C₅²×D₉ #90651

order	450
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₉
unambiguous semidirect product	C₉⋊(C₂×C₅²)

Fitting, Hall	C₅²×C₉ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₅²

	subgroup	G/H
center, hypercenter	C₅²	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅²
Frattini	C₃	C₅²×D₃
Fitting	C₅²×C₉	C₂
socle	C₃×C₅²	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅²

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 225

A minimal faithful permutation representation — 2 generators on 19 points:

(6,7,8,9,10)(12,14)(13,17)(15,18)(16,19);(1,2,3,4,5)(11,16,14,13,18,15,17,12,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 16);