Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for U₃(5).2

Name:

U3(5).2

Group order:

252000 = 2⁵ ⋅ 3² ⋅ 5³ ⋅ 7

Number of classes:

19

InfoText value:

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

Duplicates:

HSM3

Maximal subgroups:

	Order	Index	Structure	Name
1	126000	2	U3(5)	U3(5)
2	5040	50	S7	A7.2
3	2000	126	51+2+:8:2	5^(1+2):(8.2)
4	1440	175	A6.22	A6.2^2
5	480	525	2S5.2	2S5.2
6	336	750	L3(2).2	L3(2).2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	32	7875	U3(5).2N2	U3(5).2N2
5	2000	126	51+2+:8:2	5^(1+2):(8.2)

Available Brauer tables:

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

Atlas representations:

33 available

Group constructions in GAP:

AtlasGroup( "U3(5).2" ), AtlasStabilizer( "HS", "HSG1-p176aB0" ), AtlasStabilizer( "HS", "HSG1-p176bB0" ), AtlasStabilizer( "McL.2", "McLd2G1-p7128B0" ), AtlasSubgroup( "HS", 2 ), AtlasSubgroup( "HS", 3 ), AtlasSubgroup( "McL.2", 3 ), AtlasSubgroup( "Ru", 5 ), PrimitiveGroup( 50, 2 ), PrimitiveGroup( 126, 4 ), PrimitiveGroup( 175, 4 ), PrimitiveGroup( 525, 2 ), PrimitiveGroup( 750, 1 )

Stored class fusions from this table:

Co₃, HS, M^cL.2, Ru, U₃(5).3.2

Stored class fusions to this table:

2S₅.2, 3.U₃(5).2, 5¹⁺²₊:8:2, (D₁₀ × U₃(5)).2, A₆.2², S₇, Isoclinic(U₃(5).2 × 2), L₃(2).2, U₃(5), U₃(5).2N2

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