Extensions 1→N→G→Q→1 with N=C₄○D₂₀ and Q=S₃

Direct product G=N×Q with N=C₄○D₂₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₄○D₂₀		120	4	S3xC4oD20	480,1091

Semidirect products G=N:Q with N=C₄○D₂₀ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₂₀⋊₁S₃ = D₂₀.₃₁D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	240	4	C4oD20:1S3	480,387
C₄○D₂₀⋊₂S₃ = D₂₀.₃₄D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	240	4	C4oD20:2S3	480,373
C₄○D₂₀⋊₃S₃ = D₂₀⋊₂₁D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	120	4	C4oD20:3S3	480,375
C₄○D₂₀⋊₄S₃ = D₂₀⋊₁₉D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	120	4+	C4oD20:4S3	480,377
C₄○D₂₀⋊₅S₃ = D₂₀.₃₈D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	240	4	C4oD20:5S3	480,1076
C₄○D₂₀⋊₆S₃ = D₂₀.₃₉D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	240	4-	C4oD20:6S3	480,1077
C₄○D₂₀⋊₇S₃ = D₂₀⋊₂₄D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	120	4	C4oD20:7S3	480,1092
C₄○D₂₀⋊₈S₃ = D₂₀⋊₂₆D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	120	4	C4oD20:8S3	480,1094
C₄○D₂₀⋊₉S₃ = D₂₀⋊₂₉D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	120	4+	C4oD20:9S3	480,1095

Non-split extensions G=N.Q with N=C₄○D₂₀ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₂₀.₁S₃ = C₆₀.₉₇D₄	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	120	4	C4oD20.1S3	480,53
C₄○D₂₀.₂S₃ = C₆₀.₉₆D₄	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	120	4	C4oD20.2S3	480,52
C₄○D₂₀.₃S₃ = D₂₀.₂Dic₃	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	240	4	C4oD20.3S3	480,360
C₄○D₂₀.₄S₃ = D₂₀.₃₇D₆	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	240	4	C4oD20.4S3	480,383
C₄○D₂₀.₅S₃ = C₆₀.₆₃D₄	φ: S₃/C₃ → C₂ ⊆ Out C₄○D₂₀	240	4-	C4oD20.5S3	480,389
C₄○D₂₀.₆S₃ = D₂₀.₃Dic₃	φ: trivial image	240	4	C4oD20.6S3	480,359

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