Extensions 1→N→G→Q→1 with N=C₉ and Q=C₃×C₉

Direct product G=N×Q with N=C₉ and Q=C₃×C₉

		d	ρ	Label	ID
C₃×C₉²		243		C3xC9^2	243,31

Semidirect products G=N:Q with N=C₉ and Q=C₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉⋊₁(C₃×C₉) = C₉×3_-¹⁺²	φ: C₃×C₉/C₉ → C₃ ⊆ Aut C₉	81		C9:1(C3xC9)	243,36
C₉⋊₂(C₃×C₉) = C₃×C₉⋊C₉	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₉	243		C9:2(C3xC9)	243,33

Non-split extensions G=N.Q with N=C₉ and Q=C₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉.₁(C₃×C₉) = C₂₇○He₃	φ: C₃×C₉/C₉ → C₃ ⊆ Aut C₉	81	3	C9.1(C3xC9)	243,50
C₉.₂(C₃×C₉) = C₂₇⋊C₉	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₉	27	9	C9.2(C3xC9)	243,22
C₉.₃(C₃×C₉) = C₉²⋊₃C₃	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₉	81		C9.3(C3xC9)	243,34
C₉.₄(C₃×C₉) = C₃×C₂₇⋊C₃	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₉	81		C9.4(C3xC9)	243,49
C₉.₅(C₃×C₉) = C₂₇⋊₂C₉	central extension (φ=1)	243		C9.5(C3xC9)	243,11
C₉.₆(C₃×C₉) = C₈₁⋊C₃	central extension (φ=1)	81	3	C9.6(C3xC9)	243,24

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