Extensions 1→N→G→Q→1 with N=D₈₀ and Q=C₂

Direct product G=N×Q with N=D₈₀ and Q=C₂

		d	ρ	Label	ID
C₂×D₈₀		160		C2xD80	320,529

Semidirect products G=N:Q with N=D₈₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₈₀⋊₁C₂ = D₁₆₀	φ: C₂/C₁ → C₂ ⊆ Out D₈₀	160	2+	D80:1C2	320,6
D₈₀⋊₂C₂ = D₈₀⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out D₈₀	80	4+	D80:2C2	320,535
D₈₀⋊₃C₂ = C₅⋊D₃₂	φ: C₂/C₁ → C₂ ⊆ Out D₈₀	160	4+	D80:3C2	320,77
D₈₀⋊₄C₂ = D₅×D₁₆	φ: C₂/C₁ → C₂ ⊆ Out D₈₀	80	4+	D80:4C2	320,537
D₈₀⋊₅C₂ = D₈₀⋊₅C₂	φ: C₂/C₁ → C₂ ⊆ Out D₈₀	160	4+	D80:5C2	320,546
D₈₀⋊₆C₂ = C₁₆⋊D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₈₀	80	4+	D80:6C2	320,541
D₈₀⋊₇C₂ = D₈₀⋊₇C₂	φ: trivial image	160	2	D80:7C2	320,531

Non-split extensions G=N.Q with N=D₈₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₈₀.₁C₂ = C₁₆₀⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out D₈₀	160	2	D80.1C2	320,7
D₈₀.₂C₂ = C₅⋊SD₆₄	φ: C₂/C₁ → C₂ ⊆ Out D₈₀	160	4+	D80.2C2	320,79

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