Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for ³D₄(2).3

Name:

3D4(2).3

Group order:

634023936 = 2¹² ⋅ 3⁵ ⋅ 7² ⋅ 13

Number of classes:

49

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., constructions: Aut(3D4(2))

Duplicates:

F4(2)M10

Maximal subgroups:

	Order	Index	Structure	Name
1	211341312	3	3D4(2)	3D4(2)
2	774144	819	21+8+:L2(8):3	2^(1+8)_+:L2(8):3
3	258048	2457	22.[29]:(7:3 × S3)	2^2.[2^9]:(7:3xS3)
4	36288	17472	3 × U3(3).2	3xU3(3).2
5	9072	69888	S3 × L2(8).3	s3xpsl(2,8).3
6	7056	89856	(7:3 × L2(7)):2	(7:3xL2(7)):2
7	3888	163072	31+2+.(2S4 × 3)	3^(1+2)_+.(2S4x3)
8	3528	179712	72:(3 × 2A4)	7^2:(3x2A4)
9	648	978432	32:2A4 × 3	3^2:2A4x3
10	156	4064256	13:12	13:12

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
7	3528	179712	72:(3 × 2A4)	7^2:(3x2A4)

Available Brauer tables:

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

Atlas representations:

13 available

Group constructions in GAP:

AtlasGroup( "3D4(2).3" ), AtlasSubgroup( "Th", 1 ), AutomorphismGroup( AtlasGroup( "3D4(2)" ) ), PrimitiveGroup( 819, 6 ), PrimitiveGroup( 2457, 2 )

Stored class fusions from this table:

F₄(2), Th

Stored class fusions to this table:

2².[2⁹]:(7:3 × S₃), 2¹⁺⁸₊:L₂(8):3, ³D₄(2), 3²:2A₄ × 3, 3¹⁺²₊.(2S₄ × 3), 3 × U₃(3).2, 7²:(3 × 2A₄), 13:12, (7:3 × L₂(7)):2, S₃ × L₂(8).3

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