 0 1 1 0 
0 0 1 1 1 0 
0 1 1 0 1 0 
0 1 1 1 1 1 
, 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 0 0 0 0 0 
1 0 0 0 1 1 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 1 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5)(8, 11)(9, 12)(10, 13)(19, 20), 
(3, 4)(7, 8)(12, 14)(13, 15)(18, 19), 
(2, 4)(7, 9)(11, 14)(13, 16)(17, 19), 
(2, 13, 5, 16, 4, 10)(3, 15)(6, 21)(7, 9, 12)(8, 14, 11)(17, 19, 20), 
(1, 5)(2, 4)(6, 20)(7, 16)(8, 15)(9, 13)(11, 14)(17, 19), 
(1, 2)(6, 17)(9, 10)(12, 13)(14, 15)
orbits: { 1, 5, 2, 4, 13, 10, 3, 16, 15, 9, 12, 7, 8, 14, 11 }, { 6, 21, 20, 17, 19, 18 }

code no       6:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 192
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 1 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 1 1 1 0 0 
1 1 1 0 0 0 
1 0 1 0 1 0 
1 0 1 0 0 1 
, 
0 1 0 0 0 0 
1 0 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
0 1 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(6, 16)(12, 13)(14, 15)(17, 18)(19, 20), 
(5, 16)(6, 11)(12, 18)(13, 17)(14, 20)(15, 19), 
(4, 9)(5, 12)(6, 17)(8, 10)(11, 13)(16, 18), 
(4, 10)(5, 13)(6, 18)(8, 9)(11, 12)(16, 17), 
(3, 7)(4, 8)(5, 11)(6, 16), 
(3, 8, 10)(4, 9, 7)(5, 15, 12)(6, 20, 17)(11, 14, 13)(16, 19, 18), 
(1, 2)(4, 10, 8, 9)(5, 13, 11, 12)(6, 17, 16, 18)(14, 15)
orbits: { 1, 2 }, { 3, 7, 10, 9, 8, 4 }, { 5, 11, 16, 12, 13, 6, 18, 17, 15, 14, 19, 20 }, { 21 }

code no       7:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 32
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 1 1 1 0 0 
0 1 1 0 1 0 
0 1 1 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
0 1 1 1 0 0 
0 1 1 0 0 1 
0 1 1 0 1 0 
, 
0 0 1 0 0 0 
1 1 1 0 0 0 
1 0 0 0 0 0 
1 0 1 1 0 0 
0 0 0 0 1 0 
1 0 1 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 10)(5, 13)(6, 18)(8, 9)(11, 12)(16, 17), 
(4, 8)(5, 11)(6, 16)(9, 10)(12, 13)(17, 18), 
(2, 3)(4, 10)(5, 18)(6, 13)(11, 16)(12, 17)(14, 19)(15, 20), 
(1, 3)(2, 7)(4, 9)(6, 17)(8, 10)(16, 18)(19, 20)
orbits: { 1, 3, 2, 7 }, { 4, 10, 8, 9 }, { 5, 13, 11, 18, 12, 6, 16, 17 }, { 14, 19, 20, 15 }, { 21 }

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

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

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

code no      11:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 1 1 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 1
the automorphism group has order 1008
and is strongly generated by the following 7 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
0 0 1 0 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 0 0 0 0 1 
1 0 0 1 1 0 
1 0 1 1 0 0 
0 0 0 1 0 0 
0 1 0 0 0 0 
, 
0 1 1 1 0 0 
1 0 1 1 0 0 
1 1 0 1 0 0 
1 1 1 0 0 0 
1 1 0 0 1 0 
0 0 1 1 0 1 
, 
1 1 0 1 0 0 
0 0 0 1 0 0 
0 1 1 1 0 0 
0 1 0 0 0 0 
1 1 0 0 1 0 
1 0 0 1 0 1 
, 
1 0 1 0 0 1 
0 0 1 0 0 0 
0 0 0 0 0 1 
0 0 1 1 0 1 
1 0 0 0 1 1 
1 1 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 5)(8, 11)(9, 12)(10, 13)(17, 19)(18, 20), 
(4, 9)(5, 12)(8, 10)(11, 13)(17, 18)(19, 20), 
(3, 5, 4)(7, 11, 8)(9, 12, 14)(10, 13, 15)(16, 19, 17)(18, 20, 21), 
(2, 6)(3, 14)(4, 5, 12, 9)(7, 21)(8, 19, 13, 18)(10, 17, 11, 20)(15, 16), 
(1, 10)(2, 9)(3, 8)(4, 7)(5, 11)(6, 18)(12, 13)(14, 15)(16, 17), 
(1, 8)(2, 4)(3, 10)(5, 11)(6, 17)(7, 9)(12, 13)(14, 15)(16, 18), 
(1, 7, 6, 3, 2, 16)(4, 10, 17, 9, 8, 18)(5, 11, 19)(12, 13, 20)(14, 15, 21)
orbits: { 1, 10, 8, 16, 13, 15, 20, 3, 4, 11, 18, 9, 17, 2, 19, 12, 14, 6, 5, 7, 21 }

