Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for U₃(5).3

Name:

U3(5).3

Group order:

378000 = 2⁴ ⋅ 3³ ⋅ 5³ ⋅ 7

Number of classes:

34

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	126000	3	U3(5)	U3(5)
2	3000	126	5(1+2)+:24	5^(1+2)+:24
3	720	525	3 × 2S5	3x2S5
4	216	1750	32:2A4	3^2:2A4
5	216	1750	62:S3	6^2:S3
6	63	6000	7:3 × 3	7:3x3

Available Brauer tables:

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

Group constructions in GAP:

PGU( 3, 5 ), PrimitiveGroup( 126, 5 ), PrimitiveGroup( 525, 3 ), PrimitiveGroup( 1750, 1 ), PrimitiveGroup( 1750, 2 )

Stored class fusions from this table:

U₃(5).3.2

Stored class fusions to this table:

3.U₃(5).3, 3²:2A₄, 3 × 2S₅, 5⁽¹⁺²⁾⁺:24, 6²:S₃, 7:3 × 3, U₃(5)

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