Extensions 1→N→G→Q→1 with N=C₄₀ and Q=S₃

Direct product G=N×Q with N=C₄₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₄₀		120	2	S3xC40	240,49

Semidirect products G=N:Q with N=C₄₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₀⋊₁S₃ = D₁₂₀	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	120	2+	C40:1S3	240,68
C₄₀⋊₂S₃ = C₂₄⋊D₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	120	2	C40:2S3	240,67
C₄₀⋊₃S₃ = C₈×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	120	2	C40:3S3	240,65
C₄₀⋊₄S₃ = C₄₀⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	120	2	C40:4S3	240,66
C₄₀⋊₅S₃ = C₅×D₂₄	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	120	2	C40:5S3	240,52
C₄₀⋊₆S₃ = C₅×C₂₄⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	120	2	C40:6S3	240,51
C₄₀⋊₇S₃ = C₅×C₈⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	120	2	C40:7S3	240,50

Non-split extensions G=N.Q with N=C₄₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄₀.₁S₃ = Dic₆₀	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	240	2-	C40.1S3	240,69
C₄₀.₂S₃ = C₁₅⋊₃C₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	240	2	C40.2S3	240,3
C₄₀.₃S₃ = C₅×Dic₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₄₀	240	2	C40.3S3	240,53
C₄₀.₄S₃ = C₅×C₃⋊C₁₆	central extension (φ=1)	240	2	C40.4S3	240,1

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