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.