Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for F₄(2)

Name:

F4(2)

Group order:

3311126603366400 = 2²⁴ ⋅ 3⁶ ⋅ 5² ⋅ 7² ⋅ 13 ⋅ 17

Number of classes:

95

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r.

Duplicates:

2E6(2)M4, 2E6(2)M5

Maximal subgroups:

	Order	Index	Structure	Name
1	47563407360	69615	(21+8 × 26):S6(2)	(2^(1+8)x2^6):S6(2)
2	47563407360	69615	(21+8 × 26):S6(2)	F4(2)M2
3	47377612800	69888	S8(2)	S8(2)
4	47377612800	69888	S8(2)	F4(2)M4
5	1056964608	3132675	[220]:(S3 × L3(2))	[2^20]:(S3xL3(2))
6	1056964608	3132675	[220]:(S3 × L3(2))	F4(2)M6
7	1045094400	3168256	O8+(2).3.2	O8+(2).3.2
8	1045094400	3168256	O8+(2).3.2	F4(2)M8
9	634023936	5222400	3D4(2).3	3D4(2).3
10	634023936	5222400	3D4(2).3	F4(2)M10
11	35942400	92123136	2F4(2)'.2	2F4(2)'.2
12	12130560	272957440	L4(3).22	L4(3).2_2
13	93312	35484467200	3.(32:Q8 × 32:Q8).S3	F4(2)M13
14	56448	58657996800	(L3(2) × L3(2)):2	(L3(2)xL3(2)):2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
5	2400	1379636084736	52:4S4	Fi22N5
7	3528	938527948800	72:(3 × 2A4)	7^2:(3x2A4)
13	156	21225170534400	13:12	13:12
17	136	24346519142400	17:8	17:8

Available Brauer tables:

p
2	dec. matrix (PDF)
3	dec. matrix (PDF)
5	dec. matrix (PDF)
7	dec. matrix (PDF)
13	dec. matrix (PDF)
17	dec. matrix (PDF)

Atlas representations:

2 available

Group constructions in GAP:

AtlasGroup( "F4(2)" )

Stored class fusions from this table:

²E₆(2), E₆(2), F₄(2).2

Stored class fusions to this table:

2.F₄(2), ²F₄(2)'.2, 2 × 2.F₄(2), ³D₄(2).3, 5:4 × S₆, 6 × 2.F₄(2), 7²:(3 × 2A₄), 13:12, 17:8, (2¹⁺⁸ × 2⁶):S₆(2), (7:3 × L₂(7)):2, (L₃(2) × L₃(2)):2, (2¹⁺⁸ × 2⁶):S₆(2), S₈(2), [2²⁰]:(S₃ × L₃(2)), O₈⁺(2).3.2, ³D₄(2).3, 3.(3²:Q₈ × 3²:Q₈).S₃, (7:3 × L₂(7)):2, 5²:4S₄, L₄(3).2₂, O₈⁺(2).3.2, S₃ × S₆(2), S₈(2), [2²⁰]:(S₃ × L₃(2))

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