About this representation

Group Fi22
Group generators Standard generators
Number of points 61776
Primitivity information Primitive
Transitivity degree 1
Rank 4
Suborbit lengths 1, 1575, 22400, 37800
Character 1+3080+13650+45045
Contributed by Not recorded

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This representation is available in the following formats:

MeatAxe a b
MeatAxe binary a b
GAP a b
GAP a, b
Magma a, b

On conjugacy classes

Conjugacy class Fixed points Cycle type
1A 61776
2A 6336 227720
2B 656 230560
2C 288 230744
3A 666 320370
3B 216 320520
3C 36 320580
3D 27 320583
4A 40 2308, 415280
4B 76 2290, 415280
4C 16 2320, 415280
4D 12 2138, 415372
4E 20 2318, 415280
5A 1 512355
6A 36 2315, 32100, 69135
6B 72 272, 32088, 69216
6C 8 2104, 3216, 610152
6D 26 2320, 3210, 610080
6E 18 29, 32106, 69237
6F 36 2315, 384, 610143
6G 24 296, 388, 610216
6H 12 212, 392, 610244
6I 8 214, 3216, 610182
6J 6 215, 394, 610243
6K 3 212, 395, 610244
7A 1 78825
8A 4 218, 4154, 87640
8B 8 216, 4154, 87640
8C 0 28, 4160, 87640
8D 2 25, 469, 87686
9A 6 370, 96840
9B 3 371, 96840
9C 0 39, 96861
10A 1 51267, 105544
10B 1 5131, 106112
11A 0 115616
11B 0 115616
12A 4 22, 312, 452, 6102, 125076
12B 10 28, 310, 4160, 6100, 125040
12C 4 211, 312, 4160, 699, 125040
12D 4 211, 324, 4160, 693, 125040
12E 0 212, 34, 448, 642, 125108
12F 0 212, 34, 448, 642, 125108
12G 0 26, 34, 46, 644, 125122
12H 4 22, 34, 452, 6106, 125076
12I 2 212, 36, 4160, 6102, 125040
12J 4 22, 324, 47, 696, 125091
12K 3 33, 46, 646, 125122
13A 0 134752
13B 0 134752
14A 1 7905, 143960
15A 1 5133, 154074
16A 0 44, 880, 163820
16B 0 44, 880, 163820
18A 0 23, 324, 623, 9696, 183072
18B 0 23, 324, 623, 9696, 183072
18C 3 323, 624, 9696, 183072
18D 2 22, 32, 634, 972, 183384
20A 1 515, 1058, 203056
21A 1 795, 212910
22A 0 11576, 222520
22B 0 11576, 222520
24A 2 24, 32, 44, 64, 880, 1250, 242520
24B 4 23, 44, 65, 880, 1250, 242520
30A 1 57, 1063, 15420, 301827

Checks applied

Check Description Date Checked by Result
Presentation Check against the relations in a presentation. If this test passes, then the group is of the correct isomorphism type, and the generators are those stated. Note that the presentation itself is not checked here. Aug 2, 2006 certify.pl version 0.05 Pass
Semi-presentation Check against a semi-presentation. If this fails, then the representation is not on standard generators, and may generate the wrong group. Note that the semi-presentation itself is not checked here. Jul 4, 2006 certify.pl version 0.05 Pass
Order Check that the elements generate a group of the correct order. Jul 4, 2006 permanalyse version 0.03 Pass
Number of points Check whether the permutation representation is acting on the stated number of points. Jul 4, 2006 certify.pl version 0.05 Pass
Files exist Check whether files exist (where stated). Jul 4, 2006 certify.pl version 0.05 Pass