#63419⋊C₃ #11720717

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

Aliases

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

91 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 36

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 684);