Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for 2.HS

Name:
2.HS
Group order:
88704000 = 210 ⋅ 32 ⋅ 53 ⋅ 7 ⋅ 11
Number of classes:
42
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]
Maximal subgroups:
  Order Index Structure Name
1 887040 100 2.M22 2.M22
2 504000 176 Isoclinic(U3(5).2 × 2) Isoclinic(U3(5).2x2)
3 504000 176 Isoclinic(U3(5).2 × 2) 2.HSM3
4 80640 1100 Isoclinic(2.L3(4).21) Isoclinic(2.L3(4).2_1)
5 80640 1100 Isoclinic(S8 × 2) Isoclinic(S8x2)
6 23040 3850 2.24.S6 2.2^4.S6
7 21504 4125 2.43.L3(2) 2.4^3.L3(2)
8 15840 5600 2 × M11 2xM11
9 15840 5600 2 × M11 2.HSM9
10 15360 5775 2.4.24.S5 2.HSM10
11 5760 15400 2.(2 × A6.22) 2.HSM11
12 2400 36960 5:4 × 2.A5 5:4x2.A5
Stored Sylow p normalizers:
p Order Index Structure Name
2 1024 86625 2.HSN2 2.HSN2
3 576 154000 2.HSN3 2.HSN3
5 4000 22176 51+2:8:4 5^(1+2):8:4
7 84 1056000 7:12 7:12
11 110 806400 2 × 11:5 2x11:5
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:
13 available
Group constructions in GAP:
AtlasGroup( "2.HS" ), AtlasSubgroup( "2.HS.2", 1 )
Stored class fusions from this table:
2.HS.2, HS
Stored class fusions to this table:
2.24.S6, 2.43.L3(2), Isoclinic(U3(5).2 × 2), 2 × M11, 2.4.24.S5, 2.(2 × A6.22), 2.HSN2, 2.HSN3, 2.HSN3A, 2.M22, 2 × 11:5, 2 × M11, 5:4 × 2.A5, 51+2:8:4, 7:12, Isoclinic(2.L3(4).21), Isoclinic(S8 × 2), Isoclinic(U3(5).2 × 2), NDG(2.HS, Q8)

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