#564⋊C₉ #10589568

order	576
isoclinism	isoclinic class of #564⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉ · Schur multiplier (H₂) = C₂⁴

Aliases

#564 ⋊ C₉

	subgroup	G/H
center, hypercenter	C₃	#564⋊C₃
commutator, hypocenter	#564	C₉
Frattini, socle, prime radical	C₂²×C₃	C₂²⋊A₄
Fitting, cosocle	C₃×#564	C₃
LCS	G ▷ #564
UCS	C₁ ◁ C₃

76 conjugacy classes of subgroups.

μ_t(G) = 144

Polycyclic presentation:

3^2,2^6|a^3=b,c^2=h,d^2=g,e^2=h,f^2=g,c^a=cd,d^a=cg,e^a=ef,f^a=eg,g^a=h,h^a=gh,e^c=egh,f^c=fg,e^d=eg,f^d=fh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 1450);