Extensions 1→N→G→Q→1 with N=C₃ and Q=S₃×SL₂(𝔽₃)

Direct product G=N×Q with N=C₃ and Q=S₃×SL₂(𝔽₃)

		d	ρ	Label	ID
C₃×S₃×SL₂(𝔽₃)		48	4	C3xS3xSL(2,3)	432,623

Semidirect products G=N:Q with N=C₃ and Q=S₃×SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(S₃×SL₂(𝔽₃)) = C₃⋊S₃×SL₂(𝔽₃)	φ: S₃×SL₂(𝔽₃)/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	72		C3:(S3xSL(2,3))	432,626

Non-split extensions G=N.Q with N=C₃ and Q=S₃×SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(S₃×SL₂(𝔽₃)) = D₁₈.A₄	φ: S₃×SL₂(𝔽₃)/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	72	12-	C3.1(S3xSL(2,3))	432,263
C₃.₂(S₃×SL₂(𝔽₃)) = D₉×SL₂(𝔽₃)	φ: S₃×SL₂(𝔽₃)/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	72	4-	C3.2(S3xSL(2,3))	432,264
C₃.₃(S₃×SL₂(𝔽₃)) = Q₈⋊He₃⋊C₂	φ: S₃×SL₂(𝔽₃)/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	72	12-	C3.3(S3xSL(2,3))	432,270
C₃.₄(S₃×SL₂(𝔽₃)) = S₃×Q₈⋊C₉	central extension (φ=1)	144	4	C3.4(S3xSL(2,3))	432,268

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