Extensions 1→N→G→Q→1 with N=C₃ and Q=S₃×C₃×C₉

Direct product G=N×Q with N=C₃ and Q=S₃×C₃×C₉

		d	ρ	Label	ID
S₃×C₃²×C₉		162		S3xC3^2xC9	486,221

Semidirect products G=N:Q with N=C₃ and Q=S₃×C₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(S₃×C₃×C₉) = C₃⋊S₃×C₃×C₉	φ: S₃×C₃×C₉/C₃²×C₉ → C₂ ⊆ Aut C₃	54		C3:(S3xC3xC9)	486,228

Non-split extensions G=N.Q with N=C₃ and Q=S₃×C₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(S₃×C₃×C₉) = D₉×C₃×C₉	φ: S₃×C₃×C₉/C₃²×C₉ → C₂ ⊆ Aut C₃	54		C3.1(S3xC3xC9)	486,91
C₃.₂(S₃×C₃×C₉) = C₃×C₃²⋊C₁₈	φ: S₃×C₃×C₉/C₃²×C₉ → C₂ ⊆ Aut C₃	54		C3.2(S3xC3xC9)	486,93
C₃.₃(S₃×C₃×C₉) = C₃×C₉⋊C₁₈	φ: S₃×C₃×C₉/C₃²×C₉ → C₂ ⊆ Aut C₃	54		C3.3(S3xC3xC9)	486,96
C₃.₄(S₃×C₃×C₉) = C₉×C₃²⋊C₆	φ: S₃×C₃×C₉/C₃²×C₉ → C₂ ⊆ Aut C₃	54	6	C3.4(S3xC3xC9)	486,98
C₃.₅(S₃×C₃×C₉) = C₉×C₉⋊C₆	φ: S₃×C₃×C₉/C₃²×C₉ → C₂ ⊆ Aut C₃	54	6	C3.5(S3xC3xC9)	486,100
C₃.₆(S₃×C₃×C₉) = S₃×C₉²	central extension (φ=1)	162		C3.6(S3xC3xC9)	486,92
C₃.₇(S₃×C₃×C₉) = S₃×C₃×C₂₇	central extension (φ=1)	162		C3.7(S3xC3xC9)	486,112
C₃.₈(S₃×C₃×C₉) = S₃×C₃²⋊C₉	central stem extension (φ=1)	54		C3.8(S3xC3xC9)	486,95
C₃.₉(S₃×C₃×C₉) = S₃×C₉⋊C₉	central stem extension (φ=1)	162		C3.9(S3xC3xC9)	486,97
C₃.₁₀(S₃×C₃×C₉) = S₃×C₂₇⋊C₃	central stem extension (φ=1)	54	6	C3.10(S3xC3xC9)	486,114

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