Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for He.2

Name:
He.2
Group order:
8060774400 = 211 ⋅ 33 ⋅ 52 ⋅ 73 ⋅ 17
Number of classes:
45
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,17], constructions: Aut(He)
Duplicates:
F3+M14
Maximal subgroups:
  Order Index Structure Name
1 4030387200 2 He He
2 3916800 2058 S4(4).4 S4(4).4
3 967680 8330 22.L3(4).D12 2^2.L3(4).D12
4 43008 187425 21+6+.L3(2).2 2^(1+6)_+.L3(2).2
5 32928 244800 72:2.L2(7).2 7^2:2.L2(7).2
6 30240 266560 3.S7 × 2 3.s7x2
7 28800 279888 (S5 × S5):2 s5wrs2
8 18432 437325 24+4.(S3 × S3).2 2^(4+4).(S3xS3).2
9 12348 652800 71+2:(S3 × 6) 7^(1+2):(S3x6)
10 8064 999600 S4 × L3(2).2 S4xL3(2).2
11 7056 1142400 7:6 × L3(2) 7:6xL3(2)
12 2400 3358656 52:4S4 Fi22N5
Stored Sylow p normalizers:
p Order Index Structure Name
5 2400 3358656 52:4S4 Fi22N5
7 12348 652800 71+2:(S3 × 6) 7^(1+2):(S3x6)
17 272 29635200 17:16 17:16
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
17 dec. matrix (PDF)
Atlas representations:
21 available
Group constructions in GAP:
AtlasGroup( "He.2" ), AutomorphismGroup( AtlasGroup( "He" ) ), PrimitiveGroup( 2058, 2 )
Stored class fusions from this table:
F3+
Stored class fusions to this table:
22.L3(4).D12, 21+6+.L3(2).2, 24+4.(S3 × S3).2, 3.S7 × 2, 5:4 × S5, 7:6 × L3(2), 72:2.L2(7).2, 71+2:(S3 × 6), 17:16, (7:3 × He):2, 52:4S4, He, NDG(He.2, 32), S4(4).4, S4 × L3(2).2, (S5 × S5):2

File created automatically by GAP on 20-May-2025.