1Ambient(from generators) automorphism group of order 6912 (possibly only approximation)
2Automorphisms are integral
3************************************************************************
48 permutations of 48 input generators
5
6Perm 1: 1 2 3 4 5 6 7 8 13 14 15 16 9 10 11 12 17 18 19 20 21 22 23 24 29 30 31 32 25 26 27 28 33 34 35 36 37 38 39 40 45 46 47 48 41 42 43 44
7Perm 2: 1 2 4 3 5 6 8 7 9 10 12 11 13 14 16 15 17 18 20 19 21 22 24 23 25 26 28 27 29 30 32 31 33 34 36 35 37 38 40 39 41 42 44 43 45 46 48 47
8Perm 3: 1 2 3 4 9 10 11 12 5 6 7 8 13 14 15 16 17 18 19 20 25 26 27 28 21 22 23 24 29 30 31 32 33 34 35 36 41 42 43 44 37 38 39 40 45 46 47 48
9Perm 4: 1 3 2 4 5 7 6 8 9 11 10 12 13 15 14 16 17 19 18 20 21 23 22 24 25 27 26 28 29 31 30 32 33 35 34 36 37 39 38 40 41 43 42 44 45 47 46 48
10Perm 5: 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16 17 21 25 29 18 22 26 30 19 23 27 31 20 24 28 32 33 37 41 45 34 38 42 46 35 39 43 47 36 40 44 48
11Perm 6: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
12Perm 7: 2 1 3 4 6 5 7 8 10 9 11 12 14 13 15 16 18 17 19 20 22 21 23 24 26 25 27 28 30 29 31 32 34 33 35 36 38 37 39 40 42 41 43 44 46 45 47 48
13Perm 8: 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
14
15Cycle decompositions
16
17Perm 1: (9 13) (10 14) (11 15) (12 16) (25 29) (26 30) (27 31) (28 32) (41 45) (42 46) (43 47) (44 48) --
18Perm 2: (3 4) (7 8) (11 12) (15 16) (19 20) (23 24) (27 28) (31 32) (35 36) (39 40) (43 44) (47 48) --
19Perm 3: (5 9) (6 10) (7 11) (8 12) (21 25) (22 26) (23 27) (24 28) (37 41) (38 42) (39 43) (40 44) --
20Perm 4: (2 3) (6 7) (10 11) (14 15) (18 19) (22 23) (26 27) (30 31) (34 35) (38 39) (42 43) (46 47) --
21Perm 5: (2 5) (3 9) (4 13) (7 10) (8 14) (12 15) (18 21) (19 25) (20 29) (23 26) (24 30) (28 31) (34 37) (35 41) (36 45) (39 42) (40 46) (44 47) --
22Perm 6: (17 33) (18 34) (19 35) (20 36) (21 37) (22 38) (23 39) (24 40) (25 41) (26 42) (27 43) (28 44) (29 45) (30 46) (31 47) (32 48) --
23Perm 7: (1 2) (5 6) (9 10) (13 14) (17 18) (21 22) (25 26) (29 30) (33 34) (37 38) (41 42) (45 46) --
24Perm 8: (1 17) (2 18) (3 19) (4 20) (5 21) (6 22) (7 23) (8 24) (9 25) (10 26) (11 27) (12 28) (13 29) (14 30) (15 31) (16 32) --
25
261 orbits of input generators
27
28Orbit 1 , length 48:  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
29
30************************************************************************
318 permutations of 40 Coordinates
32
33Perm 1: 1 2 3 4 5 6 7 8 13 14 15 16 9 10 11 12 17 18 19 20 21 22 23 24 25 26 27 28 29 30 32 31 33 34 36 35 37 38 40 39
34Perm 2: 1 2 4 3 5 6 8 7 9 10 12 11 13 14 16 15 17 18 20 19 21 22 24 23 25 26 28 27 29 30 31 32 33 34 35 36 37 38 39 40
35Perm 3: 1 2 3 4 9 10 11 12 5 6 7 8 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31 30 32 33 35 34 36 37 39 38 40
36Perm 4: 1 3 2 4 5 7 6 8 9 11 10 12 13 15 14 16 17 19 18 20 21 23 22 24 25 27 26 28 29 30 31 32 33 34 35 36 37 38 39 40
37Perm 5: 1 5 9 13 2 6 10 14 3 7 11 15 4 8 12 16 29 30 31 32 33 34 35 36 37 38 39 40 17 18 19 20 21 22 23 24 25 26 27 28
38Perm 6: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 26 27 28 21 22 23 24 29 30 31 32 37 38 39 40 33 34 35 36
39Perm 7: 2 1 3 4 6 5 7 8 10 9 11 12 14 13 15 16 18 17 19 20 22 21 23 24 26 25 27 28 29 30 31 32 33 34 35 36 37 38 39 40
40Perm 8: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 21 22 23 24 17 18 19 20 25 26 27 28 33 34 35 36 29 30 31 32 37 38 39 40
41
42Cycle decompositions
43
44Perm 1: (9 13) (10 14) (11 15) (12 16) (31 32) (35 36) (39 40) --
45Perm 2: (3 4) (7 8) (11 12) (15 16) (19 20) (23 24) (27 28) --
46Perm 3: (5 9) (6 10) (7 11) (8 12) (30 31) (34 35) (38 39) --
47Perm 4: (2 3) (6 7) (10 11) (14 15) (18 19) (22 23) (26 27) --
48Perm 5: (2 5) (3 9) (4 13) (7 10) (8 14) (12 15) (17 29) (18 30) (19 31) (20 32) (21 33) (22 34) (23 35) (24 36) (25 37) (26 38) (27 39) (28 40) --
