#14309011

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#91577
commutator, prime radical, cosocle	C₂⁴×C₃×C₅	C₂³
Frattini	C₂⁴	C₂×D₃×D₅
Fitting	C₂³×C₃×C₄×C₅	C₂²
socle	C₂²×C₃×C₅	#120
hypercenter	C₂³×C₄	D₃×D₅
hypocenter	C₃×C₅	#2030
LCS	G ▷ C₂⁴×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×C₄

580 conjugacy classes of subgroups.

μ_t(G) = 480

Polycyclic presentation:

2^7,3,5|a^2=d,b^2=d,c^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,c^b=cf,e^b=eg,i^b=i^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 34709);