n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | 2.U6(2) | 3 | 3510 | 1a + 429a + 3080a | [PS97] | 1, 2 | |
2 | O7(3) | 3 | 14080 | 1a + 429a + 13650a | [PS97] | 1, 2 | |
3 | O7(3) | 3 | 14080 | 1a + 429a + 13650a | [PS97] | 1, 2 | |
4 | O8+(2):S3 | 4 | 61776 | 1a + 3080a + 13650a + 45045a | [PS97] | 1, 2 | |
5 | O8+(2):3 < O8+(2):S3 | 7 | 123552 | 1a + 1001a + 3080a + 10725a + 13650a + 45045a + 50050a | [Hoe01] | 1, 2 | |
6 | O8+(2):2 < O8+(2):S3 | 7 | 185328 | 1a + 429a + 3080a + 13650a + 45045a + 48048a + 75075a | [Hoe01] | 1, 2 | |
7 | 210:M22 | 8 | 142155 | 1a + 78a + 429a + 1430a + 3080a + 30030a + 32032a + 75075a | [Hoe01] | 1, 2 | |
8 | 26:S6(2) | 10 | 694980 | 1a + 429a + 1430a + 3080a + 13650a + 30030a + 45045a + 75075a + 205920a + 320320a | [Hoe01] | 1, 2 | |
9 | 2F4(2)' | 11 | 3592512 | 1a + 1001a + 1430a + 13650a + 30030a + 289575a + 400400ab + 579150a + 675675a + 1201200a | [Hoe01] | 1, 2 |
n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | 2.U6(2).2 | 3 | 3510 | 1a+ + 429a+ + 3080a+ | [PS97] | 1, 2 | |
2 | 2.U6(2) < 2.U6(2).2 | 6 | 7020 | 1a± + 429a± + 3080a± | [Hoe01] | 1, 2 | |
3 | O7(3) < Fi22 | 6 | 28160 | 1a± + 429a± + 13650a± | [Hoe01] | 1, 2 | |
4 | O8+(2):S3 × 2 | 4 | 61776 | 1a+ + 3080a+ + 13650a+ + 45045a+ | [PS97] | 1, 2 | |
5 | O8+(2):S3 < O8+(2):S3 × 2 | 8 | 123552 | 1a± + 3080a± + 13650a± + 45045a± | [Hoe01] | 1, 2 | |
6 | O8+(2):3 × 2 < O8+(2):S3 × 2 | 7 | 123552 | 1a+ + 1001a- + 3080a+ + 10725a+ + 13650a+ + 45045a+ + 50050a+ | [Hoe01] | 1, 2 | |
7 | O8+(2):S3 < O8+(2):S3 × 2 | 7 | 123552 | 1a+ + 1001a+ + 3080a+ + 10725a- + 13650a+ + 45045a+ + 50050a- | [Hoe01] | 1, 2 | |
8 | O8+(2):2 × 2 < O8+(2):S3 × 2 | 7 | 185328 | 1a+ + 429a+ + 3080a+ + 13650a+ + 45045a+ + 48048a+ + 75075a+ | [Hoe01] | 1, 2 | |
9 | O8+(2):3 < O8+(2):S3 × 2 | 14 | 247104 | 1a± + 1001a± + 3080a± + 10725a± + 13650a± + 45045a± + 50050a± | [Hoe01] | 1, 2 | |
10 | O8+(2):2 < Fi22 | 14 | 370656 | 1a± + 429a± + 3080a± + 13650a± + 45045a± + 48048a± + 75075a± | [Hoe01] | 1, 2 | |
11 | O8+(2):2 < O8+(2):S3 × 2 | 13 | 370656 | 1a+ + 429a± + 1001a+ + 3080a+ + 10725a- + 13650a+ + 45045a+ + 48048a± + 50050a- + 75075a± | [Hoe01] | 1, 2 | |
12 | 210:M22.2 | 8 | 142155 | 1a+ + 78a+ + 429a+ + 1430a+ + 3080a+ + 30030a+ + 32032a+ + 75075a+ | [Hoe01] | 1, 2 | |
13 | 210:M22 < 210:M22.2 | 16 | 284310 | 1a± + 78a± + 429a± + 1430a± + 3080a± + 30030a± + 32032a± + 75075a± | [Hoe01] | 1, 2 | |
14 | 27:S6(2) | 10 | 694980 | 1a+ + 429a+ + 1430a+ + 3080a+ + 13650a+ + 30030a+ + 45045a+ + 75075a+ + 205920a+ + 320320a+ | [Hoe01] | 1, 2 | |
15 | 26:S6(2) < 27:S6(2) | 20 | 1389960 | 1a± + 429a± + 1430a± + 3080a± + 13650a± + 30030a± + 45045a± + 75075a± + 205920a± + 320320a± | [Hoe01] | 1, 2 | |
