C₃⋊#63419 #11720733

order	864
isoclinism	isoclinic class of C₃⋊#63419
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂×C₃

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₄²⋊C₉	C₂
Frattini	C₂²×C₃	C₃⋊S₄
Fitting	C₃²×C₄²	D₃
socle	C₂²×C₃²	S₄
LCS	G ▷ C₃×C₄²⋊C₉
UCS	C₁

132 conjugacy classes of subgroups.

μ_t(G) = 108

Polycyclic presentation:

2,3^3,2^4|b^3=d^2,e^2=g,f^2=gh,b^a=b^2d,c^a=c^2,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, 700);