#14514567

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

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂	C₂×C₃⋊((C₂⁴⋊C₅)⋊C₂)
commutator, prime radical, cosocle	C₂×C₃×C₂⁴⋊C₅	C₂²
Fitting	C₂⁴×C₃×C₄	D₅
socle	C₂⁵×C₃	C₂×D₅
hypercenter	C₄	C₃⋊((C₂⁴⋊C₅)⋊C₂)
hypocenter	C₃×C₂⁴⋊C₅	Q₈
LCS	G ▷ C₂×C₃×C₂⁴⋊C₅ ▷ C₃×C₂⁴⋊C₅
UCS	C₁ ◁ C₂ ◁ C₄

552 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.

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

μ_t(G) = 120

Polycyclic presentation:

2^3,3,5,2^4|a^2=c,b^2=c,b^a=bc,d^a=d^2,e^a=e^4,f^a=fgi,h^a=hi,f^e=g,g^e=fgi,h^e=fh,i^e=fghi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240265);