Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for A₈

Name:

A8

Group order:

20160 = 2⁶ ⋅ 3² ⋅ 5 ⋅ 7

Number of classes:

14

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	2520	8	A7	A7
2	1344	15	23:L3(2)	2^3:sl(3,2)
3	1344	15	23:L3(2)	2^3:sl(3,2)
4	720	28	S6	A6.2_1
5	576	35	24:(S3 × S3)	2^4:(S3xS3)
6	360	56	(A5 × 3):2	(A5x3):2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	64	315	s61p	s61p
3	72	280	32:D8	s3wrs2
5	60	336	(3 × D10).2	(3xD10).2
7	21	960	7:3	7:3

Available Brauer tables:

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

Atlas representations:

21 available

Group constructions in GAP:

AlternatingGroup( 8 ), AtlasGroup( "A8" ), AtlasStabilizer( "A9", "A9G1-p9B0" ), AtlasStabilizer( "M23", "M23G1-p506B0" ), AtlasSubgroup( "M23", 4 ), AtlasSubgroup( "Ru", 8 ), PSL( 4, 2 ), PerfectGroup( 20160, 4 ), PrimitiveGroup( 8, 6 ), PrimitiveGroup( 15, 4 ), PrimitiveGroup( 28, 7 ), PrimitiveGroup( 35, 1 ), PrimitiveGroup( 56, 6 ), TransitiveGroup( 8, 49 ), TransitiveGroup( 15, 72 ), TransitiveGroup( 28, 433 )

Stored class fusions from this table:

2⁴:A₈, 2⁶:A₈, S₈, A₉, M₂₃, P31/G1/L1/V1/ext3, Ru

Stored class fusions to this table:

2.A₈, (2¹⁺⁶₊ × 2⁴).A₈, 2³.S₄v₁, 2³.S₄v₂, 2³:L₃(2), 2⁴.A₈, 2⁴:(S₃ × S₃), 2⁴:A₈, 2⁶:A₈, 2¹⁰.A₈, 2¹⁺⁶₊.A₈, 7:3, (3 × D₁₀).2, (A₅ × 3):2, S₆, A₇, 2⁷.A₈, P31/G1/L1/V1/ext3, 3²:D₈, s₆₁p

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