Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for U₄(3).2₃

Name:

U4(3).2_3

Group order:

6531840 = 2⁸ ⋅ 3⁶ ⋅ 5 ⋅ 7

Number of classes:

25

InfoText value:

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

Duplicates:

U4(3).2_3'

Maximal subgroups:

	Order	Index	Structure	Name
1	3265920	2	U4(3)	U4(3)
2	58320	112	34:M10	3^4:m10
3	40320	162	L3(4).23	L3(4).2_3
4	40320	162	L3(4).21	L3(4).2_1
5	23328	280	31+4:4S4	3^(1+4):4S4
6	12096	540	U3(3).2	U3(3).2
7	2304	2835	2(A4 × A4).4.2	2(A4xA4).4.2
8	1440	4536	M10 × 2	M10x2
9	1440	4536	A6.22	A6.2^2
10	1440	4536	A6.22	U4(3).2_3M10
11	768	8505	(42 × 2)S4	(4^2x2)S4

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
5	40	163296	2 × 5:4	2x5:4
7	42	155520	7:6	7:6

Available Brauer tables:

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

Group constructions in GAP:

AtlasStabilizer( "McL.2", "McLd2G1-p275B0" ), AtlasSubgroup( "McL.2", 2 ), PrimitiveGroup( 112, 4 ), PrimitiveGroup( 162, 2 ), PrimitiveGroup( 162, 3 ), PrimitiveGroup( 280, 16 ), PrimitiveGroup( 540, 2 ), PrimitiveGroup( 2835, 2 )

Stored class fusions from this table:

M^cL.2, U₄(3).(2²)₁₃₃, U₄(3).D₈

Stored class fusions to this table:

2(A₄ × A₄).4.2, 2.U₄(3).2₃, 2 × 5:4, 3⁴:M₁₀, 3¹⁺⁴:4S₄, 3₂.U₄(3).2₃, 4.U₄(3).2₃, 6₂.U₄(3).2₃, 7:6, 12₂.U₄(3).2₃, (4² × 2)S₄, A₆.2², Isoclinic(6₂.U₄(3).2₃), L₃(4).2₁, L₃(4).2₃, M₁₀ × 2, U₃(3).2, U₄(3), A₆.2²

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