Multiplicity-Free Endomorphism Rings

Data for Fi22

Fi22
n U rank degree permutation character PDF sources generators
1 2.U6(2) 3 3510 1a + 429a + 3080a PDF [PS97] 1, 2
2 O7(3) 3 14080 1a + 429a + 13650a PDF [PS97] 1, 2
3 O7(3) 3 14080 1a + 429a + 13650a PDF [PS97] 1, 2
4 O8+(2):S3 4 61776 1a + 3080a + 13650a + 45045a PDF [PS97] 1, 2
5 O8+(2):3 < O8+(2):S3 7 123552 1a + 1001a + 3080a + 10725a + 13650a + 45045a + 50050a PDF [Hoe01] 1, 2
6 O8+(2):2 < O8+(2):S3 7 185328 1a + 429a + 3080a + 13650a + 45045a + 48048a + 75075a PDF [Hoe01] 1, 2
7 210:M22 8 142155 1a + 78a + 429a + 1430a + 3080a + 30030a + 32032a + 75075a PDF [Hoe01] 1, 2
8 26:S6(2) 10 694980 1a + 429a + 1430a + 3080a + 13650a + 30030a + 45045a + 75075a + 205920a + 320320a PDF [Hoe01] 1, 2
9 2F4(2)' 11 3592512 1a + 1001a + 1430a + 13650a + 30030a + 289575a + 400400ab + 579150a + 675675a + 1201200a PDF [Hoe01] 1, 2
Fi22.2
n U rank degree permutation character PDF sources generators
1 2.U6(2).2 3 3510 1a+ + 429a+ + 3080a+ PDF [PS97] 1, 2
2 2.U6(2) < 2.U6(2).2 6 7020 1a± + 429a± + 3080a± PDF [Hoe01] 1, 2
3 O7(3) < Fi22 6 28160 1a± + 429a± + 13650a± PDF [Hoe01] 1, 2
4 O8+(2):S3 × 2 4 61776 1a+ + 3080a+ + 13650a+ + 45045a+ PDF [PS97] 1, 2
5 O8+(2):S3 < O8+(2):S3 × 2 8 123552 1a± + 3080a± + 13650a± + 45045a± PDF [Hoe01] 1, 2
6 O8+(2):3 × 2 < O8+(2):S3 × 2 7 123552 1a+ + 1001a- + 3080a+ + 10725a+ + 13650a+ + 45045a+ + 50050a+ PDF [Hoe01] 1, 2
7 O8+(2):S3 < O8+(2):S3 × 2 7 123552 1a+ + 1001a+ + 3080a+ + 10725a- + 13650a+ + 45045a+ + 50050a- PDF [Hoe01] 1, 2
8 O8+(2):2 × 2 < O8+(2):S3 × 2 7 185328 1a+ + 429a+ + 3080a+ + 13650a+ + 45045a+ + 48048a+ + 75075a+ PDF [Hoe01] 1, 2
9 O8+(2):3 < O8+(2):S3 × 2 14 247104 1a± + 1001a± + 3080a± + 10725a± + 13650a± + 45045a± + 50050a± PDF [Hoe01] 1, 2
10 O8+(2):2 < Fi22 14 370656 1a± + 429a± + 3080a± + 13650a± + 45045a± + 48048a± + 75075a± PDF [Hoe01] 1, 2
11 O8+(2):2 < O8+(2):S3 × 2 13 370656 1a+ + 429a± + 1001a+ + 3080a+ + 10725a- + 13650a+ + 45045a+ + 48048a± + 50050a- + 75075a± PDF [Hoe01] 1, 2
12 210:M22.2 8 142155 1a+ + 78a+ + 429a+ + 1430a+ + 3080a+ + 30030a+ + 32032a+ + 75075a+ PDF [Hoe01] 1, 2
13 210:M22 < 210:M22.2 16 284310 1a± + 78a± + 429a± + 1430a± + 3080a± + 30030a± + 32032a± + 75075a± PDF [Hoe01] 1, 2
14 27:S6(2) 10 694980 1a+ + 429a+ + 1430a+ + 3080a+ + 13650a+ + 30030a+ + 45045a+ + 75075a+ + 205920a+ + 320320a+ PDF [Hoe01] 1, 2
15 26:S6(2) < 27:S6(2) 20 1389960 1a± + 429a± + 1430a± + 3080a± + 13650a± + 30030a± + 45045a± + 75075a± + 205920a± + 320320a± PDF [Hoe01] 1, 2
16 2F4(2)'.2 10 3592512 1a+ + 1001a+ + 1430a+ + 13650a+ + 30030a+ + 289575a- + 400400ab + 579150a+ + 675675a- + 1201200a- PDF [Hoe01] 1, 2
2.Fi22
n U rank degree permutation character PDF sources generators
1 O7(3) → (Fi22,2) 5 28160 1a + 352a + 429a + 13650a + 13728a PDF [PS97] 1, 2
2 O7(3) → (Fi22,3) 5 28160 1a + 352a + 429a + 13650a + 13728b PDF [PS97] 1, 2
3 O8+(2):S3 → (Fi22,4) 6 123552 1a + 3080a + 13650a + 13728a + 45045a + 48048b PDF [Linton] 1, 2
4 O8+(2):S3 → (Fi22,4) 6 123552 1a + 3080a + 13650a + 13728b + 45045a + 48048c PDF [Linton] 1, 2
5 O8+(2):3 → (Fi22,5) 11 247104 1a + 1001a + 3080a + 10725a + 13650a + 13728ab + 45045a + 48048bc + 50050a PDF [Linton] 1, 2
6 O8+(2):2 → (Fi22,6) 11 370656 1a + 352a + 429a + 3080a + 13650a + 13728a + 45045a + 48048ab + 75075a + 123200a PDF [Linton] 1, 2
7 O8+(2):2 → (Fi22,6) 11 370656 1a + 352a + 429a + 3080a + 13650a + 13728b + 45045a + 48048ac + 75075a + 123200a PDF [Linton] 1, 2
3.Fi22
n U rank degree permutation character PDF sources generators
1 O8+(2):S3 → (Fi22,4) 10 185328 1a + 351ab + 3080a + 13650a + 19305ab + 42120ab + 45045a PDF [Linton] 1, 2
2 O8+(2):3 → (Fi22,5) 11 370656 1a + 1001a + 3080a + 10725a + 13650a + 27027ab + 45045a + 50050a + 96525ab PDF [Linton] 1, 2
