Extensions 1→N→G→Q→1 with N=C₄₂ and Q=S₃

Direct product G=NxQ with N=C₄₂ and Q=S₃

		d	ρ	Label	ID
S₃xC₄₂		84	2	S3xC42	252,42

Semidirect products G=N:Q with N=C₄₂ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂:₁S₃ = C₂xC₃:D₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	126		C42:1S3	252,45
C₄₂:₂S₃ = C₆xD₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	84	2	C42:2S3	252,43
C₄₂:₃S₃ = C₁₄xC₃:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	126		C42:3S3	252,44

Non-split extensions G=N.Q with N=C₄₂ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₂.₁S₃ = Dic₆₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	252	2-	C42.1S3	252,5
C₄₂.₂S₃ = D₁₂₆	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	126	2+	C42.2S3	252,14
C₄₂.₃S₃ = C₃:Dic₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	252		C42.3S3	252,24
C₄₂.₄S₃ = C₃xDic₂₁	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	84	2	C42.4S3	252,22
C₄₂.₅S₃ = C₇xDic₉	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	252	2	C42.5S3	252,3
C₄₂.₆S₃ = C₁₄xD₉	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	126	2	C42.6S3	252,13
C₄₂.₇S₃ = C₇xC₃:Dic₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄₂	252		C42.7S3	252,23
C₄₂.₈S₃ = Dic₃xC₂₁	central extension (φ=1)	84	2	C42.8S3	252,21

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