Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for G2(5)

Name:
G2(5)
Group order:
5859000000 = 26 ⋅ 33 ⋅ 56 ⋅ 7 ⋅ 31
Number of classes:
44
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r.
Maximal subgroups:
  Order Index Structure Name
1 1500000 3906 51+4+:GL(2, 5) 5^(1+4):GL(2,5)
2 1500000 3906 52.5.52.4S5 5^2.5.5^2.4S5
3 756000 7750 3.U3(5).2 3.U3(5).2
4 744000 7875 L3(5).2 L3(5).2
5 14400 406875 2.(A5 × A5).2 2.(A5xA5).2
6 12096 484375 U3(3).2 U3(3).2
7 1344 4359375 23.L3(2) 2^3.L3(2)
Stored Sylow p normalizers:
p Order Index Structure Name
31 186 31500000 31:6 31:6
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
31 dec. matrix (PDF)
Atlas representations:
22 available
Group constructions in GAP:
AtlasGroup( "G2(5)" ), AtlasStabilizer( "Ly", "LyG1-p8835156B0" ), AtlasSubgroup( "Ly", 1 ), PrimitiveGroup( 3906, 1 ), PrimitiveGroup( 3906, 2 ), SimpleGroup( "G", 2, 5 )
Stored class fusions from this table:
Ly, O7(5)
Stored class fusions to this table:
2.(A5 × A5).2, 23.L3(2), 3.U3(5).2, 52.5.52.4S5, 51+4+:GL(2, 5), 31:6, L3(5).2, U3(3).2

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