C₃⋊(#1020⋊C₃) #11724710

order	864
isoclinism	isoclinic class of C₃⋊(#1020⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂×C₃

Aliases

Fitting, socle	C₂⁴×C₃ ⋊ C₃×D₃
derived	C₃×C₂²⋊A₄ ⋊ C₂×C₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₂²⋊A₄	C₂×C₃
Fitting, socle	C₂⁴×C₃	C₃×D₃
LCS	G ▷ C₃×C₂²⋊A₄
UCS	C₁

145 conjugacy classes of subgroups.

μ_t(G) = 24

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(864, 4677);