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

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

		d	ρ	Label	ID
S₃×C₅₆		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 = C₈×D₂₁	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 = C₇×D₂₄	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:5S3	336,77
C₅₆⋊₆S₃ = C₇×C₂₄⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:6S3	336,76
C₅₆⋊₇S₃ = C₇×C₈⋊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 = C₇×Dic₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₅₆	336	2	C56.3S3	336,78
C₅₆.₄S₃ = C₇×C₃⋊C₁₆	central extension (φ=1)	336	2	C56.4S3	336,3

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