16 | 2F4(2)'.2 | 10 | 3592512 | 1a+ + 1001a+ + 1430a+ + 13650a+ + 30030a+ + 289575a- + 400400ab + 579150a+ + 675675a- + 1201200a- | [Hoe01] | 1, 2 |
n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | O7(3) → (Fi22,2) | 5 | 28160 | 1a + 352a + 429a + 13650a + 13728a | [PS97] | 1, 2 | |
2 | O7(3) → (Fi22,3) | 5 | 28160 | 1a + 352a + 429a + 13650a + 13728b | [PS97] | 1, 2 | |
3 | O8+(2):S3 → (Fi22,4) | 6 | 123552 | 1a + 3080a + 13650a + 13728a + 45045a + 48048b | [Linton] | 1, 2 | |
4 | O8+(2):S3 → (Fi22,4) | 6 | 123552 | 1a + 3080a + 13650a + 13728b + 45045a + 48048c | [Linton] | 1, 2 | |
5 | O8+(2):3 → (Fi22,5) | 11 | 247104 | 1a + 1001a + 3080a + 10725a + 13650a + 13728ab + 45045a + 48048bc + 50050a | [Linton] | 1, 2 | |
6 | O8+(2):2 → (Fi22,6) | 11 | 370656 | 1a + 352a + 429a + 3080a + 13650a + 13728a + 45045a + 48048ab + 75075a + 123200a | [Linton] | 1, 2 | |
7 | O8+(2):2 → (Fi22,6) | 11 | 370656 | 1a + 352a + 429a + 3080a + 13650a + 13728b + 45045a + 48048ac + 75075a + 123200a | [Linton] | 1, 2 |
n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | O8+(2):S3 → (Fi22,4) | 10 | 185328 | 1a + 351ab + 3080a + 13650a + 19305ab + 42120ab + 45045a | [Linton] | 1, 2 | |
2 | O8+(2):3 → (Fi22,5) | 11 | 370656 | 1a + 1001a + 3080a + 10725a + 13650a + 27027ab + 45045a + 50050a + 96525ab | [Linton] | 1, 2 | |
3 | O8+(2):3 → (Fi22,5) | 17 | 370656 | 1a + 351ab + 1001a + 3080a + 7722ab + 10725a + 13650a + 19305ab + 42120ab + 45045a + 50050a + 54054ab | [Linton] | 1, 2 | |
4 | O8+(2):2 → (Fi22,6) | 17 | 555984 | 1a + 351ab + 429a + 3080a + 13650a + 19305ab + 27027ab + 42120ab + 45045a + 48048a + 75075a + 96525ab | [Linton] | 1, 2 | |
5 | 26:S6(2) → (Fi22,8) | 24 | 2084940 | 1a + 351ab + 429a + 1430a + 3080a + 13650a + 19305ab + 27027ab + 30030a + 42120ab + 45045a + 75075a + 96525ab + 123552ab + 205920a + 320320a + 386100ab | [Linton] | 1, 2 | |
6 | 2F4(2)' → (Fi22,9) | 25 | 10777536 | 1a + 1001a + 1430a + 13650a + 19305ab + 27027ab + 30030a + 51975ab + 289575a + 386100ab + 400400ab + 405405ab + 579150a + 675675a + 1201200a + 1351350efgh | [Linton] | 1, 2 |
n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | O8+(2):S3 → (2.Fi22,3), (3.Fi22,1) | 14 | 370656 | 1a + 351ab + 3080a + 13650a + 13728a + 19305ab + 42120ab + 45045a + 48048b + 61776ab | [Linton] | 1, 2 | |
2 | O8+(2):S3 → (2.Fi22,4), (3.Fi22,1) | 14 | 370656 | 1a + 351ab + 3080a + 13650a + 13728b + 19305ab + 42120ab + 45045a + 48048c + 61776cd | [Linton] | 1, 2 | |
3 | O8+(2):3 → (2.Fi22,5), (3.Fi22,2) | 17 | 741312 | 1a + 1001a + 3080a + 10725a + 13650a + 13728ab + 27027ab + 45045a + 48048bc + 50050a + 96525ab + 123552cd | [Linton] | 1, 2 | |
