C₃⋊(C₃⋊#1044) #11744702

order	900
isoclinism	isoclinic class of C₃⋊(C₃⋊#1044)
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃×C₅

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²	C₄
prime radical, cosocle	C₃²×C₅⋊D₅	C₂
LCS	G ▷ C₃²×C₅²
UCS	C₁

96 conjugacy classes of subgroups.

μ_t(G) = 90

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(900, 114);