#13145690

order	1728
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂³×C₃

Aliases

No aliases for this group.

C₃³ ⋊ #342

	subgroup	G/H
center	C₂²	#88803
commutator	C₂²×C₃³	C₄²
Frattini, hypercenter	C₂⁴	D₃×C₃⋊D₃
Fitting, prime radical, cosocle	C₂⁴×C₃³	C₂²
socle	C₂²×C₃³	C₂²⋊C₄
hypocenter	C₃³	#342
LCS	G ▷ C₂²×C₃³ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₂⁴

1380 conjugacy classes of subgroups.

μ_t(G) = 144

Polycyclic presentation:

2^6,3^3|a^2=e,b^2=c,b^a=bd,d^a=df,i^a=i^2,e^b=ef,g^b=g^2,h^b=h^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1728, 11753);