Character Table info for A5
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Name:
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A5
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Group order:
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60 = 22 ⋅ 3 ⋅ 5
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Number of classes:
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5
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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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A5
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Maximal subgroups:
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| |
Order |
Index |
Structure |
Name |
| 1 |
12 |
5 |
A4 |
a4 |
| 2 |
10 |
6 |
D10 |
D10 |
| 3 |
6 |
10 |
S3 |
S3 |
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Stored Sylow p normalizers:
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| p |
Order |
Index |
Structure |
Name |
| 2 |
12 |
5 |
A4 |
a4 |
| 3 |
6 |
10 |
S3 |
S3 |
| 5 |
10 |
6 |
D10 |
D10 |
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Available Brauer tables:
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Atlas representations:
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18 available
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Group constructions in GAP:
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AlternatingGroup( 5 ),
AtlasGroup( "A5" ),
AtlasStabilizer( "A6", "A6G1-p6aB0" ),
AtlasStabilizer( "A6", "A6G1-p6bB0" ),
AtlasStabilizer( "L2(11)", "L211G1-p11aB0" ),
AtlasStabilizer( "L2(11)", "L211G1-p11bB0" ),
AtlasStabilizer( "L2(19)", "L219G1-p57aB0" ),
AtlasStabilizer( "L2(19)", "L219G1-p57bB0" ),
AtlasSubgroup( "A5.2", 1 ),
AtlasSubgroup( "A6", 1 ),
AtlasSubgroup( "A6", 2 ),
AtlasSubgroup( "J2", 9 ),
AtlasSubgroup( "L2(109)", 4 ),
AtlasSubgroup( "L2(109)", 5 ),
AtlasSubgroup( "L2(11)", 1 ),
AtlasSubgroup( "L2(11)", 2 ),
AtlasSubgroup( "S6(3)", 11 ),
PSL( 2, 4 ),
PSL( 2, 5 ),
PerfectGroup( 60, 1 ),
PrimitiveGroup( 5, 4 ),
PrimitiveGroup( 6, 1 ),
PrimitiveGroup( 10, 1 ),
SmallGroup( 60, 5 ),
TransitiveGroup( 5, 4 ),
TransitiveGroup( 6, 12 ),
TransitiveGroup( 10, 7 ),
TransitiveGroup( 12, 33 ),
TransitiveGroup( 15, 5 ),
TransitiveGroup( 20, 15 ),
TransitiveGroup( 30, 9 )
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Stored class fusions from this table:
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24:A5,
S5,
A6,
J2,
L2(11),
L2(16),
L2(19),
L2(29),
L2(31),
L2(109),
L2(125),
24:A5,
S6(3)
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Stored class fusions to this table:
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2.A5,
21+4−:A5,
24:A5,
29.24.A5a,
29.24.A5b,
21+4−:2A5,
3 × 2.A5,
D10,
24:A5,
P1/G1/L1/V1/ext3,
P1/G1/L1/V1/ext4,
P1/G1/L1/V1/ext5,
P1/G1/L1/V1/ext6,
P1/G1/L1/V2/ext3,
P1/G1/L1/V2/ext6,
25:A5,
P1/G2/L1/V1/ext3,
P1/G2/L1/V1/ext4,
P1/G2/L1/V2/ext2,
P1/G2/L1/V2/ext4,
P1/G2/L2/V2/ext2,
P1/G2/L2/V2/ext4,
26.A5,
P1/G3/L2/V1/ext3,
P2/G1/L1/V1/ext2,
P2/G2/L1/V1/ext2,
P2/G2/L1/V2/ext2,
S3,
A4,
mo62p