Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for S₈(2)

Name:

S8(2)

Group order:

47377612800 = 2¹⁶ ⋅ 3⁵ ⋅ 5² ⋅ 7 ⋅ 17

Number of classes:

81

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r.

Duplicates:

F4(2)M4

Maximal subgroups:

	Order	Index	Structure	Name
1	394813440	120	O8−(2).2	O8-(2).2
2	348364800	136	O8+(2).2	O8+(2).2
3	185794560	255	27:S6(2)	S8(2)M3
4	20643840	2295	210.A8	2^10.A8
5	8847360	5355	23+8:(S3 × S6)	2^(3+8):(S3xS6)
6	8709120	5440	S3 × S6(2)	S3xS6(2)
7	4128768	11475	26+6:(S3 × L3(2))	2^(6+6):(S3xL3(2))
8	3628800	13056	S10	A10.2
9	1958400	24192	S4(4).2	S4(4).2
10	1036800	45696	(S6 × S6):2	(S6xS6):2
11	2448	19353600	L2(17)	L2(17)

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:

24 available

Group constructions in GAP:

AtlasGroup( "S8(2)" ), AtlasStabilizer( "F4(2)", "F42G1-p69888aB0" ), AtlasStabilizer( "Fi23", "F23G1-p86316516B0" ), AtlasStabilizer( "O10+(2)", "O10p2G1-p496B0" ), AtlasStabilizer( "O10-(2)", "O10m2G1-p528B0" ), AtlasSubgroup( "F4(2)", 3 ), AtlasSubgroup( "Fi23", 4 ), AtlasSubgroup( "O10+(2)", 1 ), POmega( 9, 2 ), PSp( 8, 2 ), PrimitiveGroup( 120, 15 ), PrimitiveGroup( 136, 6 ), PrimitiveGroup( 255, 1 ), PrimitiveGroup( 2295, 1 )

Stored class fusions from this table:

2⁸:S₈(2), F₄(2), Fi₂₃, L₈(2), O₁₀⁺(2), O₁₀⁻(2)

Stored class fusions to this table:

2⁸:S₈(2), 2¹⁰.A₈, 2³⁺⁸:(S₃ × S₆), 2⁶⁺⁶:(S₃ × L₃(2)), 2⁹⁺¹⁶.S₈(2), (S₆ × S₆):2, S₁₀, L₂(17), O₈⁺(2).2, O₈⁻(2).2, S₃ × S₆(2), S₄(4).2, 2⁷:S₆(2)

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