#17309⋊C₅ #13046044

order	1280
isoclinism	isoclinic class of #17309⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₅ · Schur multiplier (H₂) = C₄²

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	#17309	C₅
Frattini, socle	C₂⁴	C₂⁴⋊C₅
LCS	G ▷ #17309
UCS	C₁

152 conjugacy classes of subgroups.

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 40

Polycyclic presentation:

5,2^8|b^2=i,c^2=h,d^2=h,e^2=i,b^a=bcfh,c^a=cdeg,d^a=bcehi,e^a=defh,f^a=hi,g^a=fgi,h^a=ghi,i^a=fhi,c^b=cf,d^b=dg,e^b=ei,d^c=dh,e^c=efg,e^d=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1116312);