Extensions 1→N→G→Q→1 with N=C₂³ and Q=F₇

Direct product G=N×Q with N=C₂³ and Q=F₇

		d	ρ	Label	ID
C₂³×F₇		56		C2^3xF7	336,216

Semidirect products G=N:Q with N=C₂³ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊F₇ = C₂×D₇⋊A₄	φ: F₇/D₇ → C₃ ⊆ Aut C₂³	42	6+	C2^3:F7	336,218
C₂³⋊₂F₇ = C₂×Dic₇⋊C₆	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂³	56		C2^3:2F7	336,130

Non-split extensions G=N.Q with N=C₂³ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.F₇ = Dic₇⋊A₄	φ: F₇/D₇ → C₃ ⊆ Aut C₂³	84	6-	C2^3.F7	336,136
C₂³.₂F₇ = C₂³.₂F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂³	56		C2^3.2F7	336,22
C₂³.₃F₇ = C₂²×C₇⋊C₁₂	central extension (φ=1)	112		C2^3.3F7	336,129

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Extensions 1→N→G→Q→1 with N=C23 and Q=F7