#14332583

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁴

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃×D₅
commutator, socle, prime radical, cosocle	C₂³×C₃×C₅	C₂⁴
Fitting	C₂×C₃×C₅×C₄⋊C₄	C₂²
hypercenter	C₂×C₄⋊C₄	D₃×D₅
hypocenter	C₃×C₅	#2399
LCS	G ▷ C₂³×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

1008 conjugacy classes of subgroups.

μ_t(G) = 1920

Polycyclic presentation:

2^7,3,5|a^2=e,b^2=e,c^2=e,d^2=ef,b^a=be,c^a=cf,c^b=cg,h^b=h^2,i^c=i^4,h^d=h^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 58281);