Character Table info for U4(3)
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Name:
-
U4(3)
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Group order:
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3265920 = 27 ⋅ 36 ⋅ 5 ⋅ 7
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Number of classes:
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20
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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 |
29160 |
112 |
34:A6 |
3^4:A6 |
2 |
25920 |
126 |
U4(2) |
U4(2) |
3 |
25920 |
126 |
U4(2) |
U4(3)M3 |
4 |
20160 |
162 |
L3(4) |
L3(4) |
5 |
20160 |
162 |
L3(4) |
L3(4) |
6 |
11664 |
280 |
31+4+.2S4 |
3^(1+4)_+.2S4 |
7 |
6048 |
540 |
U3(3) |
U3(3) |
8 |
5760 |
567 |
24:A6 |
2^4:a6 |
9 |
5760 |
567 |
24:A6 |
U4(3)M9 |
10 |
2520 |
1296 |
A7 |
A7 |
11 |
2520 |
1296 |
A7 |
A7 |
12 |
2520 |
1296 |
A7 |
U4(3)M12 |
13 |
2520 |
1296 |
A7 |
U4(3)M12 |
14 |
1152 |
2835 |
2(A4 × A4).22 |
2(A4xA4).2^2 |
15 |
720 |
4536 |
A6.23 |
A6.2_3 |
16 |
720 |
4536 |
A6.23 |
A6.2_3 |
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Stored Sylow p normalizers:
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p |
Order |
Index |
Structure |
Name |
2 |
128 |
25515 |
24:D8 |
2^4:D8 |
3 |
2916 |
1120 |
34.32:4 |
3^4.3^2:4 |
5 |
20 |
163296 |
5:4 |
5:4 |
7 |
21 |
155520 |
7:3 |
7:3 |
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Available Brauer tables:
-
-
Atlas representations:
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7 available
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Group constructions in GAP:
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AtlasGroup( "U4(3)" )
,
AtlasStabilizer( "McL", "McLG1-p275B0" )
,
AtlasSubgroup( "McL", 1 )
,
POmega( -1, 6, 3 )
,
PSU( 4, 3 )
,
PrimitiveGroup( 112, 1 )
,
PrimitiveGroup( 126, 7 )
,
PrimitiveGroup( 162, 1 )
,
PrimitiveGroup( 280, 13 )
,
PrimitiveGroup( 540, 1 )
,
PrimitiveGroup( 567, 1 )
,
PrimitiveGroup( 1296, 132 )
,
PrimitiveGroup( 2835, 1 )
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Stored class fusions from this table:
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Co3,
Fi22,
McL,
U4(3).21,
U4(3).22,
U4(3).22',
U4(3).23,
U4(3).23',
U4(3).4
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Stored class fusions to this table:
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2(A4 × A4).22,
2.U4(3),
24:D8,
24:A6,
32.U4(3),
34.32:4,
34:A6,
31+4+.2S4,
31.U4(3),
32.U4(3),
4.U4(3),
5:4,
61.U4(3),
62.U4(3),
7:3,
121.U4(3),
122.U4(3),
A6.23,
A7,
L3(4),
NRS(M22, [26]),
U3(3),
U4(2),
U4(2),
24:A6,
A7