#14309001

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

Aliases

No aliases for this group.

	subgroup	G/H
center	C₂²	#91826
commutator, prime radical, cosocle	C₂⁴×C₃×C₅	C₂³
Frattini	C₂⁴	C₂²×D₁₅
Fitting	C₃×C₅×#381	C₂
socle	C₂²×C₃×C₅	#120
hypercenter	#381	D₁₅
hypocenter	C₃×C₅	#2030
LCS	G ▷ C₂⁴×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #381

580 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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,c^b=cf,e^b=eg,h^b=h^2,i^b=i^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 34699);