Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₆₀

Direct product G=N×Q with N=Q₈ and Q=C₆₀

		d	ρ	Label	ID
Q₈×C₆₀		480		Q8xC60	480,924

Semidirect products G=N:Q with N=Q₈ and Q=C₆₀

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊C₆₀ = C₂₀×SL₂(𝔽₃)	φ: C₆₀/C₂₀ → C₃ ⊆ Out Q₈	160		Q8:C60	480,655
Q₈⋊₂C₆₀ = C₁₅×Q₈⋊C₄	φ: C₆₀/C₃₀ → C₂ ⊆ Out Q₈	480		Q8:2C60	480,206
Q₈⋊₃C₆₀ = C₁₅×C₄≀C₂	φ: C₆₀/C₃₀ → C₂ ⊆ Out Q₈	120	2	Q8:3C60	480,207

Non-split extensions G=N.Q with N=Q₈ and Q=C₆₀

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.C₆₀ = C₅×C₈.A₄	φ: C₆₀/C₂₀ → C₃ ⊆ Out Q₈	160	2	Q8.C60	480,660
Q₈.₂C₆₀ = C₁₅×C₈○D₄	φ: trivial image	240	2	Q8.2C60	480,936

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Extensions 1→N→G→Q→1 with N=Q8 and Q=C60