(C₂×D₁₁)⋊(C₃⋊Dic₃) #13097048

order	1584
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²×C₃

Aliases

(C₂×D₁₁)⋊(C₃⋊Dic₃)

	subgroup	G/H
center, Frattini, hypercenter	C₂²	C₃⋊D₃×D₁₁
commutator	C₂×C₃²×C₁₁	C₂×C₄
Fitting, socle, cosocle	C₂²×C₃²×C₁₁	C₂²
prime radical	C₂²×C₃²×D₁₁	C₂
hypocenter	C₃²×C₁₁	C₂²⋊C₄
LCS	G ▷ C₂×C₃²×C₁₁ ▷ C₃²×C₁₁
UCS	C₁ ◁ C₂²

204 conjugacy classes of subgroups.

μ_t(G) = 792

Polycyclic presentation:

2^4,3^2,11|b^2=c,b^a=bd,g^a=g^10,e^b=e^2,f^b=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 212);