Extensions 1→N→G→Q→1 with N=C₂xC₂₀ and Q=S₃

Direct product G=NxQ with N=C₂xC₂₀ and Q=S₃

		d	ρ	Label	ID
S₃xC₂xC₂₀		120		S3xC2xC20	240,166

Semidirect products G=N:Q with N=C₂xC₂₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₂₀):₁S₃ = C₅xD₆:C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	120		(C2xC20):1S3	240,59
(C₂xC₂₀):₂S₃ = D₃₀:₃C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	120		(C2xC20):2S3	240,75
(C₂xC₂₀):₃S₃ = C₂xD₆₀	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	120		(C2xC20):3S3	240,177
(C₂xC₂₀):₄S₃ = D₆₀:₁₁C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	120	2	(C2xC20):4S3	240,178
(C₂xC₂₀):₅S₃ = C₂xC₄xD₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	120		(C2xC20):5S3	240,176
(C₂xC₂₀):₆S₃ = C₁₀xD₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	120		(C2xC20):6S3	240,167
(C₂xC₂₀):₇S₃ = C₅xC₄oD₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	120	2	(C2xC20):7S3	240,168

Non-split extensions G=N.Q with N=C₂xC₂₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₂₀).₁S₃ = C₅xDic₃:C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	240		(C2xC20).1S3	240,57
(C₂xC₂₀).₂S₃ = C₃₀.₄Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	240		(C2xC20).2S3	240,73
(C₂xC₂₀).₃S₃ = C₆₀:₅C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	240		(C2xC20).3S3	240,74
(C₂xC₂₀).₄S₃ = C₂xDic₃₀	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	240		(C2xC20).4S3	240,175
(C₂xC₂₀).₅S₃ = C₆₀.₇C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	120	2	(C2xC20).5S3	240,71
(C₂xC₂₀).₆S₃ = C₂xC₁₅:₃C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	240		(C2xC20).6S3	240,70
(C₂xC₂₀).₇S₃ = C₄xDic₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	240		(C2xC20).7S3	240,72
(C₂xC₂₀).₈S₃ = C₅xC₄.Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	120	2	(C2xC20).8S3	240,55
(C₂xC₂₀).₉S₃ = C₅xC₄:Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	240		(C2xC20).9S3	240,58
(C₂xC₂₀).₁₀S₃ = C₁₀xDic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₂xC₂₀	240		(C2xC20).10S3	240,165
(C₂xC₂₀).₁₁S₃ = C₁₀xC₃:C₈	central extension (φ=1)	240		(C2xC20).11S3	240,54
(C₂xC₂₀).₁₂S₃ = Dic₃xC₂₀	central extension (φ=1)	240		(C2xC20).12S3	240,56

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