#13048173

order	1296
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₂⁴×C₃

Aliases

No aliases for this group.

C₂⁴ ⋊ #733

	subgroup	G/H
center	C₃	C₃²⋊(C₂²⋊A₄)
commutator, prime radical, cosocle	C₂⁴×C₃²	C₃²
Frattini	C₃²	C₃×C₂²⋊A₄
Fitting	C₂⁴×C₃×C₉	C₃
socle	C₂⁴×C₃	H(3,𝔽₃)
hypercenter	C₃×C₉	C₂²⋊A₄
hypocenter	C₂⁴	#733
LCS	G ▷ C₂⁴×C₃² ▷ C₂⁴×C₃ ▷ C₂⁴
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉

291 conjugacy classes of subgroups.

μ_t(G) = 108

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1891);