C₃³×D₅ #63205

order	270
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃³ · Schur multiplier (H₂) = C₃³

Aliases

direct product	C₃³×D₅
unambiguous semidirect product	C₅⋊(C₂×C₃³)

Fitting, socle, Hall	C₃³×C₅ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₃³

	subgroup	G/H
center, hypercenter	C₃³	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃³
Frattini	C₁	G
Fitting, socle	C₃³×C₅	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃³

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 135

A minimal faithful permutation representation — 3 generators on 14 points:

(7,8,9)(11,12)(13,14);(4,5,6)(10,11,13,14,12);(1,2,3)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(270, 23);