Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for 12.M22

Name:
12.M22
Group order:
5322240 = 29 ⋅ 33 ⋅ 5 ⋅ 7 ⋅ 11
Number of classes:
109
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]
Maximal subgroups:
  Order Index Structure Name
1 241920 22 121.L3(4) 12_1.L3(4)
2 69120 77 2.25:3A6 12.M22M2
3 30240 176 2.(2 × 3.A7) 2.(2x3.A7)
4 30240 176 2.(2 × 3.A7) 2.(2x3.A7)
5 23040 231 3 × 2.(25:S5) 3x4.M22M5
6 16128 330 3 × 2.(2 × 23:L3(2)) 3x4.M22M6
7 8640 616 (4 × 3.A6).23 12.M22M7
8 7920 672 3 × 2.(2 × L2(11)) 3x2.(2xL2(11))
Stored Sylow p normalizers:
p Order Index Structure Name
2 1536 3465 3 × 4.M22N2 3x4.M22N2
3 864 6160 12.M22N3 12.M22N3
5 240 22176 3 × Isoclinic(2 × 5:8) 3xIsoclinic(2x5:8)
7 252 21120 12 × 7:3 12x7:3
11 660 8064 12 × 11:5 12x11:5
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
11 dec. matrix (PDF)
Atlas representations:
22 available
Group constructions in GAP:
AtlasGroup( "12.M22" )
Stored class fusions from this table:
2.M22, 3.M22, 4.M22, 6.M22, 12.M22.2, M22
Stored class fusions to this table:
2.(2 × 3.A7), 3 × 2.(2 × L2(11)), 3 × 2.(25:S5), 3 × 2.(2 × 23:L3(2)), 3 × 4.M22N2, 3 × Isoclinic(2 × 5:8), 2.25:3A6, (4 × 3.A6).23, 12.M22N3, 121.L3(4), 12 × 7:3, 12 × 11:5, NDG(12.M22, 32)

File created automatically by GAP on 13-Mar-2024.