D₃₁⋊((C₅⋊D₅)⋊C₉) #42124513

order	27900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

unambiguous semidirect product	D₃₁⋊((C₅⋊D₅)⋊C₉)
unambiguous semidirect product	#28358426⋊C₂
unambiguous semidirect product	((C₅⋊D₅)⋊(C₃₁⋊C₉))⋊C₂
unambiguous semidirect product	(D₃₁⋊(C₅²⋊C₉))⋊C₂

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₃₁⋊((C₅⋊D₅)⋊C₃)
commutator, hypocenter	C₅²×C₃₁	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅²×C₃₁	C₂²×C₃
prime radical	C₃×C₅⋊D₅×D₃₁	C₃
LCS	G ▷ C₅²×C₃₁
UCS	C₁ ◁ C₃

100 conjugacy classes of subgroups.

Polycyclic presentation:

2^2,3,5^2,31,3|c^3=g,f^a=f^30,d^b=d^4,e^b=e^4,d^c=de^3,e^c=d^4e^3,f^c=f^5

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 260);