Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for He

Name:

He

Group order:

4030387200 = 2¹⁰ ⋅ 3³ ⋅ 5² ⋅ 7³ ⋅ 17

Number of classes:

33

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,17]

Maximal subgroups:

	Order	Index	Structure	Name
1	1958400	2058	S4(4).2	S4(4).2
2	483840	8330	22.L3(4).S3	2^2.psl(3,4).s3
3	138240	29155	26:3.S6	2^6:3.s6
4	138240	29155	26:3.S6	2^6:3.s6
5	21504	187425	21+6+.L3(2)	2^1+6.psl(3,2)
6	16464	244800	72:2L2(7)	7^2:2psl(2,7)
7	15120	266560	3.A7.2	3.A7.2
8	6174	652800	71+2:(S3 × 3)	7^(1+2):(S3x3)
9	4032	999600	S4 × L3(2)	s4xpsl(3,2)
10	3528	1142400	7:3 × L3(2)	7:3xpsl(3,2)
11	1200	3358656	52:4A4	5^2:4A4

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	1024	3935925	M24N2	M24N2
3	216	18659200	31+2:D8	3^(1+2):D8
5	1200	3358656	52:4A4	5^2:4A4
7	6174	652800	71+2:(S3 × 3)	7^(1+2):(S3x3)
17	136	29635200	17:8	17:8

Available Brauer tables:

p
2	dec. matrix (PDF)
3	dec. matrix (PDF)
5	dec. matrix (PDF)
7	dec. matrix (PDF)
17	dec. matrix (PDF)

Atlas representations:

29 available

Group constructions in GAP:

AtlasGroup( "He" ), AtlasSubgroup( "He.2", 1 ), PrimitiveGroup( 2058, 1 )

Stored class fusions from this table:

He.2

Stored class fusions to this table:

2¹⁺⁶₊.L₃(2), 2².L₃(4).S₃, 2⁶:3.S₆, 2⁶:3¹⁺².D₈, 2²⁺²⁺⁴.(S₃ × S₃), 3.A₇.2, 3¹⁺²:D₈, 5²:4A₄, 7:3 × L₃(2), 7²:2L₂(7), 7¹⁺²:(S₃ × 3), 17:8, (A₅ × D₁₀).2, D₈ × L₃(2), L₃(2) × S₃, M₂₄N2, NRS(M₂₄, 2^(2+2+4)a), NRS(M₂₄, 2⁴⁺⁴), NRS(M₂₄, [2⁹]a), NRS(M₂₄, [2⁹]b), S₄(4).2, [2⁹].S₃a, [2⁹].S₃b, hed₃, S₄ × L₃(2)

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