Extensions 1→N→G→Q→1 with N=C₅₆ and Q=S₃

Direct product G=NxQ with N=C₅₆ and Q=S₃

		d	ρ	Label	ID
S₃xC₅₆		168	2	S3xC56	336,74

Semidirect products G=N:Q with N=C₅₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆:₁S₃ = D₁₆₈	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	168	2+	C56:1S3	336,93
C₅₆:₂S₃ = C₈:D₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:2S3	336,92
C₅₆:₃S₃ = C₈xD₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:3S3	336,90
C₅₆:₄S₃ = C₅₆:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:4S3	336,91
C₅₆:₅S₃ = C₇xD₂₄	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:5S3	336,77
C₅₆:₆S₃ = C₇xC₂₄:C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:6S3	336,76
C₅₆:₇S₃ = C₇xC₈:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:7S3	336,75

Non-split extensions G=N.Q with N=C₅₆ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆.₁S₃ = Dic₈₄	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	336	2-	C56.1S3	336,94
C₅₆.₂S₃ = C₂₁:C₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	336	2	C56.2S3	336,5
C₅₆.₃S₃ = C₇xDic₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	336	2	C56.3S3	336,78
C₅₆.₄S₃ = C₇xC₃:C₁₆	central extension (φ=1)	336	2	C56.4S3	336,3

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