#13084752

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₄	D₅×C₃⋊D₃
commutator	C₂×C₃²×C₅	C₂×C₈
Fitting, cosocle	C₂×C₃²×C₄×C₅	C₂²
socle, prime radical	C₂²×C₃²×C₅	C₂×C₄
hypocenter	C₃²×C₅	C₄⋊C₈
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂×C₄

228 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 114 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=d,b^2=c,d^2=e,b^a=bc,h^a=h^4,f^b=f^2,g^b=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1069);