Extensions 1→N→G→Q→1 with N=GL₂(𝔽₃) and Q=S₃

Direct product G=N×Q with N=GL₂(𝔽₃) and Q=S₃

		d	ρ	Label	ID
S₃×GL₂(𝔽₃)		24	4	S3xGL(2,3)	288,851

Semidirect products G=N:Q with N=GL₂(𝔽₃) and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
GL₂(𝔽₃)⋊₁S₃ = GL₂(𝔽₃)⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out GL₂(𝔽₃)	48	4+	GL(2,3):1S3	288,847
GL₂(𝔽₃)⋊₂S₃ = D₆.S₄	φ: S₃/C₃ → C₂ ⊆ Out GL₂(𝔽₃)	48	4-	GL(2,3):2S3	288,849
GL₂(𝔽₃)⋊₃S₃ = Dic₃.₄S₄	φ: trivial image	48	4	GL(2,3):3S3	288,845

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