Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for L₃(3).2

Name:

L3(3).2

Group order:

11232 = 2⁵ ⋅ 3³ ⋅ 13

Number of classes:

15

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,13], constructions: Aut(L3(3))

Duplicates:

2F4(2)'M2, G2(3)M6

Maximal subgroups:

	Order	Index	Structure	Name
1	5616	2	L3(3)	L3(3)
2	216	52	31+2:D8	3^(1+2):D8
3	96	117	group6	group6
4	78	144	13:6	13:6
5	48	234	2 × S4	2xSymm(4)

Available Brauer tables:

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

Atlas representations:

20 available

Group constructions in GAP:

AtlasGroup( "L3(3).2" ), AtlasStabilizer( "2F4(2)'", "TF42G1-p1600B0" ), AtlasStabilizer( "2F4(2)'", "TF42G1-p1600bB0" ), AtlasSubgroup( "2F4(2)'", 1 ), AtlasSubgroup( "2F4(2)'", 2 ), AtlasSubgroup( "G2(3)", 5 ), AtlasSubgroup( "G2(3)", 6 ), AtlasSubgroup( "S6(3)", 8 ), AtlasSubgroup( "Suz", 14 ), AtlasSubgroup( "Suz", 15 ), AutomorphismGroup( AtlasGroup( "L3(3)" ) ), PrimitiveGroup( 52, 1 ), PrimitiveGroup( 117, 1 ), PrimitiveGroup( 144, 2 ), PrimitiveGroup( 234, 2 ), TransitiveGroup( 26, 49 )

Stored class fusions from this table:

²F₄(2)', G₂(3), S₆(3), Suz

Stored class fusions to this table:

2 × S₄, 3¹⁺²:D₈, 13:6, (2 × L₃(3)).2, (13:6 × L₃(3)).2, L₃(3), group₆

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