#14513019

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²	C₂×D₅×S₄
commutator, prime radical, cosocle	C₂²×C₅×A₄	C₂³
Fitting	C₂³×C₄×C₅	C₂×D₃
socle	C₂⁴×C₅	C₂²×D₃
hypercenter	C₂×C₄	D₅×S₄
hypocenter	C₅×A₄	#125
LCS	G ▷ C₂²×C₅×A₄ ▷ C₅×A₄
UCS	C₁ ◁ C₂² ◁ C₂×C₄

510 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 63 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:

2^5,3,5,2^2|a^2=e,b^2=d,c^2=de,c^a=cde,g^a=g^4,c^b=cd,f^b=f^2,h^b=hi,h^f=i,i^f=hi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 238717);