Extensions 1→N→G→Q→1 with N=C₇₀ and Q=C₆

Direct product G=N×Q with N=C₇₀ and Q=C₆

		d	ρ	Label	ID
C₂×C₂₁₀		420		C2xC210	420,41

Semidirect products G=N:Q with N=C₇₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₀⋊₁C₆ = C₂×C₅⋊F₇	φ: C₆/C₁ → C₆ ⊆ Aut C₇₀	70	6+	C70:1C6	420,19
C₇₀⋊₂C₆ = C₁₀×F₇	φ: C₆/C₁ → C₆ ⊆ Aut C₇₀	70	6	C70:2C6	420,17
C₇₀⋊₃C₆ = C₂×D₅×C₇⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₇₀	70	6	C70:3C6	420,18
C₇₀⋊₄C₆ = C₂×C₁₀×C₇⋊C₃	φ: C₆/C₂ → C₃ ⊆ Aut C₇₀	140		C70:4C6	420,31
C₇₀⋊₅C₆ = C₆×D₃₅	φ: C₆/C₃ → C₂ ⊆ Aut C₇₀	210	2	C70:5C6	420,36
C₇₀⋊₆C₆ = D₇×C₃₀	φ: C₆/C₃ → C₂ ⊆ Aut C₇₀	210	2	C70:6C6	420,34
C₇₀⋊₇C₆ = D₅×C₄₂	φ: C₆/C₃ → C₂ ⊆ Aut C₇₀	210	2	C70:7C6	420,35

Non-split extensions G=N.Q with N=C₇₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₀.₁C₆ = C₃₅⋊₃C₁₂	φ: C₆/C₁ → C₆ ⊆ Aut C₇₀	140	6-	C70.1C6	420,3
C₇₀.₂C₆ = C₅×C₇⋊C₁₂	φ: C₆/C₁ → C₆ ⊆ Aut C₇₀	140	6	C70.2C6	420,1
C₇₀.₃C₆ = Dic₅×C₇⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₇₀	140	6	C70.3C6	420,2
C₇₀.₄C₆ = C₂₀×C₇⋊C₃	φ: C₆/C₂ → C₃ ⊆ Aut C₇₀	140	3	C70.4C6	420,4
C₇₀.₅C₆ = C₃×Dic₃₅	φ: C₆/C₃ → C₂ ⊆ Aut C₇₀	420	2	C70.5C6	420,7
C₇₀.₆C₆ = C₁₅×Dic₇	φ: C₆/C₃ → C₂ ⊆ Aut C₇₀	420	2	C70.6C6	420,5
C₇₀.₇C₆ = Dic₅×C₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₇₀	420	2	C70.7C6	420,6

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