C₅×#376⋊C₃ #11749528

order	960
isoclinism	isoclinic class of #95⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×#376⋊C₃
unambiguous semidirect product	#376⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#376)⋊C₃

Fitting, Hall	C₅×#376 ⋊ C₃
Sylow	#376 ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₄×C₅	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₂×C₃×C₅
Frattini	C₂³	C₂×C₅×A₄
Fitting	C₅×#376	C₃
socle	C₂³×C₅	C₂×A₄
prime radical	C₅×#95⋊C₃	C₂
LCS	G ▷ #95
UCS	C₁ ◁ C₄×C₅

86 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 2 generators on 29 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3723);