Extensions 1→N→G→Q→1 with N=S₃×C₂₀ and Q=C₂

Direct product G=N×Q with N=S₃×C₂₀ and Q=C₂

		d	ρ	Label	ID
S₃×C₂×C₂₀		120		S3xC2xC20	240,166

Semidirect products G=N:Q with N=S₃×C₂₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(S₃×C₂₀)⋊₁C₂ = D₂₀⋊₅S₃	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	4-	(S3xC20):1C2	240,126
(S₃×C₂₀)⋊₂C₂ = D₆₀⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	4+	(S3xC20):2C2	240,130
(S₃×C₂₀)⋊₃C₂ = S₃×D₂₀	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	60	4+	(S3xC20):3C2	240,137
(S₃×C₂₀)⋊₄C₂ = D₆.D₁₀	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	4	(S3xC20):4C2	240,132
(S₃×C₂₀)⋊₅C₂ = C₄×S₃×D₅	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	60	4	(S3xC20):5C2	240,135
(S₃×C₂₀)⋊₆C₂ = C₅×S₃×D₄	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	60	4	(S3xC20):6C2	240,169
(S₃×C₂₀)⋊₇C₂ = C₅×D₄⋊₂S₃	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	4	(S3xC20):7C2	240,170
(S₃×C₂₀)⋊₈C₂ = C₅×Q₈⋊₃S₃	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	4	(S3xC20):8C2	240,172
(S₃×C₂₀)⋊₉C₂ = C₅×C₄○D₁₂	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	2	(S3xC20):9C2	240,168

Non-split extensions G=N.Q with N=S₃×C₂₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(S₃×C₂₀).₁C₂ = S₃×Dic₁₀	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	4-	(S3xC20).1C2	240,128
(S₃×C₂₀).₂C₂ = S₃×C₅⋊₂C₈	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	4	(S3xC20).2C2	240,8
(S₃×C₂₀).₃C₂ = D₆.Dic₅	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	4	(S3xC20).3C2	240,11
(S₃×C₂₀).₄C₂ = C₅×S₃×Q₈	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	4	(S3xC20).4C2	240,171
(S₃×C₂₀).₅C₂ = C₅×C₈⋊S₃	φ: C₂/C₁ → C₂ ⊆ Out S₃×C₂₀	120	2	(S3xC20).5C2	240,50
(S₃×C₂₀).₆C₂ = S₃×C₄₀	φ: trivial image	120	2	(S3xC20).6C2	240,49

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