#10603783⋊C₃ #14511593

order	1920
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

Hall	#10603783 ⋊ C₃
Sylow	C₅ ⋊ #1840⋊C₃

	subgroup	G/H
center, hypercenter	C₂	#65690⋊C₃
commutator, Fitting, hypocenter	C₅×#95	C₃×C₄
Frattini	C₂³	A₄×AGL(1,𝔽₅)
socle	C₂³×C₅	C₄×A₄
prime radical	C₅×#95⋊C₃	C₄
cosocle	#64937	C₂×C₃
LCS	G ▷ C₅×#95
UCS	C₁ ◁ C₂

102 conjugacy classes of subgroups.

μ_t(G) = 240

Polycyclic presentation:

2,3,2^3,5,2^3|a^2=c,c^2=gh,d^2=g,e^2=gi,d^a=dhi,e^a=ei,f^a=f^2,d^b=de,e^b=dhi,g^b=ghi,h^b=i,i^b=hi,f^c=f^4,e^d=egh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237291);