Extensions 1→N→G→Q→1 with N=C₃ and Q=C₆×SL₂(𝔽₃)

Direct product G=N×Q with N=C₃ and Q=C₆×SL₂(𝔽₃)

		d	ρ	Label	ID
C₃×C₆×SL₂(𝔽₃)		144		C3xC6xSL(2,3)	432,698

Semidirect products G=N:Q with N=C₃ and Q=C₆×SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₆×SL₂(𝔽₃)) = C₃×S₃×SL₂(𝔽₃)	φ: C₆×SL₂(𝔽₃)/C₃×SL₂(𝔽₃) → C₂ ⊆ Aut C₃	48	4	C3:(C6xSL(2,3))	432,623

Non-split extensions G=N.Q with N=C₃ and Q=C₆×SL₂(𝔽₃)

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₆×SL₂(𝔽₃)) = C₁₈×SL₂(𝔽₃)	central extension (φ=1)	144		C3.1(C6xSL(2,3))	432,327
C₃.₂(C₆×SL₂(𝔽₃)) = C₆×Q₈⋊C₉	central extension (φ=1)	432		C3.2(C6xSL(2,3))	432,334
C₃.₃(C₆×SL₂(𝔽₃)) = C₂×C₁₈.A₄	central stem extension (φ=1)	144		C3.3(C6xSL(2,3))	432,328
C₃.₄(C₆×SL₂(𝔽₃)) = C₂×Q₈⋊3_-¹⁺²	central stem extension (φ=1)	144		C3.4(C6xSL(2,3))	432,335
C₃.₅(C₆×SL₂(𝔽₃)) = C₂×Q₈⋊He₃	central stem extension (φ=1)	144		C3.5(C6xSL(2,3))	432,336

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