Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for M^cL

Name:

McL

Group order:

898128000 = 2⁷ ⋅ 3⁶ ⋅ 5³ ⋅ 7 ⋅ 11

Number of classes:

24

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	3265920	275	U4(3)	U4(3)
2	443520	2025	M22	M22
3	443520	2025	M22	McLM3
4	126000	7128	U3(5)	U3(5)
5	58320	15400	31+4+:2S5	3^(1+4):2S5
6	58320	15400	34:M10	3^4:m10
7	40320	22275	L3(4).22	L3(4).2_2
8	40320	22275	2.A8	2.A8
9	40320	22275	24:A7	2^4:a7
10	40320	22275	24:A7	McLM10
11	7920	113400	M11	M11
12	3000	299376	51+2+:3:8	5^(1+2):3:8

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	128	7016625	McLN2	McLN2
3	5832	154000	34:(32:Q8)	3^4:(3^2:Q8)
5	3000	299376	51+2+:3:8	5^(1+2):3:8
7	42	21384000	2 × 7:3	2x7:3
11	55	16329600	11:5	11:5

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( "McL" ), AtlasStabilizer( "Co2", "Co2G1-p47104B0" ), AtlasSubgroup( "Co2", 3 ), AtlasSubgroup( "McL.2", 1 ), PrimitiveGroup( 275, 1 ), PrimitiveGroup( 2025, 34 )

Stored class fusions from this table:

Co₂, Co₃, M^cL.2

Stored class fusions to this table:

2(A₄ × A₄).2², 2.A₈, 2⁴:A₇, 2^1+1+2+2:S₃, 2¹⁺³:L₃(2), 2²⁺⁴.S₃, 2²⁺⁴:(3 × 3):2, 2 × 7:3, 3.M^cL, 3⁴.3².Q₈, 3⁴:(3²:Q₈), 3⁴:M₁₀, 3¹⁺⁴₊:2S₅, 3¹⁺⁴₊.2S₄, 5¹⁺²₊:3:8, 11:5, L₃(4).2₂, M₁₁, M₂₂, M₂₂C2A, M₂₂, 2⁴:A₇, M^cLN2, U₃(5), U₄(3)

File created automatically by GAP on 6-May-2025.