Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for HS

Name:

HS

Group order:

44352000 = 2⁹ ⋅ 3² ⋅ 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	443520	100	M22	M22
2	252000	176	U3(5).2	U3(5).2
3	252000	176	U3(5).2	HSM3
4	40320	1100	L3(4).21	L3(4).2_1
5	40320	1100	S8	A8.2
6	11520	3850	24.S6	2^4.s6
7	10752	4125	43:L3(2)	4^3:psl(3,2)
8	7920	5600	M11	M11
9	7920	5600	M11	HSM9
10	7680	5775	4.24.S5	4.2^4.S5
11	2880	15400	2 × A6.22	2xa6.2^2
12	1200	36960	5:4 × A5	5:4xa5

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	512	86625	HSN2	HSN2
3	288	154000	2 × (32.QD16)	2x(3^2.QD16)
5	2000	22176	51+2+:8:2	5^(1+2):(8.2)
7	42	1056000	7:6	7:6
11	55	806400	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:

80 available

Group constructions in GAP:

AtlasGroup( "HS" ), AtlasStabilizer( "Co3", "Co3G1-p11178B0" ), AtlasSubgroup( "Co3", 2 ), AtlasSubgroup( "HS.2", 1 ), PrimitiveGroup( 100, 3 ), PrimitiveGroup( 176, 4 ), PrimitiveGroup( 1100, 1 ), PrimitiveGroup( 1100, 2 ), PrimitiveGroup( 3850, 1 )

Stored class fusions from this table:

Co₃, HS.2

Stored class fusions to this table:

2.HS, 2⁴.(S₄ × 2), 2⁴.S₆, 2 × (3².QD₁₆), 2 × A₆.2², 4.2⁴, 4.2⁴.S₅, 4.2⁴:(2 × S₃), 4.2⁴:S₄, 4³:S₄, 4³:L₃(2), 5:4 × 2², 5:4 × A₄, 5:4 × A₅, 5¹⁺²₊:8:2, 7:6, 11:5, A₄ × C₄, S₈, D₈ × V₄, U₃(5).2, M₁₁, HSN2, Isoclinic(2.HS × 2), L₃(4).2₁, M₁₁, M₂₂, S₄ × 2², S₅ × S₃, U₃(5).2

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