Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for S9

Name:
A9.2
Group order:
362880 = 27 ⋅ 34 ⋅ 5 ⋅ 7
Number of classes:
30
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7], constructions: Aut(A9)
Duplicates:
O7(3)M11
Maximal subgroups:
  Order Index Structure Name
1 181440 2 A9 A9
2 40320 9 S8 A8.2
3 10080 36 S7 × 2 S7x2
4 4320 84 S3 × S6 S3xS6
5 2880 126 S5 × S4 S5xS4
6 1296 280 33:(S4 × 2) s3wrs3
7 432 840 32.2.S4 3^2.2.S4
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
Atlas representations:
1 available
Group constructions in GAP:
AtlasGroup( "A9.2" ), AtlasStabilizer( "A10.2", "S10G1-p10B0" ), AtlasStabilizer( "A11", "A11G1-p55B0" ), AutomorphismGroup( AlternatingGroup( 9 ) ), PrimitiveGroup( 9, 11 ), PrimitiveGroup( 36, 12 ), PrimitiveGroup( 84, 2 ), PrimitiveGroup( 126, 13 ), PrimitiveGroup( 280, 2 ), PrimitiveGroup( 840, 2 ), SymmetricGroup( 9 ), TransitiveGroup( 9, 34 ), TransitiveGroup( 18, 887 )
Stored class fusions from this table:
S10, A11, O7(3)
Stored class fusions to this table:
2.A9.2, 32.2.S4, 3 × Isoclinic(2.A9.2), (A5 × A9):2, (A9 × 3):2, (A9 × A4):2, (D10 × A9).2, S8, A9, Isoclinic(2.A9.2), S3 × S6, S5 × S4, S7 × 2, 33:(S4 × 2)

File created automatically by GAP on 20-May-2025.