Character Table info for S8
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Name:
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A8.2
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Group order:
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40320 = 27 ⋅ 32 ⋅ 5 ⋅ 7
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Number of classes:
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22
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InfoText value:
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origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7],
constructions: Aut(A8)
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Maximal subgroups:
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Stored Sylow p normalizers:
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p |
Order |
Index |
Structure |
Name |
2 |
128 |
315 |
S8N2 |
A8.2N2 |
5 |
120 |
336 |
S3 × 5:4 |
S3x5:4 |
7 |
42 |
960 |
7:6 |
7:6 |
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Available Brauer tables:
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Atlas representations:
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6 available
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Group constructions in GAP:
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AtlasGroup( "A8.2" )
,
AtlasStabilizer( "A10", "A10G1-p45B0" )
,
AtlasStabilizer( "A9.2", "S9G1-p9B0" )
,
AtlasStabilizer( "HS", "HSG1-p1100bB0" )
,
AtlasStabilizer( "S6(2)", "S62G1-p36B0" )
,
AtlasSubgroup( "HS", 5 )
,
AtlasSubgroup( "S6(2)", 2 )
,
AutomorphismGroup( AlternatingGroup( 8 ) )
,
PrimitiveGroup( 8, 7 )
,
PrimitiveGroup( 28, 8 )
,
PrimitiveGroup( 35, 2 )
,
PrimitiveGroup( 56, 7 )
,
PrimitiveGroup( 105, 7 )
,
PrimitiveGroup( 120, 11 )
,
SymmetricGroup( 8 )
,
TransitiveGroup( 8, 50 )
,
TransitiveGroup( 16, 1838 )
,
TransitiveGroup( 28, 502 )
,
TransitiveGroup( 30, 1153 )
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Stored class fusions from this table:
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26:S8,
28:S8,
S9,
A10,
HS,
S6(2)
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Stored class fusions to this table:
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2.A8.2,
26:S8,
28:S8,
7:6,
(A8 × 3):2,
(A8 × A4):2,
(A8 × A5):2,
S7,
A8,
S8N2,
Isoclinic(2.A8.2),
Isoclinic(S8 × 2),
L3(2).2,
S3 × 5:4,
S5 × S3,
S6 × 2,
(S4 × S4):2,
mo81,
24:S4