Character Table info for A6
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Name:
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A6
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Group order:
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360 = 23 ⋅ 32 ⋅ 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]
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Duplicates:
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L3(4)M4,
L3(4)M5
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Maximal subgroups:
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| |
Order |
Index |
Structure |
Name |
| 1 |
60 |
6 |
A5 |
A5 |
| 2 |
60 |
6 |
A5 |
A6M2 |
| 3 |
36 |
10 |
32:4 |
3^2:4 |
| 4 |
24 |
15 |
S4 |
s4 |
| 5 |
24 |
15 |
S4 |
A6M5 |
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Stored Sylow p normalizers:
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| p |
Order |
Index |
Structure |
Name |
| 2 |
8 |
45 |
D8 |
D8 |
| 3 |
36 |
10 |
32:4 |
3^2:4 |
| 5 |
10 |
36 |
D10 |
D10 |
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Available Brauer tables:
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Atlas representations:
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26 available
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Group constructions in GAP:
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AlternatingGroup( 6 ),
AtlasGroup( "A6" ),
AtlasStabilizer( "A7", "A7G1-p7B0" ),
AtlasStabilizer( "L3(4)", "L34G1-p56aB0" ),
AtlasStabilizer( "L3(4)", "L34G1-p56bB0" ),
AtlasStabilizer( "L3(4)", "L34G1-p56cB0" ),
AtlasSubgroup( "A6.2_1", 1 ),
AtlasSubgroup( "A7", 1 ),
AtlasSubgroup( "L3(4)", 3 ),
AtlasSubgroup( "L3(4)", 4 ),
AtlasSubgroup( "L3(4)", 5 ),
AtlasSubgroup( "S4(5)", 8 ),
PSL( 2, 9 ),
PerfectGroup( 360, 1 ),
PrimitiveGroup( 6, 3 ),
PrimitiveGroup( 10, 3 ),
PrimitiveGroup( 15, 2 ),
SmallGroup( 360, 118 ),
TransitiveGroup( 6, 15 ),
TransitiveGroup( 10, 26 ),
TransitiveGroup( 15, 20 ),
TransitiveGroup( 20, 89 ),
TransitiveGroup( 30, 88 )
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Stored class fusions from this table:
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24:A6,
34:A6,
S6,
A6.22,
A6.23,
A7,
L3(4),
S4(5),
U3(11)
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Stored class fusions to this table:
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2.A6,
25:A6,
24:A6,
25:A6,
3.A6,
32:4,
34:A6,
2.25:A6,
6.A6,
A5,
A5,
S4,
D8,
D10,
25:A6,
P21/G1/L1/V1/ext3,
P21/G1/L1/V1/ext4,
P21/G1/L3/V2/ext3,
P21/G2/L1/V1/ext2,
P21/G2/L1/V2/ext2,
P21/G2/L1/V3/ext2,
P21/G2/L2/V1/ext2,
P21/G2/L2/V2/ext2,
P21/G2/L2/V3/ext2,
P21/G2/L5/V2/ext2,
P21/G3/L2/V1/ext2,
P21/G3/L5/V1/ext2,
S4