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C₅×#4543 #11746242

order	960
isoclinism	isoclinic class of #4537
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Hall	C₃×C₅ ⋊ #330
Sylow	C₃ ⋊ C₅×#330

Subgroups

	subgroup	G/H
center	C₂²×C₅	#217
commutator	C₂×C₃×C₄	C₂×C₄×C₅
Frattini	C₄²	C₂×C₅×D₃
Fitting	C₃×C₅×#125	C₂
socle, prime radical	C₂²×C₃×C₅	C₂²⋊C₄
cosocle	C₃×C₄²	C₂²×C₅
hypercenter	C₅×#125	D₃
hypocenter	C₃	C₅×#330
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#125

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,3,4,5)(6,7,8)(9,10,12,14)(11,15,16,13)(17,19)(18,21)(20,23)(22,24);(7,8)(10,13,14,15)(17,18,20,22,21,19,24,23)

Conjugacy classes & character table

165 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#330, C₂×C₅×#4543, D₅×#4543, …
maximal normal subgroup of	C₅×D₃×#330, C₂×C₅×#4543, D₅×#4543, …
maximal quotient of	C₅×#67638, C₅×#67630, C₂×C₅×#4543

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 437);