C₃×D₄₅ #63194

order	270
isoclinism	isoclinic class of D₄₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₄₅
unambiguous semidirect product	C₅⋊(C₃×D₉)

	subgroup	G/H
center, hypercenter	C₃	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂×C₃
Frattini	C₃	C₃×D₁₅
Fitting	C₃×C₅×C₉	C₂
socle	C₃²×C₅	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₃

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 90

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(270, 12);