C₅×#401⋊C₃ #11749537

order	960
isoclinism	isoclinic class of #396⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×#401⋊C₃
unambiguous semidirect product	#401⋊(C₃×C₅)
unambiguous semidirect product	(C₅×#401)⋊C₃

Fitting, Hall	C₅×#401 ⋊ C₃
Sylow	#401 ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₂×C₅	#126⋊C₃
commutator, cosocle, hypocenter	#95	C₂×C₃×C₅
Frattini	C₂³	C₂×C₅×A₄
Fitting	C₅×#401	C₃
socle	C₂³×C₅	C₂×A₄
prime radical	C₅×#95⋊C₃	C₂
LCS	G ▷ #95
UCS	C₁ ◁ C₂×C₅

66 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)(6,11,24,13,8,20,10,22,14,7,17,27)(9,25,23,12,16,29,19,21,26,18,15,28);(6,9)(7,18)(10,19)(11,22)(12,13)(14,26,24,23)(15,16)(20,28,27,29)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 3732);