Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for Fi₂₂.2

Name:

Fi22.2

Group order:

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

Number of classes:

112

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., constructions: Aut(Fi22)

Maximal subgroups:

	Order	Index	Structure	Name
1	64561751654400	2	Fi22	Fi22
2	36787322880	3510	2.U6(2).2	2.U6(2).2
3	2090188800	61776	O8+(2):S3 × 2	O8+(2):S3x2
4	908328960	142155	210:M22:2	Fi22.2M4
5	185794560	694980	27:S6(2)	2^7:S6(2)
6	106168320	1216215	(2 × 21+8):(U4(2):2 × 2)	(2x2^(1+8)):(U4(2):2x2)
7	78382080	1647360	S3 × U4(3).(22)122	S3xU4(3).(2^2)_{122}
8	35942400	3592512	2F4(2)'.2	2F4(2)'.2
9	35389440	3648645	25+8:(S3 × S6)	2^(5+8):(S3xS6)
10	25194240	5125120	35:(2 × U4(2).2)	3^5:(2xU4(2).2)
11	10077696	12812800	31+6+:23+4:(S3 × S3)	3^(1+6)_+:2^(3+4):(S3xS3)
12	8491392	15206400	G2(3).2	G2(3).2
13	190080	679311360	M12.2	M12.2

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:

32 available

Group constructions in GAP:

AtlasGroup( "Fi22.2" ), AutomorphismGroup( AtlasGroup( "Fi22" ) ), PrimitiveGroup( 3510, 2 )

Stored class fusions from this table:

²E₆(2).2

Stored class fusions to this table:

2.Fi₂₂.2, 2.U₆(2).2, ²F₄(2)'.2, 2².Fi₂₂.2, 2⁷:S₆(2), 2⁵⁺⁸:(S₃ × S₆), 2 × Fi₂₂N5, 3.Fi₂₂.2, 3⁵:(2 × U₄(2).2), 3¹⁺⁶₊:2³⁺⁴:(S₃ × S₃), 5:4 × S₅ × 2, 6.Fi₂₂.2, 13:12, (2 × 2¹⁺⁸):(U₄(2):2 × 2), Fi₂₂, 2¹⁰:M₂₂:2, G₂(3).2, Isoclinic(2.Fi₂₂.2), Isoclinic(6.Fi₂₂.2), M₁₂.2, O₈⁺(2):S₃ × 2, S₃ × U₄(3).(2²)₁₂₂

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