C₉⋊#857 #11720729

order	864
isoclinism	isoclinic class of C₉⋊#857
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂×C₃

Aliases

Fitting	C₄²×C₉ ⋊ D₃
derived	C₉×C₄²⋊C₃ ⋊ C₂

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉×C₄²⋊C₃	C₂
Frattini, socle	C₂²×C₃	C₃⋊S₄
Fitting	C₄²×C₉	D₃
LCS	G ▷ C₉×C₄²⋊C₃
UCS	C₁

96 conjugacy classes of subgroups.

μ_t(G) = 108

Polycyclic presentation:

2,3^3,2^4|c^3=d^2,e^2=g,f^2=gh,b^a=b^2,c^a=c^2d,d^a=d^2,e^a=fh,f^a=eh,g^a=gh,e^b=fg,f^b=ef,g^b=gh,h^b=g

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 696);