About this representation
| Group |
Fi22 |
| Group generators |
Standard generators |
| Number of
points |
3510 |
| Primitivity
information |
Primitive |
|
Transitivity degree |
1 |
| Rank |
3 |
| Suborbit
lengths |
1, 693, 2816 |
|
Character |
1+429+3080 |
| Contributed
by |
Not recorded |
Download
This representation is available in the following
formats:
On conjugacy classes
| Conjugacy class |
Fixed points |
Cycle type |
| 1A |
3510 |
|
| 2A |
694 |
21408 |
| 2B |
182 |
21664 |
| 2C |
54 |
21728 |
| 3A |
126 |
31128 |
| 3B |
27 |
31161 |
| 3C |
36 |
31158 |
| 3D |
0 |
31170 |
| 4A |
38 |
272, 4832 |
| 4B |
30 |
276, 4832 |
| 4C |
6 |
288, 4832 |
| 4D |
6 |
224, 4864 |
| 4E |
14 |
284, 4832 |
| 5A |
10 |
5700 |
| 6A |
46 |
240, 3216,
6456 |
| 6B |
19 |
24, 3225,
6468 |
| 6C |
11 |
28, 357,
6552 |
| 6D |
14 |
256, 356,
6536 |
| 6E |
10 |
213, 3228,
6465 |
| 6F |
6 |
260, 316,
6556 |
| 6G |
3 |
212, 317,
6572 |
| 6H |
12 |
212, 314,
6572 |
| 6I |
8 |
214, 358,
6550 |
| 6J |
6 |
215, 316,
6571 |
| 6K |
0 |
318, 6576 |
| 7A |
3 |
7501 |
| 8A |
6 |
216, 436,
8416 |
| 8B |
6 |
216, 436,
8416 |
| 8C |
2 |
22, 444,
8416 |
| 8D |
2 |
22, 412,
8432 |
| 9A |
6 |
37, 9387 |
| 9B |
3 |
38, 9387 |
| 9C |
0 |
9390 |
| 10A |
4 |
23, 5138,
10281 |
| 10B |
2 |
24, 536,
10332 |
| 11A |
1 |
11319 |
| 11B |
1 |
11319 |
| 12A |
11 |
39, 44,
624, 12276 |
| 12B |
2 |
26, 312,
428, 622, 12268 |
| 12C |
2 |
26, 312,
428, 622, 12268 |
| 12D |
6 |
24, 38,
428, 624, 12268 |
| 12E |
3 |
3, 46, 68,
12286 |
| 12F |
3 |
3, 46, 68,
12286 |
| 12G |
0 |
26, 32,
46, 66, 12286 |
| 12H |
3 |
24, 3, 44,
628, 12276 |
| 12I |
2 |
26, 34,
428, 626, 12268 |
| 12J |
0 |
24, 310,
47, 624, 12275 |
| 12K |
0 |
32, 68,
12288 |
| 13A |
0 |
13270 |
| 13B |
0 |
13270 |
| 14A |
1 |
2, 799,
14201 |
| 15A |
1 |
33, 525,
15225 |
| 16A |
0 |
2, 4, 822,
16208 |
| 16B |
0 |
2, 4, 822,
16208 |
| 18A |
4 |
2, 35, 6, 975,
18156 |
| 18B |
4 |
2, 35, 6, 975,
18156 |
| 18C |
1 |
2, 36, 6, 975,
18156 |
| 18D |
2 |
22, 33,
62, 919, 18184 |
| 20A |
0 |
2, 42, 56,
1015, 20166 |
| 21A |
0 |
3, 718,
21161 |
| 22A |
1 |
1163, 22128 |
| 22B |
1 |
1163, 22128 |
| 24A |
0 |
2, 32, 43,
65, 814, 1211,
24134 |
| 24B |
0 |
2, 32, 43,
65, 814, 1211,
24134 |
| 30A |
1 |
3, 59, 6, 108,
1543, 3091 |
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 |