C₃⋊(C₃⋊#4208) #13091703

order	1458
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₃⁵

Aliases

	subgroup	G/H
center, hypercenter	C₉	C₃⋊(C₃⋊(C₃⋊D₃))
commutator, cosocle, hypocenter	C₃²×H(3,𝔽₃)	C₂×C₃
Frattini	C₃	C₃×C₃⋊(C₃⋊(C₃⋊D₃))
Fitting	C₃²×#737	C₂
socle	C₃³	C₃×C₃⋊D₃
prime radical	C₃⋊(C₃⋊#272)	C₃
LCS	G ▷ C₃²×H(3,𝔽₃)
UCS	C₁ ◁ C₉

2228 conjugacy classes of subgroups.

μ_t(G) = 162

Polycyclic presentation:

2,3^6|d^3=g,b^a=b^2g,c^a=c^2g,d^a=de^2,e^a=e^2,f^a=f^2,c^b=cg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 1777);