#13088889

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

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂	C₂×C₅⋊PSU(3,𝔽₂)
commutator, prime radical, cosocle	C₂×C₅×C₃⋊D₃	C₂³
Fitting	C₃²×C₄×C₅	Q₈
socle	C₂×C₃²×C₅	C₂×Q₈
hypercenter	C₄	C₅⋊PSU(3,𝔽₂)
hypocenter	C₃²×C₅	#125
LCS	G ▷ C₂×C₅×C₃⋊D₃ ▷ C₃²×C₅
UCS	C₁ ◁ C₂ ◁ C₄

128 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.

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

μ_t(G) = 240

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 5206);