code no      12:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 1 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 0 1 1 0 0 
1 0 1 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
0 0 0 0 1 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
0 1 1 1 0 0 
1 1 0 0 1 0 
1 0 1 0 0 1 
, 
1 1 0 0 1 0 
0 0 0 0 1 0 
0 1 1 0 1 0 
0 1 0 0 0 0 
1 1 0 1 0 0 
1 0 0 0 1 1 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 12)(8, 10)(11, 13)(17, 18)(19, 20), 
(4, 5)(8, 11)(9, 12)(10, 13)(17, 19)(18, 20), 
(1, 7)(2, 3)(4, 10)(5, 11)(6, 16)(8, 9)(12, 13)(14, 15)(17, 18), 
(1, 8, 5, 2, 4, 11)(3, 10, 12, 7, 9, 13)(6, 17, 19)(14, 15)(16, 18, 20)
orbits: { 1, 7, 11, 12, 13, 8, 5, 4, 9, 10, 2, 3 }, { 6, 16, 19, 20, 17, 18 }, { 14, 15 }, { 21 }

code no      13:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 32
and is strongly generated by the following 5 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
0 0 1 0 0 0 
1 1 0 0 1 0 
1 1 0 1 0 0 
0 0 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 0 0 0 1 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 1 0 0 
1 1 1 0 0 0 
1 1 0 0 0 1 
1 1 0 0 1 0 
, 
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 0 0 0 1 
1 1 0 1 0 0 
1 1 0 0 1 0 
1 1 1 0 0 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 8)(5, 11)(9, 10)(12, 13)(17, 18)(19, 20), 
(4, 11)(5, 8)(9, 13)(10, 12)(17, 20)(18, 19), 
(3, 7)(4, 8)(5, 11)(6, 15), 
(3, 8)(4, 7)(5, 15)(6, 11)(12, 17)(13, 18)(14, 16), 
(3, 15)(4, 8)(5, 11)(6, 7)(9, 17)(10, 18)(12, 19)(13, 20)
orbits: { 1 }, { 2 }, { 3, 7, 8, 15, 4, 6, 5, 11 }, { 9, 10, 13, 17, 12, 18, 20, 19 }, { 14, 16 }, { 21 }

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

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

code no      16:
================
1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
1 1 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 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
1 0 0 0 1 1 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 1 0 0
0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
the automorphism group has order 48
and is strongly generated by the following 4 elements:
(
1 0 0 0 0 0 
0 1 0 0 0 0 
1 1 1 0 0 0 
0 0 0 1 0 0 
0 0 0 0 1 0 
1 0 0 1 0 1 
, 
1 0 0 0 0 0 
0 0 0 1 0 0 
0 0 0 0 0 1 
0 1 0 0 0 0 
0 0 0 0 1 0 
0 0 1 0 0 0 
, 
0 0 0 1 0 0 
1 1 0 1 0 0 
1 0 1 1 0 0 
1 0 0 0 0 0 
0 0 0 0 1 0 
1 0 0 1 0 1 
, 
1 1 1 0 0 0 
0 0 1 0 0 0 
0 1 0 0 0 0 
1 0 1 1 0 0 
1 1 0 0 1 0 
0 0 0 0 0 1 
)
acting on the columns of the generator matrix as follows (in order):
(3, 7)(6, 16)(9, 10)(12, 13)(15, 17)(18, 20)(19, 21), 
(2, 4)(3, 6)(7, 16)(9, 15)(10, 17)(11, 14)(12, 18)(13, 20), 
(1, 4)(2, 8)(3, 9)(6, 16)(7, 10)(15, 17), 
(1, 7)(2, 3)(4, 9)(5, 11)(8, 10)(12, 13)(16, 17)(18, 19)(20, 21)
orbits: { 1, 4, 7, 2, 9, 3, 16, 10, 8, 15, 6, 17 }, { 5, 11, 14 }, { 12, 13, 18, 20, 19, 21 }