C₅⋊(#1712⋊C₃) #14511545

order	1920
isoclinism	isoclinic class of C₅⋊(#1712⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₈

Aliases

unambiguous semidirect product	C₅⋊(#1712⋊C₃)
unambiguous semidirect product	#10598855⋊C₃

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₈²	C₂×C₃
Frattini	C₄²	D₅×A₄
socle	C₂²×C₅	#127⋊C₃
LCS	G ▷ C₅×C₈²
UCS	C₁

120 conjugacy classes of subgroups.

μ_t(G) = 120

Polycyclic presentation:

2,3,2^2,5,2^4|c^2=g,d^2=fghi,f^2=h,g^2=i,c^a=cgi,d^a=dfg,e^a=e^4,f^a=fh,g^a=gi,c^b=d,d^b=cdf,f^b=g,g^b=fghi,h^b=i,i^b=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237243);