4 | O8+(2):3 → (2.Fi22,5), (3.Fi22,3) | 25 | 741312 | 1a + 351ab + 1001a + 3080a + 7722ab + 10725a + 13650a + 13728ab + 19305ab + 42120ab + 45045a + 48048bc + 50050a + 54054ab + 61776abcd | [Linton] | 1, 2 | |
5 | O8+(2):2 → (2.Fi22,6), (3.Fi22,4) | 25 | 1111968 | 1a + 351ab + 352a + 429a + 3080a + 13650a + 13728a + 19305ab + 27027ab + 42120ab + 45045a + 48048ab + 61776ab + 75075a + 96525ab + 123200a + 123552cd | [Linton] | 1, 2 | |
6 | O8+(2):2 → (2.Fi22,7), (3.Fi22,4) | 25 | 1111968 | 1a + 351ab + 352a + 429a + 3080a + 13650a + 13728b + 19305ab + 27027ab + 42120ab + 45045a + 48048ac + 61776cd + 75075a + 96525ab + 123200a + 123552cd | [Linton] | 1, 2 |
n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | O7(3) → (Fi22.2,3) | 9 | 56320 | 1a± + 352a± + 429a± + 13650a± + 13728ab | [Mue08b] | 1, 2 | |
2 | O8+(2):S3 → (Fi22.2,5) | 10 | 247104 | 1a± + 3080a± + 13650a± + 13728ab + 45045a± + 48048bc | [Mue08b] | 1, 2 | |
3 | O8+(2):3 × 2 → (Fi22.2,6) | 9 | 247104 | 1a+ + 1001a- + 3080a+ + 10725a+ + 13650a+ + 13728ab + 45045a+ + 48048bc + 50050a+ | [Mue08b] | 1, 2 | |
4 | O8+(2):2 → (Fi22.2,10) | 20 | 741312 | 1a± + 352a± + 429a± + 3080a± + 13650a± + 13728ab + 45045a± + 48048a±bc + 75075a± + 123200a± | [Mue08b] | 1, 2 | |
5 | 2F4(2)'.2 → (Fi22.2,16) | 13 | 7185024 | 1a+ + 1001a+ + 1430a+ + 13650a+ + 30030a+ + 133056a± + 289575a- + 400400ab + 579150a+ + 675675a- + 1201200a- + 1663200ab | [Mue08b] | 1, 2 | |
6 | 2F4(2)'.2 → (Fi22.2,16) | 13 | 7185024 | 1a+ + 1001a+ + 1430a+ + 13650a+ + 30030a+ + 133056a± + 289575a- + 400400ab + 579150a+ + 675675a- + 1201200a- + 1663200ab | [Mue08b] | 1, 2 |
n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | O7(3) → (Fi22.2,3) | 9 | 56320 | 1a± + 352a± + 429a± + 13650a± + 13728ab | [Mue08b] | 1, 2 | |
2 | O8+(2):S3 → (Fi22.2,5) | 10 | 247104 | 1a± + 3080a± + 13650a± + 13728ab + 45045a± + 48048bc | [Mue08b] | 1, 2 | |
3 | O8+(2):S3 → (Fi22.2,7) | 9 | 247104 | 1a+ + 1001a+ + 3080a+ + 10725a- + 13650a+ + 13728ab + 45045a+ + 48048bc + 50050a- | [Mue08b] | 1, 2 | |
4 | O8+(2):2 → (Fi22.2,10) | 20 | 741312 | 1a± + 352a± + 429a± + 3080a± + 13650a± + 13728ab + 45045a± + 48048a±bc + 75075a± + 123200a± | [Mue08b] | 1, 2 | |
5 | O8+(2):2 → (Fi22.2,11) | 19 | 741312 | 1a+ + 352a± + 429a± + 1001a+ + 3080a+ + 10725a- + 13650a+ + 13728ab + 45045a+ + 48048a±bc + 50050a- + 75075a± + 123200a± | [Mue08b] | 1, 2 |
n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | O8+(2):S3 × 2 → (Fi22.2,4) | 7 | 185328 | 1a+ + 351ab + 3080a+ + 13650a+ + 19305ab + 42120ab + 45045a+ | [Mue08b] | 1, 2 | |
