C₃⋊#66244 #11756804

order	960
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊((C₂⁴⋊C₅)⋊C₂)
commutator, cosocle, hypocenter	C₃×2₋¹⁺⁴⋊C₅	C₂
Fitting	C₃×2₋¹⁺⁴	D₅
socle	C₂×C₃	(C₂⁴⋊C₅)⋊C₂
LCS	G ▷ C₃×2₋¹⁺⁴⋊C₅
UCS	C₁ ◁ C₂

104 conjugacy classes of subgroups.

μ_t(G) = 96

Polycyclic presentation:

2,3,5,2^5|d^2=h,f^2=h,g^2=h,b^a=b^2,c^a=c^4,d^a=fh,e^a=defh,f^a=dh,g^a=deg,d^c=de,e^c=defh,f^c=eg,g^c=degh,f^d=fh,g^d=gh,f^e=fh,g^f=gh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10999);