Extensions 1→N→G→Q→1 with N=C₅₁ and Q=S₃

Direct product G=N×Q with N=C₅₁ and Q=S₃

		d	ρ	Label	ID
S₃×C₅₁		102	2	S3xC51	306,6

Semidirect products G=N:Q with N=C₅₁ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₁⋊₁S₃ = C₃⋊D₅₁	φ: S₃/C₃ → C₂ ⊆ Aut C₅₁	153		C51:1S3	306,9
C₅₁⋊₂S₃ = C₃×D₅₁	φ: S₃/C₃ → C₂ ⊆ Aut C₅₁	102	2	C51:2S3	306,7
C₅₁⋊₃S₃ = C₁₇×C₃⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₅₁	153		C51:3S3	306,8

Non-split extensions G=N.Q with N=C₅₁ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₁.₁S₃ = D₁₅₃	φ: S₃/C₃ → C₂ ⊆ Aut C₅₁	153	2+	C51.1S3	306,3
C₅₁.₂S₃ = C₁₇×D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₅₁	153	2	C51.2S3	306,1

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Extensions 1→N→G→Q→1 with N=C51 and Q=S3