the 21 isometry classes of irreducible [20,16,4]_5 codes are:

code no       1:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
1 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
2 2 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
0 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
0 2 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
3 3 2 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
0 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
3 2 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
2 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 120
and is strongly generated by the following 4 elements:
(
3 0 0 0 
0 3 0 0 
2 2 1 1 
2 2 3 4 
, 
1 0 0 0 
0 0 1 0 
4 4 2 2 
4 4 1 3 
, 
2 1 1 0 
1 2 1 0 
1 1 4 2 
1 1 3 3 
, 
1 1 1 1 
0 4 3 3 
0 0 0 1 
0 0 1 0 
)
acting on the columns of the generator matrix as follows (in order):
(3, 12)(4, 16)(5, 8)(6, 11)(7, 13)(9, 14)(10, 15), 
(2, 12, 3)(4, 18, 16)(5, 15, 7)(6, 11, 19)(8, 13, 10)(9, 14, 20), 
(1, 11, 6)(2, 13, 7)(3, 5, 16)(4, 8, 12)(9, 17, 14)(10, 18, 15), 
(1, 5)(2, 13)(3, 4)(6, 9)(7, 20)(8, 17)(10, 19)(11, 12)(14, 16)(15, 18)
orbits: { 1, 6, 5, 11, 19, 9, 8, 7, 3, 12, 10, 14, 20, 4, 17, 13, 15, 16, 2, 18 }

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

code no      20:
================
1 1 1 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 1 1 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 2 1 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0
3 3 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0
2 1 0 1 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
3 2 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0
4 4 0 1 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0
3 0 1 1 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
4 3 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 0 2 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0
3 4 2 1 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0
0 1 3 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0
4 2 3 1 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0
1 0 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
4 1 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0
3 3 4 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
the automorphism group has order 240
and is strongly generated by the following 7 elements:
(
3 0 0 0 
0 3 0 0 
0 0 3 0 
4 2 0 2 
, 
2 0 0 0 
1 0 1 3 
3 4 0 4 
0 0 0 2 
, 
1 0 0 0 
0 1 3 1 
0 0 0 3 
0 0 2 0 
, 
3 0 0 0 
1 1 2 0 
3 4 4 0 
2 1 4 3 
, 
0 0 4 0 
4 2 2 0 
1 0 0 0 
0 0 0 2 
, 
3 2 3 2 
3 0 3 4 
0 3 4 3 
0 0 0 1 
, 
4 4 2 3 
2 2 2 2 
2 2 4 0 
2 4 2 0 
)
acting on the columns of the generator matrix as follows (in order):
(4, 9)(5, 18)(10, 11)(12, 19)(13, 20)(14, 16)(15, 17), 
(2, 14)(3, 9)(5, 19)(6, 17)(8, 13)(10, 18)(11, 12), 
(2, 16)(3, 4)(5, 11)(6, 15)(8, 20)(10, 19)(12, 18), 
(2, 8)(3, 6)(4, 17)(5, 10)(9, 15)(11, 18)(13, 16)(14, 20), 
(1, 3)(2, 6)(5, 16)(7, 8)(10, 17)(11, 15)(14, 18), 
(1, 5, 9, 16, 3, 19)(2, 10, 17, 6, 18, 14)(7, 11, 13, 15, 8, 12), 
(1, 20)(2, 5)(3, 8)(4, 7)(6, 11)(9, 13)(10, 18)(12, 17)(14, 19)
orbits: { 1, 3, 19, 20, 9, 4, 6, 16, 8, 12, 5, 10, 14, 13, 15, 17, 7, 2, 11, 18 }

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