Extensions 1→N→G→Q→1 with N=3_-¹⁺² and Q=C₃

Direct product G=N×Q with N=3_-¹⁺² and Q=C₃

		d	ρ	Label	ID
C₃×3_-¹⁺²		27		C3xES-(3,1)	81,13

Semidirect products G=N:Q with N=3_-¹⁺² and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
3_-¹⁺²⋊₁C₃ = C₃≀C₃	φ: C₃/C₁ → C₃ ⊆ Out 3_-¹⁺²	9	3	ES-(3,1):1C3	81,7
3_-¹⁺²⋊₂C₃ = He₃.C₃	φ: C₃/C₁ → C₃ ⊆ Out 3_-¹⁺²	27	3	ES-(3,1):2C3	81,8
3_-¹⁺²⋊₃C₃ = C₉○He₃	φ: trivial image	27	3	ES-(3,1):3C3	81,14

Non-split extensions G=N.Q with N=3_-¹⁺² and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
3_-¹⁺².C₃ = C₃.He₃	φ: C₃/C₁ → C₃ ⊆ Out 3_-¹⁺²	27	3	ES-(3,1).C3	81,10

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Extensions 1→N→G→Q→1 with N=3- 1+2 and Q=C3