Extensions 1→N→G→Q→1 with N=C₂×C₄ and Q=F₇

Direct product G=N×Q with N=C₂×C₄ and Q=F₇

		d	ρ	Label	ID
C₂×C₄×F₇		56		C2xC4xF7	336,122

Semidirect products G=N:Q with N=C₂×C₄ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄)⋊₁F₇ = D₁₄⋊C₁₂	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂×C₄	56		(C2xC4):1F7	336,17
(C₂×C₄)⋊₂F₇ = C₂×C₄⋊F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂×C₄	56		(C2xC4):2F7	336,123
(C₂×C₄)⋊₃F₇ = D₂₈⋊₆C₆	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂×C₄	56	6	(C2xC4):3F7	336,124

Non-split extensions G=N.Q with N=C₂×C₄ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄).₁F₇ = Dic₇⋊C₁₂	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂×C₄	112		(C2xC4).1F7	336,15
(C₂×C₄).₂F₇ = C₂₈.C₁₂	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂×C₄	56	6	(C2xC4).2F7	336,13
(C₂×C₄).₃F₇ = C₂₈⋊C₁₂	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂×C₄	112		(C2xC4).3F7	336,16
(C₂×C₄).₄F₇ = C₂×C₄.F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₂×C₄	112		(C2xC4).4F7	336,121
(C₂×C₄).₅F₇ = C₂×C₇⋊C₂₄	central extension (φ=1)	112		(C2xC4).5F7	336,12
(C₂×C₄).₆F₇ = C₄×C₇⋊C₁₂	central extension (φ=1)	112		(C2xC4).6F7	336,14

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