Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for HS.2

Name:
HS.2
Group order:
88704000 = 210 ⋅ 32 ⋅ 53 ⋅ 7 ⋅ 11
Number of classes:
39
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11], constructions: Aut(HS)
Maximal subgroups:
  Order Index Structure Name
1 44352000 2 HS HS
2 887040 100 M22.2 M22.2
3 80640 1100 L3(4).22 L3(4).2^2
4 80640 1100 S8 × 2 S8x2
5 23040 3850 25.S6 2^5.S6
6 21504 4125 43:(L3(2) × 2) 4^3:(L3(2)x2)
7 15360 5775 21+6+:S5 2^(1+6)_+:S5
8 5760 15400 (2 × A6.22).2 (2xA6.2^2).2
9 4000 22176 51+2+:[25] HS.2N5
10 2400 36960 5:4 × S5 5:4xS5
Stored Sylow p normalizers:
p Order Index Structure Name
5 4000 22176 51+2+:[25] HS.2N5
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:
68 available
Group constructions in GAP:
AtlasGroup( "HS.2" ), AtlasStabilizer( "Co2", "Co2G1-p476928B0" ), AtlasSubgroup( "Co2", 5 ), AutomorphismGroup( AtlasGroup( "HS" ) ), PrimitiveGroup( 100, 4 ), PrimitiveGroup( 1100, 3 ), PrimitiveGroup( 1100, 4 ), PrimitiveGroup( 3850, 2 )
Stored class fusions from this table:
Co2
Stored class fusions to this table:
2.HS.2, 25.S6, 21+6+:S5, 4.HS.2, 43:(L3(2) × 2), 5:4 × S5, 11:10, (2 × A6.22).2, HS, 51+2+:[25], Isoclinic(2.HS.2), L3(4).22, M22.2, S8 × 2

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