Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 6.M₂₂

Name:

6.M22

Group order:

2661120 = 2⁸ ⋅ 3³ ⋅ 5 ⋅ 7 ⋅ 11

Number of classes:

65

InfoText value:

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

Duplicates:

6.U6(2)M13

Maximal subgroups:

	Order	Index	Structure	Name
1	120960	22	6.L3(4)	6.L3(4)
2	34560	77	25:3A6	6.M22M2
3	15120	176	2 × (3.A7)	2x(3.A7)
4	15120	176	2 × (3.A7)	2x(3.A7)
5	11520	231	3 × 25:S5	3x2.M22M5
6	8064	330	6 × 23:L3(2)	6x2^3:L3(2)
7	4320	616	Isoclinic(3.A6.23 × 2)	6.M22M7
8	3960	672	6 × L2(11)	6xL2(11)

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	768	3465	3 × 2.M22N2	3x2.M22N2
3	432	6160	Isoclinic(2 × 31+2+:Q8)	Isoclinic(2x3^(1+2)_+:Q8)
5	120	22176	6 × 5:4	6x5:4
7	126	21120	6 × 7:3	6x7:3
11	330	8064	6 × 11:5	6x11:5

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:

30 available

Group constructions in GAP:

AtlasGroup( "6.M22" ), AtlasSubgroup( "6.M22.2", 1 ), AtlasSubgroup( "6.U6(2)", 12 ), AtlasSubgroup( "6.U6(2)", 13 )

Stored class fusions from this table:

2.M₂₂, 3.M₂₂, 6.M₂₂.2, 6.U₆(2), M₂₂

Stored class fusions to this table:

2 × 3.(A₄ × 3):2, 2 × (3.A₇), 3 × 2⁵:S₅, 3 × 2.M₂₂N2, 6.L₃(4), 2⁵:3A₆, Isoclinic(3.A₆.2₃ × 2), 6 × 2³:L₃(2), 6 × 5:4, 6 × 7:3, 6 × 11:5, 6 × L₂(11), 12.M₂₂, 2 × 6.M₂₂, Isoclinic(2 × 3¹⁺²₊:Q₈)

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