Extensions 1→N→G→Q→1 with N=Q₈ and Q=F₇

Direct product G=N×Q with N=Q₈ and Q=F₇

		d	ρ	Label	ID
Q₈×F₇		56	12-	Q8xF7	336,127

Semidirect products G=N:Q with N=Q₈ and Q=F₇

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊F₇ = Q₈⋊F₇	φ: F₇/D₇ → C₃ ⊆ Out Q₈	56	12-	Q8:F7	336,135
Q₈⋊₂F₇ = Q₈⋊₂F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Out Q₈	56	12+	Q8:2F7	336,20
Q₈⋊₃F₇ = Q₈⋊₃F₇	φ: trivial image	56	12+	Q8:3F7	336,128

Non-split extensions G=N.Q with N=Q₈ and Q=F₇

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.F₇ = Q₈.F₇	φ: F₇/D₇ → C₃ ⊆ Out Q₈	112	12+	Q8.F7	336,134
Q₈.₂F₇ = Q₈.₂F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Out Q₈	112	12-	Q8.2F7	336,21

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Extensions 1→N→G→Q→1 with N=Q8 and Q=F7