C₅⋊(#1747⋊C₃) #14511547

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

Aliases

unambiguous semidirect product	C₅⋊(#1747⋊C₃)
unambiguous semidirect product	#10599510⋊C₃

Hall	#10599510 ⋊ C₃
Sylow	C₅ ⋊ #1747⋊C₃

	subgroup	G/H
center, hypercenter	C₄	D₅×C₄²⋊C₃
commutator, Fitting, cosocle, hypocenter	C₅×#338	C₂×C₃
Frattini	C₂²×C₄	D₅×A₄
socle	C₂×C₅	#376⋊C₃
prime radical	C₅×#338⋊C₃	C₂
LCS	G ▷ C₅×#338
UCS	C₁ ◁ C₄

100 conjugacy classes of subgroups.

μ_t(G) = 160

Polycyclic presentation:

2,3,2^2,5,2^4|a^2=fh,c^2=f,d^2=fg,f^2=i,e^a=e^4,c^b=d,d^b=cdg,f^b=fg,g^b=hi,h^b=gh,d^c=dfh,g^c=gi,f^d=fi,g^d=gi,h^d=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237245);