Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for 3.M₂₂

Name:

3.M22

Group order:

1330560 = 2⁷ ⋅ 3³ ⋅ 5 ⋅ 7 ⋅ 11

Number of classes:

34

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]

Duplicates:

3.M₂₂, 3.M₂₂, 3.M₂₂

Maximal subgroups:

	Order	Index	Structure	Name
1	60480	22	3.L3(4)	3.L3(4)
2	17280	77	24:3A6	3.M22M2
3	7560	176	3.A7	3.A7
4	7560	176	3.A7	3.A7
5	5760	231	3 × 24:S5	3x2^4:s5
6	4032	330	3 × 23:L3(2)	3x2^3:L3(2)
7	2160	616	3.A6.23	3.A6.2_3
8	1980	672	3 × L2(11)	3xL2(11)

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	384	3465	3 × McLN2	3xMcLN2
3	216	6160	31+2+:Q8	3^(1+2)_+:Q8
5	60	22176	5:4 × 3	5:4x3
7	63	21120	7:3 × 3	7:3x3
11	165	8064	3 × 11:5	3x11:5

Available Brauer tables:

p
2	dec. matrix (PDF)
3	dec. matrix (PDF)
5	dec. matrix (PDF)
7	dec. matrix (PDF)
11	dec. matrix (PDF)

Atlas representations:

40 available

Group constructions in GAP:

AtlasGroup( "3.M22" ), AtlasSubgroup( "3.M22.2", 1 ), AtlasSubgroup( "3.McL", 2 ), AtlasSubgroup( "3.McL", 3 ), AtlasSubgroup( "3.U6(2)", 11 ), AtlasSubgroup( "3.U6(2)", 12 ), AtlasSubgroup( "3.U6(2)", 13 ), PerfectGroup( 1330560, 2 )

Stored class fusions from this table:

3.M₂₂.2, 3.M^cL, 3.U₆(2), M₂₂

Stored class fusions to this table:

2 × 6.M₂₂, 3.(A₄ × 3):2, 3.A₆.2₃, 3.A₇, 2¹⁰:3.M₂₂, 3.L₃(4), 2⁴:3A₆, 3¹⁺²₊:Q₈, 3 × 2³.S₄v₁, 3 × 2³:L₃(2), 3 × 2⁴:S₅, 3 × 11:5, 3 × L₂(11), 3 × M₂₂C2A, 3 × M^cLN2, 3 × NRS(M₂₂, [2⁶]), 5:4 × 3, 2¹¹.3.M₂₂, 6.M₂₂, 7:3 × 3, 12.M₂₂

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