D₅⋊#3771 #13088379

order	1440
isoclinism	isoclinic class of D₅⋊AGL(1,𝔽₉)
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅⋊AGL(1,𝔽₉)
commutator, hypocenter	C₃²×C₅	C₂×C₁₆
Fitting, socle	C₂×C₃²×C₅	C₂×C₈
prime radical	C₂×C₃²×D₅	C₈
cosocle	#67126	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂

72 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,f^a=f^2g^2,g^a=f^2,h^a=h^2,f^b=f^2g,g^b=fg,f^c=f^2g,g^c=fg,h^c=h^4,f^d=f^2,g^d=g^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4696);