C₃²×C₅⋊D₅ #90662

order	450
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃×C₅

Aliases

direct product	C₃²×C₅⋊D₅
unambiguous semidirect product	C₅⋊(C₃²×D₅)

Fitting, socle, Hall	C₃²×C₅² ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₃²

	subgroup	G/H
center, hypercenter	C₃²	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃²

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 225

A minimal faithful permutation representation — 3 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 27);