Extensions 1→N→G→Q→1 with N=SL₂(𝔽₃) and Q=S₃

Direct product G=N×Q with N=SL₂(𝔽₃) and Q=S₃

		d	ρ	Label	ID
S₃×SL₂(𝔽₃)		24	4-	S3xSL(2,3)	144,128

Semidirect products G=N:Q with N=SL₂(𝔽₃) and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃)⋊S₃ = C₆.₆S₄	φ: S₃/C₃ → C₂ ⊆ Out SL₂(𝔽₃)	24	4+	SL(2,3):S3	144,125
SL₂(𝔽₃)⋊₂S₃ = Dic₃.A₄	φ: trivial image	48	4+	SL(2,3):2S3	144,127

Non-split extensions G=N.Q with N=SL₂(𝔽₃) and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
SL₂(𝔽₃).S₃ = C₆.₅S₄	φ: S₃/C₃ → C₂ ⊆ Out SL₂(𝔽₃)	48	4-	SL(2,3).S3	144,124

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Extensions 1→N→G→Q→1 with N=SL2(𝔽3) and Q=S3