Finite Group Databasebeta

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C₅×#4513 #11746212

order	960
isoclinism	isoclinic class of #4513
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Hall	C₃×C₅ ⋊ #365
Sylow	C₃ ⋊ C₅×#365

Subgroups

	subgroup	G/H
center	C₂×C₅	#817
commutator	C₃×C₈	C₂×C₄×C₅
Frattini	C₂×C₈	C₂×C₅×D₃
Fitting	C₃×C₅×M₃₂	C₂
socle	C₂×C₃×C₅	#106
prime radical	C₂²×C₃×C₅	SD₁₆
cosocle	C₂×C₃×C₈	C₂²×C₅
hypercenter	C₅×M₃₂	D₃
hypocenter	C₃	C₅×#365
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂×C₄×C₅ ◁ C₂×C₅×C₈ ◁ C₅×M₃₂

84 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

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

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₃×#365, C₂×C₅×#4513, D₅×#4513, …
maximal normal subgroup of	C₅×D₃×#365, C₂×C₅×#4513, D₅×#4513, …
maximal quotient of	C₅×#67513, C₅×#67816, C₂×C₅×#4513

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 407);