#13088366

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini, hypercenter	C₂	#10624306
commutator	C₅×C₃⋊Dic₃	C₂×C₄
Fitting, socle	C₂×C₃²×C₅	C₄⋊C₄
prime radical	C₂×C₃²×D₅	D₄
cosocle	D₅×C₃⋊Dic₃	C₂²
hypocenter	C₃²×C₅	#107
LCS	G ▷ C₅×C₃⋊Dic₃ ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₂

124 conjugacy classes of subgroups.

μ_t(G) = 120

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4683);