the 9 isometry classes of irreducible [20,15,4]_3 codes are:

code no       1:
================
1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 0 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
0 2 1 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
2 1 2 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
1 2 2 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
2 0 0 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
0 2 0 1 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
2 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 1 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 36
and is strongly generated by the following 5 elements:
(
2 0 0 0 0 
0 2 0 0 0 
0 0 2 0 0 
0 0 0 2 0 
2 2 1 1 1 
, 
2 0 0 0 0 
0 0 2 0 0 
0 2 0 0 0 
0 0 0 2 0 
0 1 2 0 2 
, 
0 1 0 2 2 
1 0 0 2 2 
1 1 2 2 2 
0 0 0 2 0 
0 0 0 0 2 
, 
0 2 0 0 0 
0 0 2 0 0 
2 0 0 0 0 
0 0 0 2 0 
1 0 2 0 2 
, 
1 0 2 0 2 
0 1 2 0 2 
0 0 0 0 2 
0 0 0 1 0 
1 1 2 2 2 
)
acting on the columns of the generator matrix as follows (in order):
(5, 18)(6, 11)(12, 17)(13, 16)(14, 20)(15, 19), 
(2, 3)(5, 13)(6, 19)(8, 9)(11, 15)(16, 18), 
(1, 17)(2, 16)(3, 18)(8, 11)(9, 15)(10, 14), 
(1, 3, 2)(5, 13, 12)(6, 19, 20)(8, 9, 10)(11, 15, 14)(16, 17, 18), 
(1, 17, 12)(2, 16, 13)(3, 18, 5)(6, 8, 11)(9, 15, 19)(10, 14, 20)
orbits: { 1, 17, 2, 12, 16, 3, 13, 18, 5 }, { 4 }, { 6, 11, 19, 20, 15, 8, 14, 9, 10 }, { 7 }

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

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

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

code no       5:
================
1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
0 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 0 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
0 2 1 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
2 1 2 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
2 0 0 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 2 0 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
1 2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
0 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 36
and is strongly generated by the following 4 elements:
(
2 0 0 0 0 
0 0 2 2 1 
1 2 0 2 1 
2 0 0 1 1 
0 0 0 0 2 
, 
0 2 0 0 0 
2 0 0 0 0 
0 0 0 2 0 
0 0 2 0 0 
0 0 0 0 2 
, 
0 0 2 2 1 
0 2 0 0 0 
0 2 1 0 1 
2 1 2 0 1 
0 0 0 0 2 
, 
1 2 0 2 1 
2 2 0 0 2 
0 2 0 0 0 
2 2 2 0 0 
0 0 0 0 2 
)
acting on the columns of the generator matrix as follows (in order):
(2, 20)(3, 18)(4, 15)(7, 19)(8, 12)(9, 11)(13, 14)(16, 17), 
(1, 2)(3, 4)(7, 8)(9, 10)(12, 16)(13, 15)(14, 18)(17, 19), 
(1, 20)(3, 13)(4, 14)(7, 16)(8, 17)(10, 11)(12, 19)(15, 18), 
(1, 13, 19, 18)(2, 3, 16, 11)(4, 7)(8, 14, 20, 9)(10, 17, 15, 12)
orbits: { 1, 2, 20, 18, 11, 14, 3, 15, 19, 9, 10, 16, 13, 4, 8, 17, 7, 12 }, { 5 }, { 6 }

