D₃×C₅²⋊C₃ #90658

order	450
isoclinism	isoclinic class of D₃×C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	D₃×C₅²⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₅²⋊C₃)
unambiguous semidirect product	(C₅²×D₃)⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²	C₂×C₃
LCS	G ▷ C₃×C₅²
UCS	C₁

26 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 45

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 23);