Extensions 1→N→G→Q→1 with N=SL₂(𝔽₃) and Q=D₆

Direct product G=N×Q with N=SL₂(𝔽₃) and Q=D₆

		d	ρ	Label	ID
C₂×S₃×SL₂(𝔽₃)		48		C2xS3xSL(2,3)	288,922

Semidirect products G=N:Q with N=SL₂(𝔽₃) and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃)⋊₁D₆ = GL₂(𝔽₃)⋊S₃	φ: D₆/S₃ → C₂ ⊆ Out SL₂(𝔽₃)	48	4+	SL(2,3):1D6	288,847
SL₂(𝔽₃)⋊₂D₆ = S₃×GL₂(𝔽₃)	φ: D₆/S₃ → C₂ ⊆ Out SL₂(𝔽₃)	24	4	SL(2,3):2D6	288,851
SL₂(𝔽₃)⋊₃D₆ = C₂×C₆.₆S₄	φ: D₆/C₆ → C₂ ⊆ Out SL₂(𝔽₃)	48		SL(2,3):3D6	288,911
SL₂(𝔽₃)⋊₄D₆ = C₁₂.₇S₄	φ: D₆/C₆ → C₂ ⊆ Out SL₂(𝔽₃)	48	4+	SL(2,3):4D6	288,915
SL₂(𝔽₃)⋊₅D₆ = C₂×Dic₃.A₄	φ: trivial image	96		SL(2,3):5D6	288,921
SL₂(𝔽₃)⋊₆D₆ = Dic₆.A₄	φ: trivial image	72	4+	SL(2,3):6D6	288,924
SL₂(𝔽₃)⋊₇D₆ = S₃×C₄.A₄	φ: trivial image	48	4	SL(2,3):7D6	288,925

Non-split extensions G=N.Q with N=SL₂(𝔽₃) and Q=D₆

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃).₁D₆ = CSU₂(𝔽₃)⋊S₃	φ: D₆/S₃ → C₂ ⊆ Out SL₂(𝔽₃)	96	4	SL(2,3).1D6	288,844
SL₂(𝔽₃).₂D₆ = Dic₃.₄S₄	φ: D₆/S₃ → C₂ ⊆ Out SL₂(𝔽₃)	48	4	SL(2,3).2D6	288,845
SL₂(𝔽₃).₃D₆ = Dic₃.₅S₄	φ: D₆/S₃ → C₂ ⊆ Out SL₂(𝔽₃)	48	4+	SL(2,3).3D6	288,846
SL₂(𝔽₃).₄D₆ = S₃×CSU₂(𝔽₃)	φ: D₆/S₃ → C₂ ⊆ Out SL₂(𝔽₃)	48	4-	SL(2,3).4D6	288,848
SL₂(𝔽₃).₅D₆ = D₆.S₄	φ: D₆/S₃ → C₂ ⊆ Out SL₂(𝔽₃)	48	4-	SL(2,3).5D6	288,849
SL₂(𝔽₃).₆D₆ = D₆.₂S₄	φ: D₆/S₃ → C₂ ⊆ Out SL₂(𝔽₃)	48	4	SL(2,3).6D6	288,850
SL₂(𝔽₃).₇D₆ = C₂×C₆.₅S₄	φ: D₆/C₆ → C₂ ⊆ Out SL₂(𝔽₃)	96		SL(2,3).7D6	288,910
SL₂(𝔽₃).₈D₆ = SL₂(𝔽₃).D₆	φ: D₆/C₆ → C₂ ⊆ Out SL₂(𝔽₃)	48	4	SL(2,3).8D6	288,912
SL₂(𝔽₃).₉D₆ = C₁₂.₆S₄	φ: D₆/C₆ → C₂ ⊆ Out SL₂(𝔽₃)	96	4-	SL(2,3).9D6	288,913
SL₂(𝔽₃).₁₀D₆ = C₁₂.₁₄S₄	φ: D₆/C₆ → C₂ ⊆ Out SL₂(𝔽₃)	48	4	SL(2,3).10D6	288,914
SL₂(𝔽₃).₁₁D₆ = SL₂(𝔽₃).₁₁D₆	φ: trivial image	48	4	SL(2,3).11D6	288,923
SL₂(𝔽₃).₁₂D₆ = D₁₂.A₄	φ: trivial image	48	4-	SL(2,3).12D6	288,926

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