Character Table info for L3(4)
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Name:
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L3(4)
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Group order:
-
20160 = 26 ⋅ 32 ⋅ 5 ⋅ 7
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Number of classes:
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10
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InfoText value:
-
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]
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Maximal subgroups:
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|
Order |
Index |
Structure |
Name |
1 |
960 |
21 |
24:A5 |
2^4:A5 |
2 |
960 |
21 |
24:A5 |
2^4:A5 |
3 |
360 |
56 |
A6 |
A6 |
4 |
360 |
56 |
A6 |
L3(4)M4 |
5 |
360 |
56 |
A6 |
L3(4)M5 |
6 |
168 |
120 |
L3(2) |
L3(2) |
7 |
168 |
120 |
L3(2) |
L3(4)M7 |
8 |
168 |
120 |
L3(2) |
L3(4)M8 |
9 |
72 |
280 |
32:Q8 |
3^2:Q8 |
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Stored Sylow p normalizers:
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p |
Order |
Index |
Structure |
Name |
2 |
192 |
105 |
24:A4b |
2^4:A4b |
3 |
72 |
280 |
32:Q8 |
3^2:Q8 |
5 |
10 |
2016 |
D10 |
D10 |
7 |
21 |
960 |
7:3 |
7:3 |
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Available Brauer tables:
-
-
Atlas representations:
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48 available
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Group constructions in GAP:
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AtlasGroup( "L3(4)" )
,
AtlasStabilizer( "M22", "M22G1-p22B0" )
,
AtlasSubgroup( "M22", 1 )
,
PSL( 3, 4 )
,
PerfectGroup( 20160, 5 )
,
PrimitiveGroup( 21, 4 )
,
PrimitiveGroup( 56, 1 )
,
PrimitiveGroup( 120, 6 )
,
PrimitiveGroup( 280, 3 )
,
TransitiveGroup( 21, 67 )
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Stored class fusions from this table:
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29.L3(4),
L3(4).21,
L3(4).22,
L3(4).23,
L3(4).3,
L3(4).6,
M22,
U4(3)
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Stored class fusions to this table:
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2.L3(4),
210:L3(4),
22.L3(4),
210:2.L3(4),
24:A4b,
24:A5,
29.L3(4),
3.L3(4),
32:Q8,
41.L3(4),
42.L3(4),
6.L3(4),
7:3,
121.L3(4),
122.L3(4),
(22 × 3).L3(4),
A6,
D10,
L3(2),
A6,
A6,
L3(2),
L3(2),
L3(4)Syl2