#13086770

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²	C₂×D₅×C₃⋊D₃
commutator, socle, prime radical, cosocle	C₂²×C₃²×C₅	C₂³
Fitting	C₂×C₃²×C₄×C₅	C₂²
hypercenter	C₂×C₄	D₅×C₃⋊D₃
hypocenter	C₃²×C₅	#125
LCS	G ▷ C₂²×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄

336 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

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

μ_t(G) = 1440

Polycyclic presentation:

2^5,3^2,5|a^2=e,b^2=d,c^2=e,c^a=cd,h^a=h^4,c^b=ce,f^b=f^2,g^b=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 3087);