#13027184

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×AGL(1,𝔽₅)
commutator, socle, prime radical	C₂³×C₅	C₂²×C₈
Fitting	C₂×C₅×C₄⋊C₈	C₄
cosocle	C₂²×#168	C₂³
hypercenter	C₂×C₄⋊C₈	AGL(1,𝔽₅)
hypocenter	C₅	#13160
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

338 conjugacy classes of subgroups.

μ_t(G) = 1280

Polycyclic presentation:

2^8,5|a^2=f,b^2=f,c^2=e,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^3,c^b=ch,i^b=i^2,i^f=i^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1097452);