Character Table info for A6.23
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Name:
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A6.2_3
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Group order:
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720 = 24 ⋅ 32 ⋅ 5
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Number of classes:
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8
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InfoText value:
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origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5]
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Duplicates:
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U3(5)M6,
U3(5)M7
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Maximal subgroups:
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|
Order |
Index |
Structure |
Name |
1 |
360 |
2 |
A6 |
A6 |
2 |
72 |
10 |
32:Q8 |
3^2:Q8 |
3 |
20 |
36 |
5:4 |
5:4 |
4 |
16 |
45 |
M11N2 |
M11N2 |
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Available Brauer tables:
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-
Atlas representations:
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1 available
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Group constructions in GAP:
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AtlasGroup( "A6.2_3" )
,
AtlasStabilizer( "A10", "A10G1-p2520B0" )
,
AtlasStabilizer( "M11", "M11G1-p11B0" )
,
AtlasStabilizer( "M22", "M22G1-p616B0" )
,
AtlasSubgroup( "M11", 1 )
,
AtlasSubgroup( "M22", 7 )
,
AtlasSubgroup( "Th", 14 )
,
MathieuGroup( 10 )
,
PrimitiveGroup( 10, 6 )
,
PrimitiveGroup( 36, 3 )
,
PrimitiveGroup( 45, 2 )
,
SmallGroup( 720, 765 )
,
TransitiveGroup( 10, 31 )
,
TransitiveGroup( 12, 181 )
,
TransitiveGroup( 20, 148 )
,
TransitiveGroup( 20, 150 )
,
TransitiveGroup( 30, 162 )
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Stored class fusions from this table:
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34:M10,
A6.22,
A10,
L3(4).21,
M11,
M22,
Th,
U3(5),
U4(3)
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Stored class fusions to this table:
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3.A6.23,
32:Q8,
34:M10,
35:M10,
4.A6.23,
5:4,
12.A6.23,
(2.D10 × A6).2,
(2 × A6).23,
(4 × A6).23,
(A6 × 2.A5).2,
(D10 × A6).2,
(A6 × A5).2,
A6,
M11N2,
(32:4 × A6).2