Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for M₁₂.2

Name:

M12.2

Group order:

190080 = 2⁷ ⋅ 3³ ⋅ 5 ⋅ 11

Number of classes:

21

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,11], constructions: Aut(M12)

Duplicates:

HNM12

Maximal subgroups:

	Order	Index	Structure	Name
1	95040	2	M12	M12
2	1320	144	L2(11).2	L2(11).2
3	1320	144	L2(11).2	M12.2M3
4	480	396	(22 × A5):2	(2^2xA5):2
5	384	495	23.(S4 × 2)	2^3.(S4x2)
6	384	495	42:D12.2	4^2:D12.2
7	216	880	31+2:D8	3^(1+2):D8
8	144	1320	S4 × S3	S4xS3
9	120	1584	S5	A5.2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
11	110	1728	11:10	11:10

Available Brauer tables:

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

Atlas representations:

43 available

Group constructions in GAP:

AtlasGroup( "M12.2" ), AtlasStabilizer( "M24", "M24G1-p1288B0" ), AtlasSubgroup( "Fi22.2", 13 ), AtlasSubgroup( "HN", 11 ), AtlasSubgroup( "HN", 12 ), AtlasSubgroup( "M24", 4 ), AtlasSubgroup( "Suz", 10 ), AutomorphismGroup( AtlasGroup( "M12" ) ), PrimitiveGroup( 144, 4 ), PrimitiveGroup( 144, 5 ), PrimitiveGroup( 396, 2 ), PrimitiveGroup( 495, 4 ), PrimitiveGroup( 495, 6 ), PrimitiveGroup( 880, 1 ), PrimitiveGroup( 1320, 2 ), PrimitiveGroup( 1584, 1 ), TransitiveGroup( 24, 18441 )

Stored class fusions from this table:

Fi₂₂.2, HN, M₁₂.2 × 2, M₂₄, Suz

Stored class fusions to this table:

2.M₁₂.2, 2³.(S₄ × 2), 3².2.S₄, 3¹⁺²:D₈, 4²:D₁₂.2, 11:10, (2² × A₅):2, (11:5 × M₁₂):2, (L₂(11) × M₁₂):2, S₅, G₂(3).2N2, Isoclinic(2.M₁₂.2), L₂(11).2, M₁₂, L₂(11).2, S₄ × S₃

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