Overview of the GAP Character Table Library (version 1.3.8)

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:

S₉

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 13-Mar-2024.