Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 2.M₁₂

Name:

2.M12

Group order:

190080 = 2⁷ ⋅ 3³ ⋅ 5 ⋅ 11

Number of classes:

26

InfoText value:

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

Duplicates:

2.A12M8

Maximal subgroups:

	Order	Index	Structure	Name
1	15840	12	2 × M11	2xM11
2	15840	12	2 × M11	2.M12M2
3	2880	66	A6.D8	A6.D8
4	2880	66	A6.D8	2.M12M4
5	1320	144	2.L2(11)	2.L2(11)
6	864	220	2 × 32.2.S4	2x3^2.2.S4
7	864	220	2 × 32.2.S4	2.M12M7
8	480	396	4Y(2 × A5):2	2.M12M8
9	384	495	(2 × Q8).S4	2.M12M9
10	384	495	2.(42:D12)	2.M12M10
11	144	1320	2.A4 × S3	2.A4xS3

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	128	1485	2.M12N2	2.M12N2
3	216	880	2 × M12N3	2xM12N3
5	80	2376	2.M12N5	2.M12N5
11	110	1728	2 × 11:5	2x11:5

Available Brauer tables:

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

Atlas representations:

15 available

Group constructions in GAP:

AtlasGroup( "2.M12" ), PerfectGroup( 190080, 1 ), TransitiveGroup( 24, 18440 )

Stored class fusions from this table:

2.A₁₂, 2.M₁₂.2, 3⁶:2M₁₂, M₁₂

Stored class fusions to this table:

2.A₄ × S₃, 2.L₂(11), 2 × M₁₁, A₆.D₈, 2 × 3².2.S₄, 4Y(2 × A₅):2, (2 × Q₈).S₄, 2.(4²:D₁₂), 2.M₁₂N2, 2.M₁₂N5, 2 × 3².2.S₄, 2 × 11:5, 2 × M₁₁, 2 × M₁₂N3, 3⁶:2M₁₂, A₆.D₈

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