Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for M₁₂

Name:

M12

Group order:

95040 = 2⁶ ⋅ 3³ ⋅ 5 ⋅ 11

Number of classes:

15

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	7920	12	M11	M11
2	7920	12	M11	M12M2
3	1440	66	A6.22	A6.2^2
4	1440	66	A6.22	M12M4
5	660	144	L2(11)	L2(11)
6	432	220	32.2.S4	3^2.2.S4
7	432	220	32.2.S4	M12M7
8	240	396	2 × S5	2xS5
9	192	495	M8.S4	M8.S4
10	192	495	42:D12	4^2:D12
11	72	1320	A4 × S3	A4xS3

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	64	1485	M12N2	M12N2
3	108	880	M12N3	M12N3
5	40	2376	2 × 5:4	2x5:4
11	55	1728	11:5	11:5

Available Brauer tables:

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

Atlas representations:

58 available

Group constructions in GAP:

AtlasGroup( "M12" ), AtlasStabilizer( "A12", "A12G1-p2520B0" ), AtlasSubgroup( "Fi22", 14 ), AtlasSubgroup( "M12.2", 1 ), MathieuGroup( 12 ), PerfectGroup( 95040, 1 ), PrimitiveGroup( 12, 2 ), PrimitiveGroup( 66, 3 ), PrimitiveGroup( 144, 3 ), PrimitiveGroup( 220, 1 ), PrimitiveGroup( 396, 1 ), PrimitiveGroup( 495, 3 ), PrimitiveGroup( 495, 5 ), PrimitiveGroup( 1320, 1 ), TransitiveGroup( 12, 295 )

Stored class fusions from this table:

A₁₂, Fi₂₂, M₁₂.2

Stored class fusions to this table:

2.M₁₂, 2 × 5:4, 2 × S₅, 3².2.S₄, 4²:D₁₂, 11:5, A₄ × S₃, A₆.2², L₂(11), M₈.S₄, M₁₁, M₁₁, A₆.2², 3².2.S₄, M₁₂N2, M₁₂N3

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