Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for Fi₂₃

Name:

Fi23

Group order:

4089470473293004800 = 2¹⁸ ⋅ 3¹³ ⋅ 5² ⋅ 7 ⋅ 11 ⋅ 13 ⋅ 17 ⋅ 23

Number of classes:

98

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	129123503308800	31671	2.Fi22	2.Fi22
2	29713078886400	137632	O8+(3).3.2	O8+(3).3.2
3	73574645760	55582605	22.U6(2).2	2^2.U6(2).2
4	47377612800	86316516	S8(2)	S8(2)
5	27512110080	148642560	S3 × O7(3)	S3xO7(3)
6	20891566080	195747435	211.M23	2..11.m23
7	3265173504	1252451200	31+8.21+6.31+2.2S4	3^(1+8).2^(1+6).3^(1+2).2S4
8	663238368	6165913600	33.[37].(2 × L3(3))	Fi23M8
9	479001600	8537488128	S12	A12.2
10	318504960	12839581755	(22 × 21+8).(3 × U4(2)).2	(2^2x2^(1+8)).(3xU4(2)).2
11	247726080	16508033685	26+8:(A7 × S3)	2^(6+8):(A7xS3)
12	34836480	117390461760	S4 × S6(2)	S4xS6(2)
13	3916800	1044084577536	S4(4).4	S4(4).4
14	6072	673496454758400	L2(23)	L2(23)

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	262144	15600091832325	2.Fi22N2	2.Fi22N2
3	12754584	320627507200	Fi23N3	Fi23N3
5	4800	851973015269376	2 × Fi22N5	2xFi22N5
7	5040	811402871685120	7:6 × A5.2	7:6xA5.2
11	440	9294251075665920	(22 × 11:5).2	(2^2x11:5).2
13	468	8738184771993600	S3 × 13:6	S3x13:6
17	272	15034817916518400	17:16	17:16
23	253	16163914914201600	23:11	23:11

Available Brauer tables:

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

Atlas representations:

15 available

Group constructions in GAP:

AtlasGroup( "Fi23" ), AtlasStabilizer( "Fi24'", "F24G1-p306936B0" ), AtlasSubgroup( "B", 3 )

Stored class fusions from this table:

3.F₃₊, B, F₃₊

Stored class fusions to this table:

2¹¹.M₂₃, 2.Fi₂₂, 2.Fi₂₂N2, 2².U₆(2).2, 2⁶⁺⁸:(A₇ × S₃), 2 × Fi₂₂N5, 3⁶:L₄(3):2₂, 3¹⁺⁸.2¹⁺⁶.3¹⁺².2S₄, 5:4 × S₇, 7:6 × A₅.2, 17:16, 23:11, (2² × 2¹⁺⁸).(3 × U₄(2)).2, (2² × 11:5).2, S₁₂, D₈ × S₆(2), 3³.[3⁷].(2 × L₃(3)), Fi₂₃N3, L₂(23), O₈⁺(3).3.2, S₃ × 13:6, S₃ × O₇(3), S₄(4).4, S₄ × S₆(2), S₈(2)

File created automatically by GAP on 6-May-2025.