Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for 6.Fi₂₂

Name:

6.Fi22

Group order:

387370509926400 = 2¹⁸ ⋅ 3¹⁰ ⋅ 5² ⋅ 7 ⋅ 11 ⋅ 13

Number of classes:

282

InfoText value:

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

Duplicates:

6.Fi₂₂

Some maximal subgroups:

	Order	Index	Structure	Name
1	110361968640	3510	(22 × 3).U6(2)	(2^2x3).U6(2)
2	27512110080	14080	2 × 3.O7(3)	2x3.O7(3)
3	27512110080	14080	2 × 3.O7(3)	6.Fi22M3
4	6270566400	61776	6 × O8+(2):S3	6xO8+(2):S3
5	2724986880	142155	211.3.M22	6.Fi22M5
8	235146240	1647360	S3 × 61.U4(3).22	S3x6_1.U4(3).2_2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	786432	492567075	3 × 2.Fi22N2	3x2.Fi22N2
3	472392	820019200	2 × 3.Fi22N3	2x3.Fi22N3
5	14400	26900729856	6 × Fi22N5	6xFi22N5
7	1512	256197427200	6 × S3 × 7:6	6xS3x7:6
11	660	586925015040	2 × 6 × 11:5	2x6x11:5
13	468	827714764800	6 × 13:6	6x13:6

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:

6 available

Group constructions in GAP:

AtlasGroup( "6.Fi22" ), AtlasSubgroup( "6.Fi22.2", 1 )

Stored class fusions from this table:

2.Fi₂₂, Fi₂₂, 3.Fi₂₂, 3.Fi₂₂, 6.²E₆(2), 6.Fi₂₂.2, Fi₂₂

Stored class fusions to this table:

2 × 3.Fi₂₂N3, 2 × 3.O₇(3), 2 × 6 × 11:5, 3 × 2.Fi₂₂N2, 2 × 3.O₇(3), 2¹¹.3.M₂₂, 6 × 5:4 × S₅, 6 × 13:6, 6 × Fi₂₂N5, 6 × O₈⁺(2):S₃, 6 × S₃ × 7:6, 2 × 6.Fi₂₂, (2² × 3).U₆(2), S₃ × 6₁.U₄(3).2₂

File created automatically by GAP on 13-Mar-2024.