Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for U₄(3).2₁

Name:

U4(3).2_1

Group order:

6531840 = 2⁸ ⋅ 3⁶ ⋅ 5 ⋅ 7

Number of classes:

34

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7], constructions: PSO(-1,6,3)

Maximal subgroups:

	Order	Index	Structure	Name
1	3265920	2	U4(3)	U4(3)
2	58320	112	34:(2 × A6)	3^4:(2xA6)
3	51840	126	U4(2).2	U4(2).2
4	51840	126	U4(2).2	U4(3).2_1M4
5	40320	162	L3(4).22	L3(4).2_2
6	40320	162	L3(4).22	L3(4).2_2
7	23328	280	3(1+4)+.4S4	3^(1+4)+.4S4
8	12096	540	2 × U3(3)	2xU3(3)
9	11520	567	24.S6	2^4.s6
10	11520	567	24.S6	U4(3).2_1M10
11	2304	2835	4(A4 × A4).4	4(A4xA4).4
12	1440	4536	A6.22	A6.2^2
13	1440	4536	A6.22	A6.2^2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
5	40	163296	2 × 5:4	2x5:4
7	42	155520	2 × 7:3	2x7:3

Available Brauer tables:

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

Group constructions in GAP:

PSO( -1, 6, 3 ), PrimitiveGroup( 112, 3 ), PrimitiveGroup( 126, 10 ), PrimitiveGroup( 162, 4 ), PrimitiveGroup( 280, 15 ), PrimitiveGroup( 540, 3 ), PrimitiveGroup( 567, 4 ), PrimitiveGroup( 2835, 3 )

Stored class fusions from this table:

U₄(3).4, U₄(3).(2²)₁₂₂, U₄(3).(2²)₁₃₃, U₄(3).D₈

Stored class fusions to this table:

2.U₄(3).2₁, 2⁴.S₆, 2 × 5:4, 2 × 7:3, 2 × U₃(3), 3⁴:(2 × A₆), 3⁽¹⁺⁴⁾⁺.4S₄, 3₁.U₄(3).2₁, 3₂.U₄(3).2₁, 4(A₄ × A₄).4, 4.U₄(3).2₁, 6₁.U₄(3).2₁, 6₂.U₄(3).2₁, 12₁.U₄(3).2₁, 12₂.U₄(3).2₁, A₆.2², L₃(4).2₂, U₄(2).2, U₄(3), U₄(2).2, 2⁴.S₆

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