C₉⋊#1042 #11744644

order	900
isoclinism	isoclinic class of C₉⋊#1042
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₉	C₄
Frattini	C₃	C₃⋊#1042
socle	C₃×C₅²	Dic₃
prime radical	C₃×C₅×D₅	D₃
cosocle	C₅×C₉×D₅	C₂
LCS	G ▷ C₅²×C₉
UCS	C₁

39 conjugacy classes of subgroups.

μ_t(G) = 180

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(900, 56);