Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for F₃₊.2

Name:

F3+.2

Group order:

2510411418381323442585600 = 2²² ⋅ 3¹⁶ ⋅ 5² ⋅ 7³ ⋅ 11 ⋅ 13 ⋅ 17 ⋅ 23 ⋅ 29

Number of classes:

183

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., constructions: Aut(F3+)

Maximal subgroups:

	Order	Index	Structure	Name
1	1255205709190661721292800	2	F3+	F3+
2	8178940946586009600	306936	2 × Fi23	2xFi23
3	516494013235200	4860485028	22.Fi22.2	2^2.Fi22.2
4	178278473318400	14081405184	S3 × O8+(3):S3	S3xO8+(3):S3
5	50030759116800	50177360142	O10−(2).2	O10-(2).2
6	20056328248320	125168046080	37.O7(3):2	3^7.O7(3):2
7	9697565306880	258870277120	31+10:(2 × U5(2):2)	3^(1+10):(2xU5(2):2)
8	1002795171840	2503413946215	212.M24	2^12.M24
9	441447874560	5686767482760	22.U6(2):S3 × 2	2^2.U6(2):S3x2
10	321052999680	7819305288795	21+12+.31.U4(3).22122	2^(1+12)_+.3_1.U4(3).2^2_{122}
11	35814871872	70094105804800	33.[310].(L3(3) × 22)	3^3.[3^10].(L3(3)x2^2)
12	27549901440	91122337546240	32.34.38.(S5 × 2S4)	3^2.3^4.3^8.(S5x2S4)
13	25082265600	100087107696576	S4 × O8+(2):S3	S4xO8+(2):S3
14	3963617280	633363728392395	23+12.(L3(2) × S6)	2^(3+12).(L3(2)xS6)
15	3963617280	633363728392395	27+8.(S3 × A8)	2^(7+8).(S3xA8)
16	305690112	8212275503308800	(S3 × S3 × G2(3)):2	(S3xS3xG2(3)):2
17	43545600	57650174033227776	S5 × S9	S5xS9
18	1088640	2306006961329111040	S6 × L2(8):3	S6xL2(8):3
19	211680	11859464372549713920	7:6 × S7	7:6xS7
20	24696	101652551764711833600	71+2+:(6 × S3).2	7^(1+2)_+:(6xS3).2
21	812	3091639677809511628800	29:28	frob

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
5	57600	43583531569120198656	S4 × 52:4S4	S4x5^2:4S4
7	24696	101652551764711833600	71+2+:(6 × S3).2	7^(1+2)_+:(6xS3).2
29	812	3091639677809511628800	29:28	frob

Available Brauer tables:

p
11	dec. matrix (PDF)
13	dec. matrix (PDF)
23	dec. matrix (PDF)

Group constructions in GAP:

AtlasGroup( "Fi24'.2" ), AutomorphismGroup( AtlasGroup( "Fi24'" ) )

Stored class fusions to this table:

2².Fi₂₂.2, 2².U₆(2):S₃ × 2, 2¹².M₂₄, 2¹⁺¹²₊.3₁.U₄(3).2²₁₂₂, 2³⁺¹².(L₃(2) × S₆), 2⁷⁺⁸.(S₃ × A₈), 2 × Fi₂₃, 3.F₃₊.2, 3².3⁴.3⁸.(S₅ × 2S₄), 3³.[3¹⁰].(L₃(3) × 2²), 3⁷.O₇(3):2, 3¹⁺¹⁰:(2 × U₅(2):2), 3¹⁺¹⁰₊:(2 × 2¹⁺⁶₋:3¹⁺²₊:2S₄), 7:6 × S₇, 7¹⁺²₊:(6 × S₃).2, (S₃ × S₃ × G₂(3)):2, F₃₊, O₁₀⁻(2).2, S₃ × O₈⁺(3):S₃, S₄ × 5²:4S₄, S₄ × O₈⁺(2):S₃, S₅ × S₉, S₆ × L₂(8):3, 29:28

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