Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for S8

Name:
A8.2
Group order:
40320 = 27 ⋅ 32 ⋅ 5 ⋅ 7
Number of classes:
22
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7], constructions: Aut(A8)
Maximal subgroups:
  Order Index Structure Name
1 20160 2 A8 A8
2 5040 8 S7 A7.2
3 1440 28 S6 × 2 S6x2
4 1152 35 (S4 × S4):2 mo61
5 720 56 S5 × S3 S5xS3
6 384 105 24:S4 s2wrs4
7 336 120 L3(2).2 L3(2).2
Stored Sylow p normalizers:
p Order Index Structure Name
2 128 315 S8N2 A8.2N2
5 120 336 S3 × 5:4 S3x5:4
7 42 960 7:6 7:6
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
Atlas representations:
6 available
Group constructions in GAP:
AtlasGroup( "A8.2" ), AtlasStabilizer( "A10", "A10G1-p45B0" ), AtlasStabilizer( "A9.2", "S9G1-p9B0" ), AtlasStabilizer( "HS", "HSG1-p1100bB0" ), AtlasStabilizer( "S6(2)", "S62G1-p36B0" ), AtlasSubgroup( "HS", 5 ), AtlasSubgroup( "S6(2)", 2 ), AutomorphismGroup( AlternatingGroup( 8 ) ), PrimitiveGroup( 8, 7 ), PrimitiveGroup( 28, 8 ), PrimitiveGroup( 35, 2 ), PrimitiveGroup( 56, 7 ), PrimitiveGroup( 105, 7 ), PrimitiveGroup( 120, 11 ), SymmetricGroup( 8 ), TransitiveGroup( 8, 50 ), TransitiveGroup( 16, 1838 ), TransitiveGroup( 28, 502 ), TransitiveGroup( 30, 1153 )
Stored class fusions from this table:
26:S8, 28:S8, S9, A10, HS, S6(2)
Stored class fusions to this table:
2.A8.2, 26:S8, 28:S8, 7:6, (A8 × 3):2, (A8 × A4):2, (A8 × A5):2, S7, A8, S8N2, Isoclinic(2.A8.2), Isoclinic(S8 × 2), L3(2).2, S3 × 5:4, S5 × S3, S6 × 2, (S4 × S4):2, mo81, 24:S4

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