Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 2.Fi₂₂

Name:

2.Fi22

Group order:

129123503308800 = 2¹⁸ ⋅ 3⁹ ⋅ 5² ⋅ 7 ⋅ 11 ⋅ 13

Number of classes:

114

InfoText value:

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

Duplicates:

2.2E6(2)M9

Maximal subgroups:

	Order	Index	Structure	Name
1	36787322880	3510	22.U6(2)	2^2.U6(2)
2	9170703360	14080	2 × O7(3)	2xO7(3)
3	9170703360	14080	2 × O7(3)	2.Fi22M3
4	2090188800	61776	O8+(2):S3 × 2	O8+(2):S3x2
5	908328960	142155	211.M22	2.Fi22M5
6	185794560	694980	27:S6(2)	S8(2)M3
7	106168320	1216215	2.(2 × 21+8):U4(2):2	2.(2x2^(1+8)):U4(2):2
8	78382080	1647360	S3 × 2.U4(3).22	S3x2.U4(3).2_2
9	35942400	3592512	2 × 2F4(2)'	2x2F4(2)'
10	35389440	3648645	21+5+8.(S3 × A6)	2^(1+5+8).(S3xA6)
11	10077696	12812800	2.(31+6:23+4:32:2)	2.(3^(1+6):2^(3+4):3^2:2)
12	7257600	17791488	S10 × 2	S10x2
13	7257600	17791488	S10 × 2	2.Fi22M13
14	190080	679311360	2 × M12	2xm12

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	262144	492567075	2.Fi22N2	2.Fi22N2
3	157464	820019200	2 × Fi22N3	2xFi22N3
5	4800	26900729856	2 × Fi22N5	2xFi22N5
7	504	256197427200	2 × S3 × 7:6	2xS3x7:6
11	220	586925015040	22 × 11:5	2^2x11:5
13	156	827714764800	2 × 13:6	2x13:6

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)

Atlas representations:

12 available

Group constructions in GAP:

AtlasGroup( "2.Fi22" ), AtlasStabilizer( "Fi23", "F23G1-p31671B0" ), AtlasSubgroup( "Fi23", 1 )

Stored class fusions from this table:

2.²E₆(2), 2.Fi₂₂.2, Fi₂₂, Fi₂₂, Fi₂₃

Stored class fusions to this table:

2.(2 × 2¹⁺⁸):U₄(2):2, 2.(3¹⁺⁶:2³⁺⁴:3²:2), 2 × O₇(3), 2¹¹.M₂₂, S₁₀ × 2, 2.Fi₂₂N2, 2 × 2.Fi₂₂, 2².U₆(2), 2² × 11:5, 2¹⁺⁵⁺⁸.(S₃ × A₆), 2 × ²F₄(2)', 2 × 3⁵.3³.(2 × S₄), 2 × 3⁵.3¹⁺².2.S₄, 2 × 3⁵:U₄(2):2, 2 × 3³⁺³:L₃(3), 2 × 3^(3+3)b:L₃(3), 2 × 13:6, 2 × (3¹⁺⁶.3)a.2.S₄, 2 × (3¹⁺⁶.3)b.2.S₄, 2 × Fi₂₂N3, 2 × Fi₂₂N5, 2 × O₇(3), 2 × S₃ × 7:6, 2 × M₁₂, 5:4 × S₅ × 2, 6.Fi₂₂, 2 × 6.Fi₂₂, O₈⁺(2):S₃ × 2, S₃ × 2.U₄(3).2₂, 2⁷:S₆(2), S₁₀ × 2

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