Extensions 1→N→G→Q→1 with N=Q₃₂ and Q=D₅

Direct product G=N×Q with N=Q₃₂ and Q=D₅

		d	ρ	Label	ID
D₅×Q₃₂		160	4-	D5xQ32	320,544

Semidirect products G=N:Q with N=Q₃₂ and Q=D₅

extension	φ:Q→Out N	d	ρ	Label	ID
Q₃₂⋊₁D₅ = C₅⋊SD₆₄	φ: D₅/C₅ → C₂ ⊆ Out Q₃₂	160	4+	Q32:1D5	320,79
Q₃₂⋊₂D₅ = Q₃₂⋊D₅	φ: D₅/C₅ → C₂ ⊆ Out Q₃₂	160	4	Q32:2D5	320,545
Q₃₂⋊₃D₅ = D₈₀⋊₅C₂	φ: trivial image	160	4+	Q32:3D5	320,546

Non-split extensions G=N.Q with N=Q₃₂ and Q=D₅

extension	φ:Q→Out N	d	ρ	Label	ID
Q₃₂.D₅ = C₅⋊Q₆₄	φ: D₅/C₅ → C₂ ⊆ Out Q₃₂	320	4-	Q32.D5	320,80

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=Q32 and Q=D5