C₅×#4799 #11750298

order	960
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₅×#4799

Splittings

Hall	C₃×C₅ ⋊ #479
Sylow	C₃ ⋊ C₅×#479

Subgroups

	subgroup	G/H
center	C₂²×C₅	D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂³×C₅
Frattini	C₂×C₄	C₂²×C₅×D₃
Fitting	C₃×C₅×#103	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×D₄
hypercenter	C₅×#103	D₃
hypocenter	C₃	C₅×#479
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄×C₅ ◁ C₅×#103

180 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(6,7,8)(9,11,12,16)(10,13,14,15)(19,25)(21,28)(22,29)(24,32)(26,27)(30,31);(17,19,20,26)(18,22,23,30)(21,25,28,27)(24,29,32,31);(7,8)(9,10,12,14)(11,15,16,13)(17,18,20,23)(19,22,26,30)(21,24,28,32)(25,29,27,31)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#479, C₂×C₅×#4799, D₅×#4799, …
maximal normal subgroup of	C₅×D₃×#479, C₂×C₅×#4799, D₅×#4799, …
maximal quotient of	C₅×#70222, C₅×#70235, C₅×#70238, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 4493);