Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 2.M₂₂

Name:

2.M22

Group order:

887040 = 2⁸ ⋅ 3² ⋅ 5 ⋅ 7 ⋅ 11

Number of classes:

23

InfoText value:

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

Duplicates:

2.U6(2)M13

Maximal subgroups:

	Order	Index	Structure	Name
1	40320	22	2.L3(4)	2.L3(4)
2	11520	77	25:A6	2.M22M2
3	5040	176	2 × A7	2xA7
4	5040	176	2 × A7	2xA7
5	3840	231	25:S5	2.M22M5
6	2688	330	2 × 23:L3(2)	2x2^3:L3(2)
7	1440	616	(2 × A6).23	(2xA6).2_3
8	1320	672	2 × L2(11)	2xL2(11)

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	256	3465	2.M22N2	2.M22N2
3	144	6160	Isoclinic(2 × 32:Q8)	Isoclinic(2x3^2:Q8)
5	40	22176	2 × 5:4	2x5:4
7	42	21120	2 × 7:3	2x7:3
11	110	8064	2 × 11:5	2x11:5

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:

46 available

Group constructions in GAP:

AtlasGroup( "2.M22" ), AtlasSubgroup( "2.HS", 1 ), AtlasSubgroup( "2.M22.2", 1 ), AtlasSubgroup( "2.U6(2)", 12 ), AtlasSubgroup( "2.U6(2)", 13 ), PerfectGroup( 887040, 1 )

Stored class fusions from this table:

2.HS, 2.M₂₂.2, 2.U₆(2), M₂₂, M₂₂

Stored class fusions to this table:

2.L₃(4), 2⁵:A₆, 2⁵:S₅, 2.M₂₂N2, 2 × 2.M₂₂, 2 × 2³:L₃(2), 2 × 5:4, 2 × 7:3, 2 × 11:5, 2 × (A₄ × 3):2, 2 × A₇, 2 × L₂(11), 4.M₂₂, 6.M₂₂, 12.M₂₂, 2 × 6.M₂₂, (2 × A₆).2₃, Isoclinic(2 × 3²:Q₈)

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