Extensions 1→N→G→Q→1 with N=C₃ and Q=S₃×C₃²

Direct product G=N×Q with N=C₃ and Q=S₃×C₃²

		d	ρ	Label	ID
S₃×C₃³		54		S3xC3^3	162,51

Semidirect products G=N:Q with N=C₃ and Q=S₃×C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(S₃×C₃²) = C₃²×C₃⋊S₃	φ: S₃×C₃²/C₃³ → C₂ ⊆ Aut C₃	18		C3:(S3xC3^2)	162,52

Non-split extensions G=N.Q with N=C₃ and Q=S₃×C₃²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(S₃×C₃²) = C₃²×D₉	φ: S₃×C₃²/C₃³ → C₂ ⊆ Aut C₃	54		C3.1(S3xC3^2)	162,32
C₃.₂(S₃×C₃²) = C₃×C₃²⋊C₆	φ: S₃×C₃²/C₃³ → C₂ ⊆ Aut C₃	18	6	C3.2(S3xC3^2)	162,34
C₃.₃(S₃×C₃²) = C₃×C₉⋊C₆	φ: S₃×C₃²/C₃³ → C₂ ⊆ Aut C₃	18	6	C3.3(S3xC3^2)	162,36
C₃.₄(S₃×C₃²) = S₃×C₃×C₉	central extension (φ=1)	54		C3.4(S3xC3^2)	162,33
C₃.₅(S₃×C₃²) = S₃×He₃	central stem extension (φ=1)	18	6	C3.5(S3xC3^2)	162,35
C₃.₆(S₃×C₃²) = S₃×3_-¹⁺²	central stem extension (φ=1)	18	6	C3.6(S3xC3^2)	162,37

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