49Perm 6: (21 25) (22 26) (23 27) (24 28) (33 37) (34 38) (35 39) (36 40) --
50Perm 7: (1 2) (5 6) (9 10) (13 14) (17 18) (21 22) (25 26) --
51Perm 8: (17 21) (18 22) (19 23) (20 24) (29 33) (30 34) (31 35) (32 36) --
52
532 orbits of Coordinates
54
55Orbit 1 , length 16:  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
56Orbit 2 , length 24:  17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
57
58************************************************************************
59
60input generators
61
62  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
63  2:  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
64  3:  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
65  4:  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 0 0 0 0 0 0 0 0 0
66  5:  0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
67  6:  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
68  7:  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
69  8:  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
70  9:  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 0 0 0 0 0 0 0 0 0
71 10:  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 1 0 0 0 0 0 0 0 0 0
72 11:  0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
73 12:  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 1 0 0 0 0 0 0 0 0 0
74 13:  0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
75 14:  0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
76 15:  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 0 0 0 0 0 0 0 0
77 16:  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 1 0 0 0 0 0 0 0 0
78 17:  1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
79 18:  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 1 0 0 0 0 0 0 0
80 19:  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 1 0 0 0 0 0 0 0
81 20:  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 0 0
82 21:  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 1 0 0 0 0 0 0
83 22:  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
84 23:  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
85 24:  0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
86 25:  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 1 0 0 0 0 0
87 26:  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 1 0 0 0 0 0
88 27:  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
89 28:  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
90 29:  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 1 0 0 0 0
91 30:  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 1 0 0 0 0
92 31:  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 1 0 0 0 0
93 32:  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 1 0 0 0 0
94 33:  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 0 0 0 0 0 0 0 0 0 0 1 0 0 0
95 34:  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 0 0 0 0 0 0 0 0 0 1 0 0 0
96 35:  0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0
97 36:  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 0 1 0 0 0 0 0 0 0 0 1 0 0 0
98 37:  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 0 1 0 0
99 38:  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
100 39:  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 1 0 0
101 40:  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 1 0 0
102 41:  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
103 42:  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 1 0
104 43:  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
105 44:  0 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
106 45:  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
107 46:  0 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 1
108 47:  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 1
109 48:  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
110