Character Table info for S5
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Name:
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A5.2
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Group order:
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120 = 23 ⋅ 3 ⋅ 5
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Number of classes:
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7
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InfoText value:
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origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5],
constructions: Aut(A5)
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Duplicates:
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A6.2_1M3,
L2(25)M3
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Maximal subgroups:
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| |
Order |
Index |
Structure |
Name |
| 1 |
60 |
2 |
A5 |
A5 |
| 2 |
24 |
5 |
S4 |
s4 |
| 3 |
20 |
6 |
5:4 |
5:4 |
| 4 |
12 |
10 |
S3 × 2 |
S3x2 |
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Available Brauer tables:
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Atlas representations:
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9 available
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Group constructions in GAP:
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AtlasGroup( "A5.2" ),
AtlasStabilizer( "A6.2_1", "S6G1-p6aB0" ),
AtlasStabilizer( "A6.2_1", "S6G1-p6bB0" ),
AtlasStabilizer( "M11", "M11G1-p66B0" ),
AtlasSubgroup( "A6.2_1", 2 ),
AtlasSubgroup( "A6.2_1", 3 ),
AtlasSubgroup( "J2.2", 10 ),
AtlasSubgroup( "M11", 4 ),
AtlasSubgroup( "M12.2", 9 ),
AtlasSubgroup( "Th", 16 ),
AutomorphismGroup( AlternatingGroup( 5 ) ),
PrimitiveGroup( 5, 5 ),
PrimitiveGroup( 6, 2 ),
PrimitiveGroup( 10, 2 ),
SmallGroup( 120, 34 ),
SymmetricGroup( 5 ),
TransitiveGroup( 5, 5 ),
TransitiveGroup( 6, 14 ),
TransitiveGroup( 10, 12 ),
TransitiveGroup( 10, 13 ),
TransitiveGroup( 12, 74 ),
TransitiveGroup( 15, 10 ),
TransitiveGroup( 20, 30 ),
TransitiveGroup( 20, 32 ),
TransitiveGroup( 20, 35 ),
TransitiveGroup( 24, 202 ),
TransitiveGroup( 30, 22 ),
TransitiveGroup( 30, 25 ),
TransitiveGroup( 30, 27 )
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Stored class fusions from this table:
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24:S5,
34:S5,
S6,
A7,
J2.2,
L2(25),
L3(4).21,
L3(5),
M11,
M12.2,
Th,
24:S5
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Stored class fusions to this table:
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2.2.24+6:S5,
2.24+6:S5,
2.A5.2,
2.4.24.S5,
4Y(2 × A5):2,
25:S5,
24:S5,
26:S5,
210:(25:s5),
21+4.S5,
21+6+:S5,
31+4+:21+4−.S5,
34:S5,
3 × Isoclinic(2.A5.2),
4.24.S5,
2.(25:S5),
5:4,
(2.A5 × A5):2,
(22 × A5):2,
(3.A6.22 × A5):2,
(3.A6 × A5):2,
(7:3 × A5):2,
(A4 × A5):2,
(A5 × 3):2,
(A5 × A5):2,
(A5 × A9):2,
(A5 × A12):2,
(A5 × D10).2,
(A5 × J2):2,
(A5 × U3(8):3):2,
(A5 × U4(2)):2,
(A6:22 × A5).2,
(A6 × A5):2,
(A7 × A5):2,
(A8 × A5):2,
(A6 × A5).2,
A5,
Isoclinic(2.A5.2),
25:S5,
22.24.S5,
S3 × 2,
gl25,
24:S5,
25:S5,
S4,
2.(24:S5),
w(d5)