Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for A₉

Name:

A9

Group order:

181440 = 2⁶ ⋅ 3⁴ ⋅ 5 ⋅ 7

Number of classes:

18

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7]

Duplicates:

O8+(2)M8, O8+(2)M9

Maximal subgroups:

	Order	Index	Structure	Name
1	20160	9	A8	A8
2	5040	36	S7	A7.2
3	2160	84	(3 × A6).21	(3xA6).2_1
4	1512	120	L2(8).3	L2(8).3
5	1512	120	L2(8).3	A9M5
6	1440	126	(A4 × A5):2	(A4xA5):2
7	648	280	33.S4	3^3.S4
8	216	840	32:2A4	3^2:2A4

Available Brauer tables:

p
2	dec. matrix (PDF)
3	dec. matrix (PDF)
5	dec. matrix (PDF)
7	dec. matrix (PDF)

Atlas representations:

68 available

Group constructions in GAP:

AlternatingGroup( 9 ), AtlasGroup( "A9" ), AtlasStabilizer( "A10", "A10G1-p10B0" ), PerfectGroup( 181440, 1 ), PrimitiveGroup( 9, 10 ), PrimitiveGroup( 36, 11 ), PrimitiveGroup( 84, 1 ), PrimitiveGroup( 120, 2 ), PrimitiveGroup( 126, 12 ), PrimitiveGroup( 280, 1 ), PrimitiveGroup( 840, 1 ), TransitiveGroup( 9, 33 )

Stored class fusions from this table:

2⁸.A₉, S₉, A₁₀, O₈⁺(2)

Stored class fusions to this table:

2.A₉, 2¹⁺⁸.2.A₉, 2¹⁺⁸₊.A₉, 2⁸.A₉, 2 × 2.A₉, 3²:2A₄, 3³.S₄, (3 × A₆).2₁, (A₄ × A₅):2, S₇, A₈, L₂(8).3, L₂(8).3

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