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#13025969

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

Aliases

No aliases for this group.

Splittings

Fitting	C₅×C₄⋊C₁₆ ⋊ C₄
Sylow	C₅ ⋊ #12658

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂×C₄²
Frattini	C₂×C₈	C₂²×AGL(1,𝔽₅)
Fitting	C₅×C₄⋊C₁₆	C₄
socle	C₂²×C₅	C₂×#97
prime radical	C₂²×D₅	C₂×M₁₆
cosocle	C₂×C₈×D₅	C₂³
hypercenter	C₄⋊C₁₆	AGL(1,𝔽₅)
hypocenter	C₅	#12658
LCS	G ▷ C₂×C₄×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₁₆

350 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=de,d^2=h,f^2=g,g^2=h,b^a=bd,c^a=ch,f^a=fh,i^a=i^2,c^b=cg,e^b=eh,f^c=fh,i^c=i^3,i^e=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, 1096237);