Extensions 1→N→G→Q→1 with N=C₈ and Q=F₇

Direct product G=N×Q with N=C₈ and Q=F₇

		d	ρ	Label	ID
C₈×F₇		56	6	C8xF7	336,7

Semidirect products G=N:Q with N=C₈ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈⋊₁F₇ = D₅₆⋊C₃	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₈	56	6+	C8:1F7	336,10
C₈⋊₂F₇ = C₅₆⋊C₆	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₈	56	6	C8:2F7	336,9
C₈⋊₃F₇ = C₈⋊F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₈	56	6	C8:3F7	336,8

Non-split extensions G=N.Q with N=C₈ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.F₇ = C₈.F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₈	112	6-	C8.F7	336,11
C₈.₂F₇ = C₇⋊C₄₈	central extension (φ=1)	112	6	C8.2F7	336,1

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Extensions 1→N→G→Q→1 with N=C8 and Q=F7