Extensions 1→N→G→Q→1 with N=C₇₀ and Q=S₃

Direct product G=N×Q with N=C₇₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₇₀		210	2	S3xC70	420,37

Semidirect products G=N:Q with N=C₇₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₀⋊₁S₃ = D₂₁₀	φ: S₃/C₃ → C₂ ⊆ Aut C₇₀	210	2+	C70:1S3	420,40
C₇₀⋊₂S₃ = C₁₀×D₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₇₀	210	2	C70:2S3	420,38
C₇₀⋊₃S₃ = C₁₄×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₇₀	210	2	C70:3S3	420,39

Non-split extensions G=N.Q with N=C₇₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₀.₁S₃ = Dic₁₀₅	φ: S₃/C₃ → C₂ ⊆ Aut C₇₀	420	2-	C70.1S3	420,11
C₇₀.₂S₃ = C₅×Dic₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₇₀	420	2	C70.2S3	420,9
C₇₀.₃S₃ = C₇×Dic₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₇₀	420	2	C70.3S3	420,10
C₇₀.₄S₃ = Dic₃×C₃₅	central extension (φ=1)	420	2	C70.4S3	420,8

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