C₃⋊(C₉⋊#226) #13048414

order	1296
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₃³

Aliases

unambiguous semidirect product	C₃⋊(C₉⋊#226)
unambiguous semidirect product	C₉⋊(C₃⋊#226)

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₉⋊S₄)
commutator, cosocle, hypocenter	C₃×C₉×SL(2,𝔽₃)	C₂
Frattini	C₂×C₃	C₃⋊(C₃⋊S₄)
Fitting	C₃×Q₈×C₉	D₃
socle	C₂×C₃²	C₃⋊S₄
prime radical	C₃²×SL(2,𝔽₃)	D₃
LCS	G ▷ C₃×C₉×SL(2,𝔽₃)
UCS	C₁ ◁ C₂

280 conjugacy classes of subgroups.

μ_t(G) = 432

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2132);