Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for Fi₂₂

Name:

Fi22

Group order:

64561751654400 = 2¹⁷ ⋅ 3⁹ ⋅ 5² ⋅ 7 ⋅ 11 ⋅ 13

Number of classes:

65

InfoText value:

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

Duplicates:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	18393661440	3510	2.U6(2)	2.U6(2)
2	4585351680	14080	O7(3)	O7(3)
3	4585351680	14080	O7(3)	Fi22M3
4	1045094400	61776	O8+(2).3.2	O8+(2).3.2
5	454164480	142155	210:M22	2^10:m22
6	92897280	694980	26:S6(2)	2^6:s6f2
7	53084160	1216215	(2 × 21+8):U4(2):2	(2x2^(1+8)):U4(2):2
8	39191040	1647360	S3 × U4(3).22	S3xU4(3).2_2
9	17971200	3592512	2F4(2)'	2F4(2)'
10	17694720	3648645	25+8:(S3 × A6)	2^(5+8):(S3xA6)
11	5038848	12812800	31+6:23+4:32:2	3^(1+6):2^(3+4):3^2:2
12	3628800	17791488	S10	A10.2
13	3628800	17791488	S10	A10.2
14	95040	679311360	M12	M12

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	131072	492567075	f22s2	f22s2
3	78732	820019200	Fi22N3	Fi22N3
5	2400	26900729856	52:4S4	Fi22N5
7	252	256197427200	S3 × 7:6	S3x7:6
11	110	586925015040	2 × 11:5	2x11:5
13	78	827714764800	13:6	13:6

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:

24 available

Group constructions in GAP:

AtlasGroup( "Fi22" ), AtlasSubgroup( "Fi22.2", 1 ), PrimitiveGroup( 3510, 1 )

Stored class fusions from this table:

²E₆(2), Fi₂₂.2

Stored class fusions to this table:

2.Fi₂₂, 2.U₆(2), ²F₄(2)', 2⁶.2⁵.S₆, 2⁶:S₆(2), 2¹⁰.2².2².S₄, 2¹⁰.2³.L₃(2), 2¹⁰.2³.S₄, 2¹⁰.2⁴.S₅, 2¹⁰:M₂₂, 2⁵⁺⁸:(2 × A₆), 2⁵⁺⁸:(2 × S₄), 2⁵⁺⁸:(S₃ × A₆), 2⁵⁺⁸:(S₃ × D₈), 2⁵⁺⁸:(S₃ × S₄), 2 × 2.Fi₂₂, 2 × 6.Fi₂₂, 2 × 11:5, 3.Fi₂₂, 3⁵.3³.(2 × S₄), 3⁵.3¹⁺².2.S₄, 3⁵:U₄(2):2, 3¹⁺⁶:2³⁺⁴:3²:2, 3³⁺³:L₃(3), 3^(3+3)b:L₃(3), 5:4 × S₅, 6.Fi₂₂, 13:6, (2 × 2¹⁺⁸):U₄(2):2, (2 × 2¹⁺⁸₊).2.2⁴.(S₃ × S₃), (3¹⁺⁶.3)a.2.S₄, (3¹⁺⁶.3)b.2.S₄, S₁₀, O₇(3), Fi₂₂N3, 5²:4S₄, M₁₂, M₂₂, O₇(3), O₈⁺(2).2, O₈⁺(2).3.2, S₃ × 7:6, S₃ × U₄(3), S₃ × U₄(3).2₂, U₄(3), U₄(3).2₂, f₂₂s₂

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