#6057⋊C₉ #14268078

order	1800
isoclinism	isoclinic class of #6057⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉ · Schur multiplier (H₂) = C₅

Aliases

derived, Hall	#6057 ⋊ C₉
Sylow	C₅² ⋊ Q₈⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	#6057⋊C₃
commutator, hypocenter	#6057	C₉
Fitting, socle	C₃×C₅²	SL(2,𝔽₃)
prime radical	C₃×C₅⋊D₅	A₄
cosocle	C₃×#6057	C₃
LCS	G ▷ #6057
UCS	C₁ ◁ C₃

28 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 90

Polycyclic presentation:

3^2,2^3,5^2|a^3=b,c^2=e,d^2=e,c^a=d,d^a=cde,f^a=fg^3,g^a=f^4g^3,d^c=de,f^c=f^3g^3,g^c=g^2,f^d=fg,g^d=f^3g^4,f^e=f^4,g^e=g^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1800, 272);