Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂×SL₂(𝔽₃)

Direct product G=N×Q with N=C₆ and Q=C₂×SL₂(𝔽₃)

		d	ρ	Label	ID
C₂×C₆×SL₂(𝔽₃)		96		C2xC6xSL(2,3)	288,981

Semidirect products G=N:Q with N=C₆ and Q=C₂×SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₂×SL₂(𝔽₃)) = C₂×S₃×SL₂(𝔽₃)	φ: C₂×SL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₆	48		C6:(C2xSL(2,3))	288,922

Non-split extensions G=N.Q with N=C₆ and Q=C₂×SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.(C₂×SL₂(𝔽₃)) = Dic₃×SL₂(𝔽₃)	φ: C₂×SL₂(𝔽₃)/SL₂(𝔽₃) → C₂ ⊆ Aut C₆	96		C6.(C2xSL(2,3))	288,409
C₆.₂(C₂×SL₂(𝔽₃)) = C₄×Q₈⋊C₉	central extension (φ=1)	288		C6.2(C2xSL(2,3))	288,72
C₆.₃(C₂×SL₂(𝔽₃)) = C₂²×Q₈⋊C₉	central extension (φ=1)	288		C6.3(C2xSL(2,3))	288,345
C₆.₄(C₂×SL₂(𝔽₃)) = C₁₂×SL₂(𝔽₃)	central extension (φ=1)	96		C6.4(C2xSL(2,3))	288,633

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