((C₂⁴⋊C₅)⋊C₂)⋊C₉ #13088247

order	1440
isoclinism	isoclinic class of ((C₂⁴⋊C₅)⋊C₂)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	((C₂⁴⋊C₅)⋊C₂)⋊C₉
unambiguous semidirect product	((C₂⁴⋊C₅)⋊C₉)⋊C₂

derived	C₂⁴⋊C₅ ⋊ C₂×C₉
Hall	(C₂⁴⋊C₅)⋊C₂ ⋊ C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	((C₂⁴⋊C₅)⋊C₂)⋊C₃
commutator, hypocenter	C₂⁴⋊C₅	C₂×C₉
Fitting, socle	C₂⁴×C₃	C₃×D₅
prime radical	C₃×(C₂⁴⋊C₅)⋊C₂	C₃
cosocle	C₃×C₂⁴⋊C₅	C₂×C₃
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁ ◁ C₃

52 conjugacy classes of subgroups.

μ_t(G) = 90

Polycyclic presentation:

2,3^2,5,2^4|b^3=c,d^a=d^4,e^a=ef,g^a=gh,e^b=egh,f^b=fh,g^b=ef,h^b=f,e^d=ef,f^d=fg,g^d=efh,h^d=efgh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4564);