Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₃₀

Direct product G=N×Q with N=Q₈ and Q=C₃₀

		d	ρ	Label	ID
Q₈×C₃₀		240		Q8xC30	240,187

Semidirect products G=N:Q with N=Q₈ and Q=C₃₀

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊C₃₀ = C₁₀×SL₂(𝔽₃)	φ: C₃₀/C₁₀ → C₃ ⊆ Out Q₈	80		Q8:C30	240,153
Q₈⋊₂C₃₀ = C₁₅×SD₁₆	φ: C₃₀/C₁₅ → C₂ ⊆ Out Q₈	120	2	Q8:2C30	240,87
Q₈⋊₃C₃₀ = C₁₅×C₄○D₄	φ: trivial image	120	2	Q8:3C30	240,188

Non-split extensions G=N.Q with N=Q₈ and Q=C₃₀

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.C₃₀ = C₅×C₄.A₄	φ: C₃₀/C₁₀ → C₃ ⊆ Out Q₈	80	2	Q8.C30	240,154
Q₈.₂C₃₀ = C₁₅×Q₁₆	φ: C₃₀/C₁₅ → C₂ ⊆ Out Q₈	240	2	Q8.2C30	240,88

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=Q8 and Q=C30