Multiplicity-Free Endomorphism Rings

Data for M22

M22
n U rank degree permutation character PDF sources generators
1 L3(4) 2 22 1a + 21a PDF [PS97], [TomLib] 1, 2
2 24:A6 3 77 1a + 21a + 55a PDF [PS97], [TomLib] 1, 2
3 24:A5 < 24:A6 5 462 1a + 21a + 55a + 154a + 231a PDF [PS97], [TomLib] 1, 2
4 A7 3 176 1a + 21a + 154a PDF [PS97], [TomLib] 1, 2
5 A7 3 176 1a + 21a + 154a PDF [PS97], [TomLib] 1, 2
6 24:S5 4 231 1a + 21a + 55a + 154a PDF [PS97], [TomLib] 1, 2
7 23:L3(2) 5 330 1a + 21a + 55a + 99a + 154a PDF [PS97], [TomLib] 1, 2
8 A6.23 5 616 1a + 21a + 55a + 154a + 385a PDF [PS97], [TomLib] 1, 2
9 L2(11) 6 672 1a + 21a + 55a + 154a + 210a + 231a PDF [Hoe01], [TomLib] 1, 2
M22.2
n U rank degree permutation character PDF sources generators
1 L3(4).22 2 22 1a+ + 21a+ PDF [PS97], [TomLib] 1, 2
2 L3(4) < L3(4).22 4 44 1a± + 21a± PDF [PS97], [TomLib] 1, 2
3 24:S6 3 77 1a+ + 21a+ + 55a+ PDF [PS97], [TomLib] 1, 2
4 24:A5 < 24:S6 10 924 1a± + 21a± + 55a± + 154a± + 231a± PDF [Hoe01], [TomLib] 1, 2
5 24:A6 < 24:S6 6 154 1a± + 21a± + 55a± PDF [Hoe01], [TomLib] 1, 2
6 24:S5 < 24:S6 5 462 1a+ + 21a+ + 55a+ + 154a+ + 231a- PDF [PS97], [TomLib] 1, 2
7 A7 < M22 6 352 1a± + 21a± + 154a± PDF [Hoe01], [TomLib] 1, 2
8 25:S5 4 231 1a+ + 21a+ + 55a+ + 154a+ PDF [PS97], [TomLib] 1, 2
9 24:S5 < 25:S5 8 462 1a± + 21a± + 55a± + 154a± PDF [Hoe01], [TomLib] 1, 2
10 24:(A5 × 2) < 25:S5 6 462 1a+ + 21a± + 55a+ + 154a+ + 210a- PDF [Hoe01], [TomLib] 1, 2
11 23:L3(2) × 2 5 330 1a+ + 21a+ + 55a+ + 99a+ + 154a+ PDF [PS97], [TomLib] 1, 2
12 23:L3(2) < 23:L3(2) × 2 10 660 1a± + 21a± + 55a± + 99a± + 154a± PDF [Hoe01], [TomLib] 1, 2
13 A6.22 5 616 1a+ + 21a+ + 55a+ + 154a+ + 385a+ PDF [PS97], [TomLib] 1, 2
14 A6.23 < A6.22 10 1232 1a± + 21a± + 55a± + 154a± + 385a± PDF [Hoe01], [TomLib] 1, 2
15 A6.22 < A6.22 10 1232 1a+ + 21a± + 55a± + 99a- + 154a+ + 210a- + 231a- + 385a+ PDF [Hoe01], [TomLib] 1, 2
16 L2(11).2 6 672 1a+ + 21a- + 55a+ + 154a+ + 210a- + 231a- PDF [Hoe01], [TomLib] 1, 2
17 L2(11) < L2(11).2 12 1344 1a± + 21a± + 55a± + 154a± + 210a± + 231a± PDF [Hoe01], [TomLib] 1, 2
2.M22
n U rank degree permutation character PDF sources generators
1 24:A5 → (M22,3) 8 924 1a + 21a + 55a + 126ab + 154a + 210b + 231a PDF [Linton] 1, 2
2 A7 → (M22,4) 5 352 1a + 21a + 56a + 120a + 154a PDF [PS97] 1, 2
3 A7 → (M22,5) 5 352 1a + 21a + 56a + 120a + 154a PDF [PS97] 1, 2
4 23:L3(2) → (M22,7) 7 660 1a + 21a + 55a + 99a + 120a + 154a + 210b PDF [Linton] 1, 2
3.M22
n U rank degree permutation character PDF sources generators
1 24:A5 → (M22,3) 13 1386 1a + 21abc + 55a + 105abcd + 154a + 231abc PDF [Linton] 1, 2
2 24:S5 → (M22,6) 10 693 1a + 21abc + 55a + 105abcd + 154a PDF [Linton] 1, 2
3 23:L3(2) → (M22,7) 13 990 1a + 21abc + 55a + 99abc + 105abcd + 154a PDF [Linton] 1, 2
4 L2(11) → (M22,9) 16 2016 1a + 21abc + 55a + 105abcd + 154a + 210abc + 231abc PDF [Linton] 1, 2
6.M22
