#13085541

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

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₅⋊#157
commutator, socle	C₂×C₃²×C₅	C₂×C₈
Fitting	C₃²×C₄×C₅	C₂×C₄
prime radical	C₂×C₃²×D₅	C₈
cosocle	C₃⋊(C₃⋊#168)	C₂²
hypocenter	C₃²×C₅	M₃₂
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₄

96 conjugacy classes of subgroups.

μ_t(G) = 240

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1858);