C₅⋊(#2070⋊C₃) #14511552

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₅⋊(#2070⋊C₃)
unambiguous semidirect product	#10599516⋊C₃

Hall	#10599516 ⋊ C₃
Sylow	C₅ ⋊ #2070⋊C₃

	subgroup	G/H
center	C₂	C₅⋊(#396⋊C₃)
commutator, Fitting, cosocle, hypocenter	C₅×#338	C₂×C₃
Frattini	C₂²×C₄	D₅×A₄
socle	C₂×C₅	#396⋊C₃
prime radical	C₅×#338⋊C₃	C₂
hypercenter	C₄	C₅⋊(#126⋊C₃)
LCS	G ▷ C₅×#338
UCS	C₁ ◁ C₂ ◁ C₄

112 conjugacy classes of subgroups.

μ_t(G) = 160

Polycyclic presentation:

2,3,2^2,5,2^4|a^2=i,c^2=f,d^2=fghi,f^2=i,c^a=chi,d^a=dgh,e^a=e^4,f^a=fi,c^b=dg,d^b=cd,f^b=fgh,g^b=h,h^b=ghi,d^c=dfg,h^c=hi,f^d=fi,g^d=gi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237250);