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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆)⋊SL₂(𝔽₃) = C₂×ASL₂(𝔽₃)	φ: SL₂(𝔽₃)/C₁ → SL₂(𝔽₃) ⊆ Aut C₃×C₆	18	8+	(C3xC6):SL(2,3)	432,735
(C₃×C₆)⋊₂SL₂(𝔽₃) = C₂×Q₈⋊He₃	φ: SL₂(𝔽₃)/Q₈ → C₃ ⊆ Aut C₃×C₆	144		(C3xC6):2SL(2,3)	432,336

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₆).SL₂(𝔽₃) = C₂×Q₈⋊3_-¹⁺²	φ: SL₂(𝔽₃)/Q₈ → C₃ ⊆ Aut C₃×C₆	144		(C3xC6).SL(2,3)	432,335
(C₃×C₆).₂SL₂(𝔽₃) = C₆×Q₈⋊C₉	central extension (φ=1)	432		(C3xC6).2SL(2,3)	432,334

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