C₃⋊Dic₂₁₃ #14579385

order	2556
isoclinism	isoclinic class of C₃⋊D₂₁₃
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₃

Aliases

unambiguous semidirect product	C₃⋊Dic₂₁₃
unambiguous semidirect product	C₇₁⋊(C₃⋊Dic₃)

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊D₂₁₃
commutator, hypocenter	C₃²×C₇₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃²×C₇₁	C₂
LCS	G ▷ C₃²×C₇₁
UCS	C₁ ◁ C₂

36 conjugacy classes of subgroups.

μ_t(G) = 2556

Polycyclic presentation:

2,3^2,71,2|a^2=e,b^a=b^2,c^a=c^2,d^a=d^70

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2556, 16);