C₅×#458⋊C₃ #11749540

order	960
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×#458⋊C₃
unambiguous semidirect product	#458⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#458)⋊C₃

Fitting, Hall	C₅×#458 ⋊ C₃
Sylow	#458 ⋊ C₃×C₅

	subgroup	G/H
center, socle, hypercenter	C₂×C₅	#120⋊C₃
commutator, cosocle, hypocenter	H(5,𝔽₂)	C₂×C₃×C₅
Frattini	C₂³	C₂×C₅×A₄
Fitting	C₅×#458	C₃
prime radical	C₅×#997	C₂
LCS	G ▷ H(5,𝔽₂)
UCS	C₁ ◁ C₂×C₅

90 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3735);