Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for U3(5)

Name:
U3(5)
Group order:
126000 = 24 ⋅ 32 ⋅ 53 ⋅ 7
Number of classes:
14
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]
Maximal subgroups:
  Order Index Structure Name
1 2520 50 A7 A7
2 2520 50 A7 U3(5)M2
3 2520 50 A7 U3(5)M3
4 1000 126 5(1+2)+:8 5^(1+2)+:8
5 720 175 A6.23 A6.2_3
6 720 175 A6.23 U3(5)M6
7 720 175 A6.23 U3(5)M7
8 240 525 2.A5.2 2.A5.2
Stored Sylow p normalizers:
p Order Index Structure Name
3 72 1750 32:Q8 3^2:Q8
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
Atlas representations:
11 available
Group constructions in GAP:
AtlasGroup( "U3(5)" ), AtlasStabilizer( "McL", "McLG1-p7128B0" ), AtlasSubgroup( "McL", 4 ), PSU( 3, 5 ), PerfectGroup( 126000, 1 ), PrimitiveGroup( 50, 1 ), PrimitiveGroup( 126, 3 ), PrimitiveGroup( 175, 3 ), PrimitiveGroup( 525, 1 )
Stored class fusions from this table:
McL, U3(5).2, U3(5).3, U3(5).3.2
Stored class fusions to this table:
2.A5.2, 3.U3(5), 32:Q8, 5(1+2)+:8, A6.23, A7, M11N2, A7, A7, A6.23, A6.23

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