3 O8+(2):3 → (Fi22,5) 17 370656 1a + 351ab + 1001a + 3080a + 7722ab + 10725a + 13650a + 19305ab + 42120ab + 45045a + 50050a + 54054ab PDF [Linton] 1, 2
4 O8+(2):2 → (Fi22,6) 17 555984 1a + 351ab + 429a + 3080a + 13650a + 19305ab + 27027ab + 42120ab + 45045a + 48048a + 75075a + 96525ab PDF [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 PDF [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 PDF [Linton] 1, 2
6.Fi22
n U rank degree permutation character PDF sources generators
1 O8+(2):S3 → (2.Fi22,3), (3.Fi22,1) 14 370656 1a + 351ab + 3080a + 13650a + 13728a + 19305ab + 42120ab + 45045a + 48048b + 61776ab PDF [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 PDF [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 PDF [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 PDF [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 PDF [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 PDF [Linton] 1, 2
2.Fi22.2
n U rank degree permutation character PDF sources generators
1 O7(3) → (Fi22.2,3) 9 56320 1a± + 352a± + 429a± + 13650a± + 13728ab PDF [Mue08b] 1, 2
2 O8+(2):S3 → (Fi22.2,5) 10 247104 1a± + 3080a± + 13650a± + 13728ab + 45045a± + 48048bc PDF [Mue08b] 1, 2
3 O8+(2):3 × 2 → (Fi22.2,6) 9 247104 1a+ + 1001a- + 3080a+ + 10725a+ + 13650a+ + 13728ab + 45045a+ + 48048bc + 50050a+ PDF [Mue08b] 1, 2
4 O8+(2):2 → (Fi22.2,10) 20 741312 1a± + 352a± + 429a± + 3080a± + 13650a± + 13728ab + 45045a± + 48048a±bc + 75075a± + 123200a± PDF [Mue08b] 1, 2
5 2F4(2)'.2 → (Fi22.2,16) 13 7185024 1a+ + 1001a+ + 1430a+ + 13650a+ + 30030a+ + 133056a± + 289575a- + 400400ab + 579150a+ + 675675a- + 1201200a- + 1663200ab PDF [Mue08b] 1, 2
6 2F4(2)'.2 → (Fi22.2,16) 13 7185024 1a+ + 1001a+ + 1430a+ + 13650a+ + 30030a+ + 133056a± + 289575a- + 400400ab + 579150a+ + 675675a- + 1201200a- + 1663200ab PDF [Mue08b] 1, 2
Isoclinic(2.Fi22.2)
n U rank degree permutation character PDF sources generators
1 O7(3) → (Fi22.2,3) 9 56320 1a± + 352a± + 429a± + 13650a± + 13728ab PDF [Mue08b] 1, 2
2 O8+(2):S3 → (Fi22.2,5) 10 247104 1a± + 3080a± + 13650a± + 13728ab + 45045a± + 48048bc PDF [Mue08b] 1, 2
3 O8+(2):S3 → (Fi22.2,7) 9 247104 1a+ + 1001a+ + 3080a+ + 10725a- + 13650a+ + 13728ab + 45045a+ + 48048bc + 50050a- PDF [Mue08b] 1, 2
4 O8+(2):2 → (Fi22.2,10) 20 741312 1a± + 352a± + 429a± + 3080a± + 13650a± + 13728ab + 45045a± + 48048a±bc + 75075a± + 123200a± PDF [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± PDF [Mue08b] 1, 2
3.Fi22.2
n U rank degree permutation character PDF sources generators
1 O8+(2):S3 × 2 → (Fi22.2,4) 7 185328 1a+ + 351ab + 3080a+ + 13650a+ + 19305ab + 42120ab + 45045a+ PDF [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 PDF [Mue08b] 1, 2
3 O8+(2):S3 → (Fi22.2,7) 9 370656 1a+ + 1001a+ + 3080a+ + 10725a- + 13650a+ + 27027ab + 45045a+ + 50050a- + 96525ab PDF [Mue08b] 1, 2
4 O8+(2):S3 → (Fi22.2,7) 12 370656 1a+ + 351ab + 1001a+ + 3080a+ + 7722ab + 10725a- + 13650a+ + 19305ab + 42120ab + 45045a+ + 50050a- + 54054ab PDF [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 PDF [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 PDF [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 PDF [Mue08b] 1, 2
6.Fi22.2
n U rank degree permutation character PDF 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 PDF [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 PDF [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 PDF [Mue08b] 1, 2
Isoclinic(6.Fi22.2)
n U rank degree permutation character PDF 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 PDF [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 PDF [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 PDF [Mue08b] 1, 2

[ATLAS page on Fi22]

File created automatically by GAP on 2-Sep-2009.