2 | O8+(2):3 × 2 → (Fi22.2,6) | 12 | 370656 | 1a+ + 351ab + 1001a- + 3080a+ + 7722ab + 10725a+ + 13650a+ + 19305ab + 42120ab + 45045a+ + 50050a+ + 54054ab | [Mue08b] | 1, 2 | |
3 | O8+(2):S3 → (Fi22.2,7) | 9 | 370656 | 1a+ + 1001a+ + 3080a+ + 10725a- + 13650a+ + 27027ab + 45045a+ + 50050a- + 96525ab | [Mue08b] | 1, 2 | |
4 | O8+(2):S3 → (Fi22.2,7) | 12 | 370656 | 1a+ + 351ab + 1001a+ + 3080a+ + 7722ab + 10725a- + 13650a+ + 19305ab + 42120ab + 45045a+ + 50050a- + 54054ab | [Mue08b] | 1, 2 | |
5 | O8+(2):2 × 2 → (Fi22.2,8) | 12 | 555984 | 1a+ + 351ab + 429a+ + 3080a+ + 13650a+ + 19305ab + 27027ab + 42120ab + 45045a+ + 48048a+ + 75075a+ + 96525ab | [Mue08b] | 1, 2 | |
6 | 27:S6(2) → (Fi22.2,14) | 17 | 2084940 | 1a+ + 351ab + 429a+ + 1430a+ + 3080a+ + 13650a+ + 19305ab + 27027ab + 30030a+ + 42120ab + 45045a+ + 75075a+ + 96525ab + 123552ab + 205920a+ + 320320a+ + 386100ab | [Mue08b] | 1, 2 | |
7 | 2F4(2)'.2 → (Fi22.2,16) | 17 | 10777536 | 1a+ + 1001a+ + 1430a+ + 13650a+ + 19305ab + 27027ab + 30030a+ + 51975ab + 289575a- + 386100ab + 400400ab + 405405ab + 579150a+ + 675675a- + 1201200a- + 1351350efgh | [Mue08b] | 1, 2 |
n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | O8+(2):3 × 2 → (2.Fi22.2,3), (3.Fi22.2,2) | 16 | 741312 | 1a+ + 351ab + 1001a- + 3080a+ + 7722ab + 10725a+ + 13650a+ + 13728ab + 19305ab + 42120ab + 45045a+ + 48048bc + 50050a+ + 54054ab + 61776abcd | [Mue08b] | 1, 2 | |
2 | 2F4(2)'.2 → (Fi22.2,16) | 22 | 21555072 | 1a+ + 1001a+ + 1430a+ + 13650a+ + 19305ab + 27027ab + 30030a+ + 51975ab + 133056a± + 289575a- + 386100ab + 400400ab + 405405ab + 579150a+ + 675675a- + 1201200a- + 1351350efgh + 1663200ab + 1796256abcd | [Mue08b] | 1, 2 | |
3 | 2F4(2)'.2 → (Fi22.2,16) | 22 | 21555072 | 1a+ + 1001a+ + 1430a+ + 13650a+ + 19305ab + 27027ab + 30030a+ + 51975ab + 133056a± + 289575a- + 386100ab + 400400ab + 405405ab + 579150a+ + 675675a- + 1201200a- + 1351350efgh + 1663200ab + 1796256abcd | [Mue08b] | 1, 2 |
n | U | rank | degree | permutation character | sources | generators | |
---|---|---|---|---|---|---|---|
1 | O8+(2):S3 → ((2.Fi22.2)*,3), (3.Fi22.2,3) | 12 | 741312 | 1a+ + 1001a+ + 3080a+ + 10725a- + 13650a+ + 13728ab + 27027ab + 45045a+ + 48048bc + 50050a- + 96525ab + 123552cd | [Mue08b] | 1, 2 | |
2 | O8+(2):S3 → ((2.Fi22.2)*,3), (3.Fi22.2,3) | 12 | 741312 | 1a+ + 1001a+ + 3080a+ + 10725a- + 13650a+ + 13728ab + 27027ab + 45045a+ + 48048bc + 50050a- + 96525ab + 123552cd | [Mue08b] | 1, 2 | |
3 | O8+(2):S3 → ((2.Fi22.2)*,3), (3.Fi22.2,4) | 16 | 741312 | 1a+ + 351ab + 1001a+ + 3080a+ + 7722ab + 10725a- + 13650a+ + 13728ab + 19305ab + 42120ab + 45045a+ + 48048bc + 50050a- + 54054ab + 61776abcd | [Mue08b] | 1, 2 |
File created automatically by GAP on 2-Sep-2009.