Extensions 1→N→G→Q→1 with N=C₂×SL₂(𝔽₃) and Q=S₃

Direct product G=N×Q with N=C₂×SL₂(𝔽₃) and Q=S₃

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

Semidirect products G=N:Q with N=C₂×SL₂(𝔽₃) and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×SL₂(𝔽₃))⋊₁S₃ = SL₂(𝔽₃).₁₁D₆	φ: S₃/C₃ → C₂ ⊆ Out C₂×SL₂(𝔽₃)	48	4	(C2xSL(2,3)):1S3	288,923
(C₂×SL₂(𝔽₃))⋊₂S₃ = C₂×C₆.₆S₄	φ: S₃/C₃ → C₂ ⊆ Out C₂×SL₂(𝔽₃)	48		(C2xSL(2,3)):2S3	288,911
(C₂×SL₂(𝔽₃))⋊₃S₃ = SL₂(𝔽₃).D₆	φ: S₃/C₃ → C₂ ⊆ Out C₂×SL₂(𝔽₃)	48	4	(C2xSL(2,3)):3S3	288,912
(C₂×SL₂(𝔽₃))⋊₄S₃ = C₂×Dic₃.A₄	φ: trivial image	96		(C2xSL(2,3)):4S3	288,921

Non-split extensions G=N.Q with N=C₂×SL₂(𝔽₃) and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×SL₂(𝔽₃)).₁S₃ = C₆.GL₂(𝔽₃)	φ: S₃/C₃ → C₂ ⊆ Out C₂×SL₂(𝔽₃)	96		(C2xSL(2,3)).1S3	288,403
(C₂×SL₂(𝔽₃)).₂S₃ = C₂×C₆.₅S₄	φ: S₃/C₃ → C₂ ⊆ Out C₂×SL₂(𝔽₃)	96		(C2xSL(2,3)).2S3	288,910
(C₂×SL₂(𝔽₃)).₃S₃ = Dic₃×SL₂(𝔽₃)	φ: trivial image	96		(C2xSL(2,3)).3S3	288,409

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