Extensions 1→N→G→Q→1 with N=Q₈ and Q=C₄₂

Direct product G=N×Q with N=Q₈ and Q=C₄₂

		d	ρ	Label	ID
Q₈×C₄₂		336		Q8xC42	336,206

Semidirect products G=N:Q with N=Q₈ and Q=C₄₂

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊C₄₂ = C₁₄×SL₂(𝔽₃)	φ: C₄₂/C₁₄ → C₃ ⊆ Out Q₈	112		Q8:C42	336,169
Q₈⋊₂C₄₂ = SD₁₆×C₂₁	φ: C₄₂/C₂₁ → C₂ ⊆ Out Q₈	168	2	Q8:2C42	336,112
Q₈⋊₃C₄₂ = C₄○D₄×C₂₁	φ: trivial image	168	2	Q8:3C42	336,207

Non-split extensions G=N.Q with N=Q₈ and Q=C₄₂

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.C₄₂ = C₇×C₄.A₄	φ: C₄₂/C₁₄ → C₃ ⊆ Out Q₈	112	2	Q8.C42	336,170
Q₈.₂C₄₂ = Q₁₆×C₂₁	φ: C₄₂/C₂₁ → C₂ ⊆ Out Q₈	336	2	Q8.2C42	336,113

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Extensions 1→N→G→Q→1 with N=Q8 and Q=C42