#14279166

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center	C₄	#90995
commutator	C₂×C₃×C₄×C₅	C₄²
Frattini, hypercenter	C₂×#41	D₃×D₅
Fitting, prime radical, cosocle	C₂×C₃×C₅×#41	C₂²
socle	C₂×C₃×C₅	#342
hypocenter	C₃×C₅	#1395
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×#41

324 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 96 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=e,c^2=g,e^2=g,b^a=bc,c^a=cf,e^a=eg,f^a=fg,h^a=h^2,d^b=dfg,i^b=i^4,d^c=dg

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 4864);