#13085501

order	1440
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂×C₃

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₅×#157
commutator, socle	C₂×C₃²×C₅	C₄²
Fitting	C₃²×C₄×C₅	C₂×C₄
prime radical	C₂×C₅×C₃⋊D₃	C₂×C₄
cosocle	C₄×C₅×C₃⋊D₃	C₂²
hypocenter	C₃²×C₅	#97
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₄

124 conjugacy classes of subgroups.

μ_t(G) = 240

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1818);