Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for F4(2).2

Name:
F4(2).2
Group order:
6622253206732800 = 225 ⋅ 36 ⋅ 52 ⋅ 72 ⋅ 13 ⋅ 17
Number of classes:
91
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., constructions: Aut(F4(2))
Maximal subgroups:
  Order Index Structure Name
1 3311126603366400 2 F4(2) F4(2)
2 1509949440 4385745 [220]:A6.22 [2^20]:A6.2^2
3 301989888 21928725 [222]:(S3 × S3):2 [2^22]:(S3xS3):2
4 71884800 92123136 2F4(2) × 2 2F4(2)x2
5 24261120 272957440 L4(3).22 L4(3).2^2
6 3916800 1690730496 S4(4).4 S4(4).4
7 2073600 3193602048 (S6 ≀ 2).2 (S6wr2).2
8 186624 35484467200 F4(2).2M8 F4(2).2M8
9 112896 58657996800 (L3(2) × L3(2)).4 (L3(2)xL3(2)).4
10 7056 938527948800 72:(3 × 2S4) 7^2:(3x2S4)
Stored Sylow p normalizers:
p Order Index Structure Name
7 7056 938527948800 72:(3 × 2S4) 7^2:(3x2S4)
Available Brauer tables:
p  
13 dec. matrix (PDF)
Atlas representations:
2 available
Group constructions in GAP:
AtlasGroup( "F4(2).2" ), AutomorphismGroup( AtlasGroup( "F4(2)" ) )
Stored class fusions to this table:
2.(2 × F4(2)).2, 2.F4(2).2, 2F4(2) × 2, 72:(3 × 2S4), (22 × F4(2)):2, (L3(2) × L3(2)).4, (S6 ≀ 2).2, F4(2), F4(2).2M8, Isoclinic(2.F4(2).2), L4(3).22, S4(4).4, [220]:A6.22, [222]:(S3 × S3):2

File created automatically by GAP on 9-May-2025.