C₅×D₄₅ #90652

order	450
isoclinism	isoclinic class of D₄₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₄₅
unambiguous semidirect product	C₅⋊(C₅×D₉)
unambiguous semidirect product	C₉⋊(C₅×D₅)

	subgroup	G/H
center, hypercenter	C₅	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂×C₅
Frattini	C₃	C₅×D₁₅
Fitting	C₅²×C₉	C₂
socle	C₃×C₅²	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₅

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 90

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 17);