Extensions 1→N→G→Q→1 with N=C₈₀ and Q=C₂

Direct product G=N×Q with N=C₈₀ and Q=C₂

		d	ρ	Label	ID
C₂×C₈₀		160		C2xC80	160,59

Semidirect products G=N:Q with N=C₈₀ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₀⋊₁C₂ = D₈₀	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	80	2+	C80:1C2	160,6
C₈₀⋊₂C₂ = C₁₆⋊D₅	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	80	2	C80:2C2	160,7
C₈₀⋊₃C₂ = C₅×D₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	80	2	C80:3C2	160,61
C₈₀⋊₄C₂ = D₅×C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	80	2	C80:4C2	160,4
C₈₀⋊₅C₂ = C₈₀⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	80	2	C80:5C2	160,5
C₈₀⋊₆C₂ = C₅×SD₃₂	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	80	2	C80:6C2	160,62
C₈₀⋊₇C₂ = C₅×M₅(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	80	2	C80:7C2	160,60

Non-split extensions G=N.Q with N=C₈₀ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₀.₁C₂ = Dic₄₀	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	160	2-	C80.1C2	160,8
C₈₀.₂C₂ = C₅×Q₃₂	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	160	2	C80.2C2	160,63
C₈₀.₃C₂ = C₅⋊₂C₃₂	φ: C₂/C₁ → C₂ ⊆ Aut C₈₀	160	2	C80.3C2	160,1

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