Extensions 1→N→G→Q→1 with N=D₄×D₅ and Q=S₃

Direct product G=N×Q with N=D₄×D₅ and Q=S₃

		d	ρ	Label	ID
S₃×D₄×D₅		60	8+	S3xD4xD5	480,1097

Semidirect products G=N:Q with N=D₄×D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×D₅)⋊₁S₃ = D₅×D₄⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out D₄×D₅	120	8+	(D4xD5):1S3	480,553
(D₄×D₅)⋊₂S₃ = D₁₂⋊₁₀D₁₀	φ: S₃/C₃ → C₂ ⊆ Out D₄×D₅	120	8-	(D4xD5):2S3	480,565
(D₄×D₅)⋊₃S₃ = D₂₀.₉D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×D₅	120	8+	(D4xD5):3S3	480,567
(D₄×D₅)⋊₄S₃ = D₂₀⋊₁₃D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×D₅	120	8-	(D4xD5):4S3	480,1101
(D₄×D₅)⋊₅S₃ = D₂₀⋊₁₄D₆	φ: S₃/C₃ → C₂ ⊆ Out D₄×D₅	120	8+	(D4xD5):5S3	480,1102
(D₄×D₅)⋊₆S₃ = D₅×D₄⋊₂S₃	φ: trivial image	120	8-	(D4xD5):6S3	480,1098

Non-split extensions G=N.Q with N=D₄×D₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(D₄×D₅).₁S₃ = D₅×D₄.S₃	φ: S₃/C₃ → C₂ ⊆ Out D₄×D₅	120	8-	(D4xD5).1S3	480,559
(D₄×D₅).₂S₃ = D₂₀⋊Dic₃	φ: S₃/C₃ → C₂ ⊆ Out D₄×D₅	120	8	(D4xD5).2S3	480,312
(D₄×D₅).₃S₃ = D₄×C₃⋊F₅	φ: S₃/C₃ → C₂ ⊆ Out D₄×D₅	60	8	(D4xD5).3S3	480,1067

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