Multiplicity-Free Endomorphism Rings

Data for M12

M12
n U rank degree permutation character PDF sources generators
1 M11 2 12 1a + 11a PDF [PS97], [TomLib] 1, 2
2 M11 2 12 1a + 11b PDF [PS97], [TomLib] 1, 2
3 L2(11) < M11 5 144 1a + 11ab + 55a + 66a PDF [PS97], [TomLib] 1, 2
4 A6.22 3 66 1a + 11a + 54a PDF [PS97], [TomLib] 1, 2
5 A6.21 < A6.22 5 132 1a + 11ab + 54a + 55a PDF [PS97], [TomLib] 1, 2
6 A6.22 < A6.22 4 132 1a + 11a + 54a + 66a PDF [PS97], [TomLib] 1, 2
7 A6.22 3 66 1a + 11b + 54a PDF [PS97], [TomLib] 1, 2
8 A6.21 < A6.22 5 132 1a + 11ab + 54a + 55a PDF [PS97], [TomLib] 1, 2
9 A6.22 < A6.22 4 132 1a + 11b + 54a + 66a PDF [PS97], [TomLib] 1, 2
10 L2(11) 5 144 1a + 16ab + 45a + 66a PDF [PS97], [TomLib] 1, 2
11 32.2.S4 5 220 1a + 11a + 54a + 55a + 99a PDF [PS97], [TomLib] 1, 2
12 32:2.A4 < 32.2.S4 8 440 1a + 11a + 45a + 54a + 55ac + 99a + 120a PDF [Hoe01], [TomLib] 1, 2
13 32.2.S4 5 220 1a + 11b + 54a + 55a + 99a PDF [PS97], [TomLib] 1, 2
14 32:2.A4 < 32.2.S4 8 440 1a + 11b + 45a + 54a + 55ab + 99a + 120a PDF [Hoe01], [TomLib] 1, 2
M12.2
n U rank degree permutation character PDF sources generators
1 M11 < M12 3 24 1a± + 11ab PDF [PS97], [TomLib] 1, 2
2 L2(11).2 4 144 1a+ + 11ab + 55a+ + 66a+ PDF [PS97], [TomLib] 1, 2
3 A6.22 < M12 5 132 1a± + 11ab + 54a± PDF [PS97], [TomLib] 1, 2
4 A6.22 < A6.22 7 264 1a± + 11ab + 54a± + 66a± PDF [Hoe01], [TomLib] 1, 2
5 L2(11).2 4 144 1a+ + 16ab + 45a+ + 66a+ PDF [PS97], [TomLib] 1, 2
6 32.2.S4 < M12 9 440 1a± + 11ab + 54a± + 55a± + 99a± PDF [Hoe01], [TomLib] 1, 2
7 32:2.A4 < 32.2.S4 14 880 1a± + 11ab + 45a± + 54a± + 55a±bc + 99a± + 120a± PDF [Hoe01], [TomLib] 1, 2
8 (22 × A5).2 7 396 1a+ + 16ab + 45a+ + 54a± + 66a+ + 144a+ PDF [Hoe01], [TomLib] 1, 2
9 (2 × A5).2 < (22 × A5).2 11 792 1a+ + 16ab + 45a+ + 54a± + 55a- + 66a± + 99a- + 144a+ + 176a- PDF [Hoe01], [TomLib] 1, 2
10 M8.(S4 × 2) 8 495 1a+ + 11ab + 54a± + 55a+ + 66a+ + 99a- + 144a+ PDF [Hoe01], [TomLib] 1, 2
11 M8.(A4 × 2) < M8.(S4 × 2) 13 990 1a+ + 11ab + 45a- + 54a± + 55a+ + 66a± + 99a- + 120a± + 144a± PDF [Hoe01], [TomLib] 1, 2
12 42:D12.2 8 495 1a+ + 16ab + 45a- + 54a± + 66a+ + 99a- + 144a+ PDF [Hoe01], [TomLib] 1, 2
13 42:(6 × 2) < 42:D12.2 13 990 1a+ + 16ab + 45a- + 54a± + 55a±bc + 66a+ + 99a± + 144a+ + 176a+ PDF [Hoe01], [TomLib] 1, 2
2.M12
n U rank degree permutation character PDF sources generators
1 M11 → (M12,1) 3 24 1a + 11a + 12a PDF [PS97] 1, 2
2 M11 → (M12,2) 3 24 1a + 11b + 12a PDF [PS97] 1, 2
3 A6.21 → (M12,5) 7 264 1a + 11ab + 12a + 54a + 55a + 120b PDF [Linton] 1, 2
4 A6.21 → (M12,8) 7 264 1a + 11ab + 12a + 54a + 55a + 120b PDF [Linton] 1, 2
5 32.2.S4 → (M12,11) 7 440 1a + 11a + 54a + 55a + 99a + 110ab PDF [Linton] 1, 2
6 32.2.S4 → (M12,13) 7 440 1a + 11b + 54a + 55a + 99a + 110ab PDF [Linton] 1, 2
7 32.2.S4 → (M12,11) 9 440 1a + 11a + 12a + 44ab + 54a + 55a + 99a + 120b PDF [Linton] 1, 2
8 32.2.S4 → (M12,13) 9 440 1a + 11b + 12a + 44ab + 54a + 55a + 99a + 120b PDF [Linton] 1, 2
9 32:2.A4 → (M12,12) 14 880 1a + 11a + 12a + 44ab + 45a + 54a + 55ac + 99a + 110ab + 120ab PDF [Linton] 1, 2
10 32:2.A4 → (M12,14) 14 880 1a + 11b + 12a + 44ab + 45a + 54a + 55ab + 99a + 110ab + 120ab PDF [Linton] 1, 2
2.M12.2
n U rank degree permutation character PDF sources generators
1 M11 → (M12.2,1) 5 48 1a± + 11ab + 12a± PDF [PS97] 1, 2
2 L2(11).2 → (M12.2,2) 7 288 1a+ + 11ab + 12a± + 55a+ + 66a+ + 120b- PDF [Mue08b] 1, 2
3 L2(11).2 → (M12.2,2) 7 288 1a+ + 11ab + 12a± + 55a+ + 66a+ + 120b+ PDF [Mue08b] 1, 2
Isoclinic(2.M12.2)
n U rank degree permutation character PDF sources generators
1 M11 → (M12.2,1) 5 48 1a± + 11ab + 12a± PDF [PS97] 1, 2

[ATLAS page on M12]

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