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#13017013

order	1280
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

No aliases for this group.

Splittings

Fitting	C₅×D₄⋊C₈ ⋊ C₄
Sylow	C₅ ⋊ #8212

Subgroups

	subgroup	G/H
center	C₂×C₄	D₄×AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₄²	C₂²×AGL(1,𝔽₅)
Fitting	C₅×D₄⋊C₈	C₄
socle	C₂²×C₅	C₄×C₂²⋊C₄
prime radical	C₂×D₄×D₅	C₂×C₄
cosocle	C₄²×D₅	C₂³
hypercenter	D₄⋊C₈	AGL(1,𝔽₅)
hypocenter	C₅	#8212
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ D₄⋊C₈

550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 320

Polycyclic presentation:

2^8,5|a^2=e,b^2=f,c^2=e,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ch,d^a=dg,f^a=fg,i^a=i^3,c^b=cgh,i^b=i^3,i^c=i^2,i^e=i^4,i^f=i^4

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1087281);