Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for U4(3)

Name:
U4(3)
Group order:
3265920 = 27 ⋅ 36 ⋅ 5 ⋅ 7
Number of classes:
20
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]
Maximal subgroups:
  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
Stored Sylow p normalizers:
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
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
Atlas representations:
7 available
Group constructions in GAP:
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 )
Stored class fusions from this table:
Co3, Fi22, McL, U4(3).21, U4(3).22, U4(3).22', U4(3).23, U4(3).23', U4(3).4
Stored class fusions to this table:
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

File created automatically by GAP on 13-Mar-2024.