Extensions 1→N→G→Q→1 with N=C₉ and Q=C₃²×C₆

Direct product G=N×Q with N=C₉ and Q=C₃²×C₆

		d	ρ	Label	ID
C₃³×C₁₈		486		C3^3xC18	486,250

Semidirect products G=N:Q with N=C₉ and Q=C₃²×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉⋊(C₃²×C₆) = C₃²×C₉⋊C₆	φ: C₃²×C₆/C₃² → C₆ ⊆ Aut C₉	54		C9:(C3^2xC6)	486,224
C₉⋊₂(C₃²×C₆) = C₃×C₆×3_-¹⁺²	φ: C₃²×C₆/C₃×C₆ → C₃ ⊆ Aut C₉	162		C9:2(C3^2xC6)	486,252
C₉⋊₃(C₃²×C₆) = D₉×C₃³	φ: C₃²×C₆/C₃³ → C₂ ⊆ Aut C₉	162		C9:3(C3^2xC6)	486,220

Non-split extensions G=N.Q with N=C₉ and Q=C₃²×C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉.₁(C₃²×C₆) = C₆×C₉○He₃	φ: C₃²×C₆/C₃×C₆ → C₃ ⊆ Aut C₉	162		C9.1(C3^2xC6)	486,253
C₉.₂(C₃²×C₆) = C₂×3_-¹⁺⁴	φ: C₃²×C₆/C₃×C₆ → C₃ ⊆ Aut C₉	54	9	C9.2(C3^2xC6)	486,255
C₉.₃(C₃²×C₆) = C₆×C₂₇⋊C₃	central extension (φ=1)	162		C9.3(C3^2xC6)	486,208
C₉.₄(C₃²×C₆) = C₂×C₂₇○He₃	central extension (φ=1)	162	3	C9.4(C3^2xC6)	486,209

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