About this representation
| Group |
Fi22 |
| Group generators |
Standard generators |
| Number of
points |
14080 |
|
Distinguishing letter |
b |
| Primitivity
information |
Primitive |
|
Transitivity degree |
1 |
| Rank |
3 |
| Suborbit
lengths |
1, 3159, 10920 |
|
Character |
1+429+13650 |
| Contributed
by |
Not recorded |
Download
This representation is available in the following
formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A |
14080 |
|
| 2A |
1408 |
26336 |
| 2B |
256 |
26912 |
| 2C |
128 |
26976 |
| 3A |
112 |
34656 |
| 3B |
148 |
34644 |
| 3C |
49 |
34677 |
| 3D |
13 |
34689 |
| 4A |
0 |
2128, 43456 |
| 4B |
16 |
2120, 43456 |
| 4C |
0 |
2128, 43456 |
| 4D |
16 |
256, 43488 |
| 4E |
16 |
2120, 43456 |
| 5A |
5 |
52815 |
| 6A |
40 |
236, 3456,
62100 |
| 6B |
4 |
272, 3468,
62088 |
| 6C |
4 |
272, 384,
62280 |
| 6D |
16 |
248, 380,
62288 |
| 6E |
13 |
218, 3465,
62106 |
| 6F |
8 |
252, 340,
62308 |
| 6G |
20 |
264, 336,
62304 |
| 6H |
17 |
216, 337,
62320 |
| 6I |
1 |
224, 385,
62296 |
| 6J |
5 |
222, 341,
62318 |
| 6K |
5 |
24, 341,
62324 |
| 7A |
3 |
72011 |
| 8A |
0 |
464, 81728 |
| 8B |
0 |
464, 81728 |
| 8C |
0 |
464, 81728 |
| 8D |
4 |
26, 428,
81744 |
| 9A |
1 |
349, 91548 |
| 9B |
7 |
347, 91548 |
| 9C |
1 |
34, 91563 |
| 10A |
3 |
2, 5281,
101267 |
| 10B |
1 |
22, 551,
101382 |
| 11A |
0 |
111280 |
| 11B |
0 |
111280 |
| 12A |
0 |
22, 436,
642, 121140 |
| 12B |
0 |
28, 424,
640, 121144 |
| 12C |
0 |
28, 424,
640, 121144 |
| 12D |
4 |
26, 34,
424, 638, 121144 |
| 12E |
4 |
28, 34,
432, 616, 121152 |
| 12F |
4 |
28, 34,
432, 616, 121152 |
| 12G |
1 |
28, 35,
48, 616, 121160 |
| 12H |
0 |
22, 436,
642, 121140 |
| 12I |
4 |
26, 34,
424, 638, 121144 |
| 12J |
1 |
35, 412,
640, 121148 |
| 12K |
1 |
22, 35,
42, 618, 121162 |
| 13A |
1 |
131083 |
| 13B |
1 |
131083 |
| 14A |
1 |
2, 7201,
14905 |
| 15A |
2 |
3, 522,
15931 |
| 16A |
0 |
832, 16864 |
| 16B |
0 |
832, 16864 |
| 18A |
1 |
3, 624, 9156,
18696 |
| 18B |
1 |
3, 624, 9156,
18696 |
| 18C |
1 |
23, 3, 623,
9156, 18696 |
| 18D |
1 |
3, 624, 928,
18760 |
| 20A |
1 |
4, 53, 1024,
20691 |
| 21A |
0 |
3, 716,
21665 |
| 22A |
0 |
11128,
22576 |
| 22B |
0 |
11128,
22576 |
| 24A |
0 |
44, 812,
1220, 24572 |
| 24B |
0 |
44, 812,
1220, 24572 |
| 30A |
0 |
2, 3, 58, 107,
1591, 30420 |
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 |