Extensions 1→N→G→Q→1 with N=C₂₀ and Q=Q₈

Direct product G=N×Q with N=C₂₀ and Q=Q₈

		d	ρ	Label	ID
Q₈×C₂₀		160		Q8xC20	160,180

Semidirect products G=N:Q with N=C₂₀ and Q=Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀⋊Q₈ = C₂₀⋊Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂₀	160		C20:Q8	160,109
C₂₀⋊₂Q₈ = C₂₀⋊₂Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20:2Q8	160,90
C₂₀⋊₃Q₈ = C₄×Dic₁₀	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20:3Q8	160,89
C₂₀⋊₄Q₈ = C₅×C₄⋊Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20:4Q8	160,189

Non-split extensions G=N.Q with N=C₂₀ and Q=Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁Q₈ = C₁₀.D₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂₀	160		C20.1Q8	160,14
C₂₀.₂Q₈ = C₂₀.Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₂₀	160		C20.2Q8	160,15
C₂₀.₃Q₈ = C₄.Dic₁₀	φ: Q₈/C₂ → C₂² ⊆ Aut C₂₀	160		C20.3Q8	160,111
C₂₀.₄Q₈ = C₄₀⋊₆C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20.4Q8	160,24
C₂₀.₅Q₈ = C₄₀⋊₅C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20.5Q8	160,25
C₂₀.₆Q₈ = C₂₀.₆Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20.6Q8	160,91
C₂₀.₇Q₈ = C₂₀⋊₃C₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20.7Q8	160,11
C₂₀.₈Q₈ = C₂₀.₈Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20.8Q8	160,21
C₂₀.₉Q₈ = C₅×C₄.Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20.9Q8	160,56
C₂₀.₁₀Q₈ = C₅×C₂.D₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20.10Q8	160,57
C₂₀.₁₁Q₈ = C₅×C₄².C₂	φ: Q₈/C₄ → C₂ ⊆ Aut C₂₀	160		C20.11Q8	160,186
C₂₀.₁₂Q₈ = C₅×C₄⋊C₈	central extension (φ=1)	160		C20.12Q8	160,55

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