#14305033

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂³	C₂×D₃×AGL(1,𝔽₅)
commutator, socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
Fitting	C₂²×C₃×C₄×C₅	C₂×C₄
cosocle	C₂²×C₃×Dic₅	C₂³
hypercenter	C₂²×C₄	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	#1940
LCS	G ▷ C₂³×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

496 conjugacy classes of subgroups.

μ_t(G) = 1920

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 30731);