#14316014

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃×AGL(1,𝔽₅)
commutator, socle, prime radical	C₂²×C₃×C₅	C₂²×C₈
Fitting	C₃×C₄²×C₅	C₂×C₄
cosocle	C₂×C₃×#168	C₂³
hypercenter	C₄²	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#2183
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

252 conjugacy classes of subgroups.

μ_t(G) = 1920

Polycyclic presentation:

2^7,3,5|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^2,i^a=i^2,h^b=h^2,h^c=h^2,i^c=i^2,i^e=i^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 41712);