Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for G₂(3).2

Name:

G2(3).2

Group order:

8491392 = 2⁷ ⋅ 3⁶ ⋅ 7 ⋅ 13

Number of classes:

28

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., constructions: Aut(G2(3))

Maximal subgroups:

	Order	Index	Structure	Name
1	4245696	2	G2(3)	G2(3)
2	5832	1456	32.(3 × 3(1+2)+):D8	3^2.(3x3^(1+2)+):D8
3	3024	2808	L2(8):3 × 2	L2(8):3x2
4	2688	3159	23.L3(2):2	2^3.L3(2):2
5	2184	3888	L2(13).2	L2(13).2
6	1152	7371	2(1+4)+.(S3 × S3)	2^(1+4)+.(S3xS3)

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	128	66339	G2(3).2N2	G2(3).2N2

Available Brauer tables:

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

Atlas representations:

7 available

Group constructions in GAP:

AtlasGroup( "G2(3).2" ), AtlasSubgroup( "Fi22.2", 12 ), AutomorphismGroup( AtlasGroup( "G2(3)" ) ), PrimitiveGroup( 1456, 3 ), PrimitiveGroup( 2808, 2 ), PrimitiveGroup( 3159, 2 ), PrimitiveGroup( 3888, 2 )

Stored class fusions from this table:

Fi₂₂.2

Stored class fusions to this table:

2³.L₃(2):2, 2⁽¹⁺⁴⁾⁺.(S₃ × S₃), 3.G₂(3).2, 3².(3 × 3⁽¹⁺²⁾⁺):D₈, 4²:D₁₂.2, 13:12, (3²:2 × G₂(3)).2, (3 × G₂(3)):2, G₂(3), G₂(3).2N2, L₂(8):3 × 2, L₂(13).2

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