(C₅⋊D₅)⋊C₉ #90647

order	450
isoclinism	isoclinic class of (C₅⋊D₅)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₅

Aliases

(C₅⋊D₅)⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²	C₂×C₉
Fitting, socle, cosocle	C₃×C₅²	C₂×C₃
prime radical	C₃×C₅⋊D₅	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 45

A minimal faithful permutation representation — 2 generators on 24 points:

(1,2,4)(3,6,10,7,5,12)(8,13,15,14,11,9)(16,20,24,18,23,19,21,17,22);(1,3,8,14,7)(2,5,11,13,6)(4,9,10,12,15)

Polycyclic presentation:

2,3^2,5^2|b^3=c,d^a=d^4,e^a=e^4,d^b=d^3e^2,e^b=de

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(450, 12);