Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for G2(4)

Name:
G2(4)
Group order:
251596800 = 212 ⋅ 33 ⋅ 52 ⋅ 7 ⋅ 13
Number of classes:
32
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r.
Maximal subgroups:
  Order Index Structure Name
1 604800 416 J2 J2
2 184320 1365 22+8:(3 × A5) 2^(2+8):(3xA5)
3 184320 1365 24+6:(A5 × 3) 2^(4+6):(A5x3)
4 124800 2016 U3(4).2 U3(4).2
5 120960 2080 3.L3(4).23 3.L3(4).2_3
6 12096 20800 U3(3).2 U3(3).2
7 3600 69888 A5 × A5 A5xA5
8 1092 230400 L2(13) L2(13)
Stored Sylow p normalizers:
p Order Index Structure Name
2 36864 6825 G2(4)N2 G2(4)N2
3 432 582400 31+2:SD16 3^(1+2):SD16
5 300 838656 52:D12 5^2:D12
7 126 1996800 (7:3 × 3):2 (7:3x3):2
13 78 3225600 13:6 13:6
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
13 dec. matrix (PDF)
Atlas representations:
33 available
Group constructions in GAP:
AtlasGroup( "G2(4)" ), AtlasStabilizer( "Suz", "SuzG1-p1782B0" ), AtlasSubgroup( "G2(4).2", 1 ), AtlasSubgroup( "Suz", 1 ), PrimitiveGroup( 416, 7 ), PrimitiveGroup( 1365, 1 ), PrimitiveGroup( 1365, 2 ), PrimitiveGroup( 2016, 7 ), PrimitiveGroup( 2080, 7 ), SimpleGroup( "G", 2, 4 )
Stored class fusions from this table:
3D4(4), G2(4).2, Suz
Stored class fusions to this table:
2.G2(4), 22+8:(3 × A5), 24+6:(A5 × 3), 3.L3(4).23, 31+2:SD16, 52:D12, 13:6, (7:3 × 3):2, A5 × A5, D10 × A5, G2(4)N2, J2, L2(13), S3 × A5, U3(3).2, U3(4).2, A5 × D10

File created automatically by GAP on 6-May-2025.