Extensions 1→N→G→Q→1 with N=C₆ and Q=F₇

Direct product G=N×Q with N=C₆ and Q=F₇

		d	ρ	Label	ID
C₆×F₇		42	6	C6xF7	252,28

Semidirect products G=N:Q with N=C₆ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊F₇ = C₂×C₃⋊F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₆	42	6+	C6:F7	252,30

Non-split extensions G=N.Q with N=C₆ and Q=F₇

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.F₇ = C₆.F₇	φ: F₇/C₇⋊C₃ → C₂ ⊆ Aut C₆	84	6-	C6.F7	252,18
C₆.₂F₇ = C₇⋊C₃₆	central extension (φ=1)	252	6	C6.2F7	252,1
C₆.₃F₇ = C₂×C₇⋊C₁₈	central extension (φ=1)	126	6	C6.3F7	252,7
C₆.₄F₇ = C₃×C₇⋊C₁₂	central extension (φ=1)	84	6	C6.4F7	252,16

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Extensions 1→N→G→Q→1 with N=C6 and Q=F7