n U rank degree permutation character PDF sources generators
1 24:A5 → (2.M22,1), (3.M22,1) 22 2772 1a + 21abc + 55a + 105abcd + 126abcdef + 154a + 210bef + 231abc PDF [Linton] 1, 2
2 23:L3(2) → (2.M22,4), (3.M22,3) 17 1980 1a + 21abc + 55a + 99abc + 105abcd + 120a + 154a + 210b + 330de PDF [Linton] 1, 2
2.M22.2
n U rank degree permutation character PDF sources generators
1 24:S5 → (M22.2,6) 7 924 1a+ + 21a+ + 55a+ + 126ab + 154a+ + 210b- + 231a- PDF [Mue08b] 1, 2
2 24:S5 → (M22.2,6) 7 924 1a+ + 21a+ + 55a+ + 126ab + 154a+ + 210b+ + 231a- PDF [Mue08b] 1, 2
3 A7 → (M22.2,7) 10 704 1a± + 21a± + 56a± + 120a± + 154a± PDF [Mue08b] 1, 2
4 23:L3(2) × 2 → (M22.2,11) 7 660 1a+ + 21a+ + 55a+ + 99a+ + 120a- + 154a+ + 210b- PDF [Mue08b] 1, 2
5 23:L3(2) × 2 → (M22.2,11) 7 660 1a+ + 21a+ + 55a+ + 99a+ + 120a+ + 154a+ + 210b+ PDF [Mue08b] 1, 2
6 23:L3(2) → (M22.2,12) 14 1320 1a± + 21a± + 55a± + 99a± + 120a± + 154a± + 210b± PDF [Mue08b] 1, 2
7 L2(11).2 → (M22.2,16) 10 1344 1a+ + 21a- + 55a+ + 56a± + 120a- + 154a+ + 210a- + 231a- + 440a+ PDF [Mue08b] 1, 2
8 L2(11).2 → (M22.2,16) 10 1344 1a+ + 21a- + 55a+ + 56a± + 120a+ + 154a+ + 210a- + 231a- + 440a- PDF [Mue08b] 1, 2
Isoclinic(2.M22.2)
n U rank degree permutation character PDF sources generators
1 A7 → (M22.2,7) 10 704 1a± + 21a± + 56a± + 120a± + 154a± PDF [Mue08b] 1, 2
2 23:L3(2) → (M22.2,12) 14 1320 1a± + 21a± + 55a± + 99a± + 120a± + 154a± + 210b± PDF [Mue08b] 1, 2
3.M22.2
n U rank degree permutation character PDF sources generators
1 24:S5 → (M22.2,6) 9 1386 1a+ + 21a+bc + 55a+ + 105abcd + 154a+ + 231a-bc PDF [Mue08b] 1, 2
2 25:S5 → (M22.2,8) 7 693 1a+ + 21a+bc + 55a+ + 105abcd + 154a+ PDF [Mue08b] 1, 2
3 24:(A5 × 2) → (M22.2,10) 10 1386 1a+ + 21a±bc + 55a+ + 105abcd + 154a+ + 210a- + 231bc PDF [Mue08b] 1, 2
4 23:L3(2) × 2 → (M22.2,11) 9 990 1a+ + 21a+bc + 55a+ + 99a+bc + 105abcd + 154a+ PDF [Mue08b] 1, 2
5 L2(11).2 → (M22.2,16) 11 2016 1a+ + 21a-bc + 55a+ + 105abcd + 154a+ + 210a-bc + 231a-bc PDF [Mue08b] 1, 2
6.M22.2
n U rank degree permutation character PDF sources generators
1 24:S5 → (M22.2,6) 14 2772 1a+ + 21a+bc + 55a+ + 105abcd + 126abcdef + 154a+ + 210b-ef + 231a-bc PDF [Mue08b] 1, 2
2 24:S5 → (M22.2,6) 14 2772 1a+ + 21a+bc + 55a+ + 105abcd + 126abcdef + 154a+ + 210b+ef + 231a-bc PDF [Mue08b] 1, 2
3 23:L3(2) × 2 → (M22.2,11) 12 1980 1a+ + 21a+bc + 55a+ + 99a+bc + 105abcd + 120a- + 154a+ + 210b- + 330de PDF [Mue08b] 1, 2
4 23:L3(2) × 2 → (M22.2,11) 12 1980 1a+ + 21a+bc + 55a+ + 99a+bc + 105abcd + 120a+ + 154a+ + 210b+ + 330de PDF [Mue08b] 1, 2
5 L2(11).2 → (M22.2,16) 20 4032 1a+ + 21a-bc + 55a+ + 56a± + 66abcd + 105abcd + 120a-bc + 154a+ + 210a-cdghij + 231a-bc + 440a+ PDF [Mue08b] 1, 2
6 L2(11).2 → (M22.2,16) 20 4032 1a+ + 21a-bc + 55a+ + 56a± + 66abcd + 105abcd + 120a+bc + 154a+ + 210a-cdghij + 231a-bc + 440a- PDF [Mue08b] 1, 2

[ATLAS page on M22]

File created automatically by GAP on 23-Jul-2009.