Character Table info for S6
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Name:
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A6.2_1
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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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11
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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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Maximal subgroups:
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| |
Order |
Index |
Structure |
Name |
| 1 |
360 |
2 |
A6 |
A6 |
| 2 |
120 |
6 |
S5 |
A5.2 |
| 3 |
120 |
6 |
S5 |
A6.2_1M3 |
| 4 |
72 |
10 |
32:D8 |
s3wrs2 |
| 5 |
48 |
15 |
2 × S4 |
2xSymm(4) |
| 6 |
48 |
15 |
S4 × 2 |
s2wrs3 |
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Available Brauer tables:
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Atlas representations:
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5 available
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Group constructions in GAP:
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AtlasGroup( "A6.2_1" ),
AtlasStabilizer( "A7.2", "S7G1-p7B0" ),
AtlasStabilizer( "U4(2)", "U42G1-p36B0" ),
AtlasSubgroup( "A7.2", 2 ),
AtlasSubgroup( "S4(4)", 7 ),
POmega( 5, 2 ),
PSp( 4, 2 ),
PrimitiveGroup( 6, 4 ),
PrimitiveGroup( 10, 5 ),
PrimitiveGroup( 15, 3 ),
SmallGroup( 720, 763 ),
SymmetricGroup( 6 ),
TransitiveGroup( 6, 16 ),
TransitiveGroup( 10, 32 ),
TransitiveGroup( 12, 183 ),
TransitiveGroup( 15, 28 ),
TransitiveGroup( 20, 145 ),
TransitiveGroup( 20, 149 ),
TransitiveGroup( 30, 164 ),
TransitiveGroup( 30, 166 ),
TransitiveGroup( 30, 176 )
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Stored class fusions from this table:
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A6.22,
S7,
A8,
L3(4).22,
S4(4),
U4(2)
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Stored class fusions to this table:
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2.24.S6,
2.A6.21,
24.S6,
25:S6,
26:S6,
23+8:(S3 × S6),
2 × S4,
3.A6.21,
34:S6,
5:4,
6.A6.21,
(32:4 × A6).2,
(32:8 × A6).2,
(31+2:4 × A6).2,
(31+2:8 × A6).2,
(3 × A6).21,
(4 × A6):2,
(A6 × A4):2,
(A6 × A5):2,
(A6 × U3(3)):2,
(A7 × A6):2,
S5,
A6,
S5,
D8 × 2,
24:S6,
S4 × 2,
32:D8,
suzdx