Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 3.Fi₂₂

Name:

3.Fi22

Group order:

193685254963200 = 2¹⁷ ⋅ 3¹⁰ ⋅ 5² ⋅ 7 ⋅ 11 ⋅ 13

Number of classes:

165

InfoText value:

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

Duplicates:

3.2E6(2)M8, 3.2E6(2)M9

Maximal subgroups:

	Order	Index	Structure	Name
1	55180984320	3510	6.U6(2)	6.U6(2)
2	13756055040	14080	3.O7(3)	3.O7(3)
3	13756055040	14080	3.O7(3)	3.Fi22M3
4	3135283200	61776	3 × O8+(2):S3	3xO8+(2):S3
5	1362493440	142155	210:3.M22	3.Fi22M5
6	278691840	694980	3 × 26:S6(2)	3x2^6:S6(2)
7	159252480	1216215	3 × (2 × 21+8):U4(2):2	3x(2x2^(1+8)):U4(2):2
8	117573120	1647360	S3 × 31.U4(3).22	S3x3_1.U4(3).2_2
9	53913600	3592512	3 × 2F4(2)'	3x2F4(2)'
10	53084160	3648645	25+8:(S3 × 3.A6)	2^(5+8):(S3x3.A6)
11	15116544	12812800	3.31+6:23+4:32:2	3.3^(1+6):2^(3+4):3^2:2
12	10886400	17791488	3 × A10.2	3xA10.2
13	10886400	17791488	3 × A10.2	3xA10.2
14	285120	679311360	3 × M12	3xM12

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	393216	492567075	3 × Fi22N2	3xFi22N2
3	236196	820019200	3.Fi22N3	3.Fi22N3
5	7200	26900729856	3 × Fi22N5	3xFi22N5
7	756	256197427200	3 × S3 × 7:6	3xS3x7:6
11	330	586925015040	6 × 11:5	6x11:5
13	234	827714764800	3 × 13:6	3x13:6

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:

8 available

Group constructions in GAP:

AtlasGroup( "3.Fi22" ), AtlasSubgroup( "3.Fi22.2", 1 )

Stored class fusions from this table:

3.²E₆(2), 3.Fi₂₂.2, Fi₂₂

Stored class fusions to this table:

2⁵⁺⁸:(2 × 3.A₆), 2⁵⁺⁸:(S₃ × 3.A₆), 2 × 6.Fi₂₂, 3.3¹⁺⁶:2³⁺⁴:3²:2, 3.O₇(3), 2¹⁰:3.M₂₂, 3.Fi₂₂N3, 3.O₇(3), 3 × ²F₄(2)', 3 × 2⁶.2⁵.S₆, 3 × 2⁶:S₆(2), 3 × 2¹⁰.2².2².S₄, 3 × 2¹⁰.2³.L₃(2), 3 × 2¹⁰.2³.S₄, 3 × 2¹⁰.2⁴.S₅, 3 × 2⁵⁺⁸:(2 × S₄), 3 × 2⁵⁺⁸:(S₃ × D₈), 3 × 2⁵⁺⁸:(S₃ × S₄), 3 × 5:4 × S₅, 3 × 13:6, 3 × (2 × 2¹⁺⁸):U₄(2):2, 3 × (2 × 2¹⁺⁸₊).2.2⁴.(S₃ × S₃), 3 × A₁₀.2, 3 × Fi₂₂N2, 3 × Fi₂₂N5, 3 × M₁₂, 3 × O₈⁺(2):S₃, 3 × S₃ × 7:6, 6.Fi₂₂, 6.U₆(2), 6 × 11:5, S₃ × 3₁.U₄(3).2₂

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