Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for M22.2

Name:
M22.2
Group order:
887040 = 28 ⋅ 32 ⋅ 5 ⋅ 7 ⋅ 11
Number of classes:
21
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11], constructions: Aut(M22)
Maximal subgroups:
  Order Index Structure Name
1 443520 2 M22 M22
2 40320 22 L3(4).22 L3(4).2_2
3 11520 77 24:S6 M22.2M3
4 3840 231 25:S5 M22.2M4
5 2688 330 2 × 23:L3(2) 2x2^3:L3(2)
6 1440 616 A6.22 A6.2^2
7 1320 672 L2(11).2 L2(11).2
Stored Sylow p normalizers:
p Order Index Structure Name
3 144 6160 32:Q8.2 3^2:Q8.2
5 40 22176 2 × 5:4 2x5:4
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
11 dec. matrix (PDF)
Atlas representations:
56 available
Group constructions in GAP:
AtlasGroup( "M22.2" ), AtlasStabilizer( "HS.2", "HSd2G1-p100B0" ), AtlasStabilizer( "M24", "M24G1-p276B0" ), AtlasStabilizer( "U6(2).2", "U62d2G1-p20736B0" ), AtlasSubgroup( "HS.2", 2 ), AtlasSubgroup( "J4", 6 ), AtlasSubgroup( "M24", 2 ), AutomorphismGroup( AtlasGroup( "M22" ) ), PrimitiveGroup( 22, 2 ), PrimitiveGroup( 77, 2 ), PrimitiveGroup( 231, 2 ), PrimitiveGroup( 330, 2 ), PrimitiveGroup( 616, 2 ), PrimitiveGroup( 672, 6 ), TransitiveGroup( 22, 41 )
Stored class fusions from this table:
210:M22:2, 210:M22:2, HS.2, J4, M24, U6(2).2
Stored class fusions to this table:
2.M22.2, 210:M22:2, 2 × 23:L3(2), 2 × 5:4, 2 × 7:3, 3.M22.2, 32:Q8.2, 4.M22.2, 6.M22.2, 11:10, 12.M22.2, A6.22, 210:M22:2, Isoclinic(2.M22.2), Isoclinic(4.M22.2), Isoclinic(6.M22.2), Isoclinic(12.M22.2), L2(11).2, L3(4).22, M22, 24:S6, 25:S5, S4 × S3, s4 ≀ s2

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