(C₂₁₁⋊C₃)⋊C₄ #14579231

order	2532
isoclinism	isoclinic class of D₂₁₁⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	(C₂₁₁⋊C₃)⋊C₄
unambiguous semidirect product	Dic₂₁₁⋊C₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₁₁⋊C₃
commutator, hypocenter	C₂₁₁	C₃×C₄
Fitting, socle, cosocle	C₂×C₂₁₁	C₂×C₃
prime radical	C₂×C₂₁₁⋊C₃	C₂
LCS	G ▷ C₂₁₁
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 215
transitive degree	μ_t(G) = 844

Polycyclic presentation:

2,3,211,2|a^2=d,c^a=c^210,c^b=c^196

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2532, 2);