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

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

code no       8:
================
1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
2 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
1 1 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 0 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
0 2 1 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
1 2 2 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
2 0 0 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 2 0 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
2 2 1 1 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
1 0 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
1 2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
1 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 2880
and is strongly generated by the following 8 elements:
(
1 0 0 0 0 
0 1 0 0 0 
0 0 1 0 0 
0 0 0 1 0 
1 1 2 2 2 
, 
2 0 0 0 0 
0 2 0 0 0 
1 1 0 0 1 
2 2 2 2 2 
1 1 1 0 0 
, 
1 0 0 0 0 
0 1 0 0 0 
1 1 1 1 1 
2 2 0 0 2 
2 2 2 0 0 
, 
1 0 0 0 0 
0 0 1 0 0 
0 1 0 0 0 
0 0 0 1 0 
0 2 1 0 1 
, 
2 0 0 0 0 
0 0 0 2 0 
1 2 0 2 1 
2 0 2 1 2 
1 1 0 1 0 
, 
2 0 0 0 0 
0 0 0 0 1 
2 2 0 2 0 
1 0 2 0 2 
0 0 0 1 0 
, 
1 2 0 2 1 
1 1 0 1 0 
2 1 1 1 0 
0 0 0 0 2 
1 0 0 2 2 
, 
2 0 2 1 2 
0 0 1 0 0 
0 0 0 0 2 
2 1 1 0 2 
1 2 0 2 1 
)
acting on the columns of the generator matrix as follows (in order):
(5, 17)(6, 11)(12, 16)(13, 15)(14, 18)(19, 20), 
(3, 11)(4, 6)(5, 7)(8, 17)(12, 13)(18, 19), 
(3, 11, 4, 6)(5, 8, 17, 7)(12, 16, 13, 15)(14, 19, 20, 18), 
(2, 3)(5, 13)(6, 18)(8, 9)(11, 14)(15, 17), 
(2, 11, 14, 18, 20, 4)(3, 6, 19)(5, 12, 8)(7, 9, 17, 15, 13, 16), 
(2, 12, 4, 5)(3, 8)(6, 9, 19, 7)(11, 13, 20, 15)(14, 17, 18, 16), 
(1, 8, 2, 15, 5, 4, 11, 19)(3, 9, 14, 6, 7, 17, 12, 10)(13, 18), 
(1, 18, 15, 7, 20)(2, 11, 19, 5, 3)(4, 16, 10, 13, 14)(6, 8, 9, 17, 12)
orbits: { 1, 19, 20, 18, 14, 6, 9, 11, 13, 7, 17, 16, 4, 3, 12, 8, 2, 15, 5, 10 }

code no       9:
================
1 1 1 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
2 1 1 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
2 1 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0
2 2 1 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0
0 2 2 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0
2 2 0 1 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0
2 0 2 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 1 2 1 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
0 2 0 2 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
2 0 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
0 1 1 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0
1 0 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
the automorphism group has order 160
and is strongly generated by the following 5 elements:
(
2 0 0 0 0 
0 2 0 0 0 
0 0 2 0 0 
0 0 0 2 0 
2 1 0 0 1 
, 
2 0 0 0 0 
0 2 0 0 0 
0 0 0 2 0 
0 0 2 0 0 
0 0 0 0 2 
, 
2 0 0 0 0 
2 0 2 2 0 
0 0 0 0 1 
1 2 0 0 2 
0 0 1 0 0 
, 
2 2 1 0 1 
1 1 0 2 2 
0 2 1 2 2 
1 0 1 2 2 
0 0 0 0 1 
, 
1 0 2 2 1 
1 1 1 1 1 
0 1 0 1 2 
0 1 1 0 2 
2 0 2 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(5, 11)(6, 20)(12, 13)(14, 17)(15, 19)(16, 18), 
(3, 4)(7, 8)(12, 14)(13, 17)(15, 18)(16, 19), 
(2, 9)(3, 5)(4, 11)(6, 8)(7, 20)(12, 15)(13, 18)(14, 19)(16, 17), 
(1, 14, 2, 12)(3, 18, 8, 16)(4, 19, 7, 15)(6, 11)(9, 13, 10, 17), 
(1, 6, 2, 20)(3, 12, 8, 17)(4, 14, 7, 13)(5, 10, 11, 9)(16, 19)
orbits: { 1, 12, 20, 13, 14, 15, 2, 3, 6, 7, 17, 18, 9, 19, 4, 5, 16, 8, 11, 10 }