C_n D_n S_n A_n ...

Extensions 1→N→G→Q→1 with N=2₊⁽¹⁺⁴⁾ and Q=S₃

Direct product G=N×Q with N=2₊⁽¹⁺⁴⁾ and Q=S₃

		d	ρ	Label	ID
S₃×2₊⁽¹⁺⁴⁾		24	8+	S3xES+(2,2)	192,1524

Semidirect products G=N:Q with N=2₊⁽¹⁺⁴⁾ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
2₊⁽¹⁺⁴⁾⋊₁S₃ = Q₈.₅S₄	φ: S₃/C₁ → S₃ ⊆ Out 2₊⁽¹⁺⁴⁾	24	4+	ES+(2,2):1S3	192,988
2₊⁽¹⁺⁴⁾⋊₂S₃ = Q₈.₆S₄	φ: S₃/C₁ → S₃ ⊆ Out 2₊⁽¹⁺⁴⁾	32	4	ES+(2,2):2S3	192,1483
2₊⁽¹⁺⁴⁾⋊₃S₃ = Q₈.₇S₄	φ: S₃/C₁ → S₃ ⊆ Out 2₊⁽¹⁺⁴⁾	32	4+	ES+(2,2):3S3	192,1484
2₊⁽¹⁺⁴⁾⋊₄S₃ = C₂³⋊S₄	φ: S₃/C₁ → S₃ ⊆ Out 2₊⁽¹⁺⁴⁾	8	4+	ES+(2,2):4S3	192,1493
2₊⁽¹⁺⁴⁾⋊₅S₃ = Q₈⋊₂S₄	φ: S₃/C₁ → S₃ ⊆ Out 2₊⁽¹⁺⁴⁾	8	4+	ES+(2,2):5S3	192,1494
2₊⁽¹⁺⁴⁾⋊₆S₃ = 2₊⁽¹⁺⁴⁾⋊₆S₃	φ: S₃/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	24	8+	ES+(2,2):6S3	192,800
2₊⁽¹⁺⁴⁾⋊₇S₃ = 2₊⁽¹⁺⁴⁾⋊₇S₃	φ: S₃/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	24	8+	ES+(2,2):7S3	192,803
2₊⁽¹⁺⁴⁾⋊₈S₃ = D₁₂.₃₂C₂³	φ: S₃/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	48	8+	ES+(2,2):8S3	192,1394
2₊⁽¹⁺⁴⁾⋊₉S₃ = D₁₂.₃₃C₂³	φ: S₃/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	48	8-	ES+(2,2):9S3	192,1395
2₊⁽¹⁺⁴⁾⋊₁₀S₃ = D₆.C₂⁴	φ: trivial image	48	8-	ES+(2,2):10S3	192,1525

Non-split extensions G=N.Q with N=2₊⁽¹⁺⁴⁾ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
2₊⁽¹⁺⁴⁾.₁S₃ = Q₈.₄S₄	φ: S₃/C₁ → S₃ ⊆ Out 2₊⁽¹⁺⁴⁾	48	4	ES+(2,2).1S3	192,987
2₊⁽¹⁺⁴⁾.₂S₃ = C₂³.S₄	φ: S₃/C₁ → S₃ ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2).2S3	192,1491
2₊⁽¹⁺⁴⁾.₃S₃ = Q₈.S₄	φ: S₃/C₁ → S₃ ⊆ Out 2₊⁽¹⁺⁴⁾	16	4	ES+(2,2).3S3	192,1492
2₊⁽¹⁺⁴⁾.₄S₃ = 2₊⁽¹⁺⁴⁾.₄S₃	φ: S₃/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	48	8-	ES+(2,2).4S3	192,801
2₊⁽¹⁺⁴⁾.₅S₃ = 2₊⁽¹⁺⁴⁾.₅S₃	φ: S₃/C₃ → C₂ ⊆ Out 2₊⁽¹⁺⁴⁾	48	8-	ES+(2,2).5S3	192,802

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