C₃⋊(A₄⋊D₁₃) #11745600

order	936
isoclinism	isoclinic class of C₃⋊(A₄⋊D₁₃)
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂×C₃

Aliases

unambiguous semidirect product	C₃⋊(A₄⋊D₁₃)
unambiguous semidirect product	A₄⋊D₃₉
unambiguous semidirect product	C₁₃⋊(C₃⋊S₄)

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×A₄×C₁₃	C₂
Fitting, socle	C₂²×C₃×C₁₃	D₃
LCS	G ▷ C₃×A₄×C₁₃
UCS	C₁

60 conjugacy classes of subgroups.

μ_t(G) = 156

Polycyclic presentation:

2,3^2,13,2^2|b^a=b^2,c^a=c^2,d^a=d^12,e^a=f,f^a=e,e^b=ef,f^b=e

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(936, 193);