Extensions 1→N→G→Q→1 with N=S₃×C₃³ and Q=C₃

Direct product G=N×Q with N=S₃×C₃³ and Q=C₃

		d	ρ	Label	ID
S₃×C₃⁴		162		S3xC3^4	486,256

Semidirect products G=N:Q with N=S₃×C₃³ and Q=C₃

extension	φ:Q→Out N	d	ρ	Label	ID
(S₃×C₃³)⋊₁C₃ = S₃×C₃≀C₃	φ: C₃/C₁ → C₃ ⊆ Out S₃×C₃³	18	6	(S3xC3^3):1C3	486,117
(S₃×C₃³)⋊₂C₃ = C₃×S₃×He₃	φ: C₃/C₁ → C₃ ⊆ Out S₃×C₃³	54		(S3xC3^3):2C3	486,223

Non-split extensions G=N.Q with N=S₃×C₃³ and Q=C₃

extension	φ:Q→Out N	d	Label	ID
(S₃×C₃³).₁C₃ = S₃×C₃²⋊C₉	φ: C₃/C₁ → C₃ ⊆ Out S₃×C₃³	54	(S3xC3^3).1C3	486,95
(S₃×C₃³).₂C₃ = C₃×S₃×3_-¹⁺²	φ: C₃/C₁ → C₃ ⊆ Out S₃×C₃³	54	(S3xC3^3).2C3	486,225
(S₃×C₃³).₃C₃ = S₃×C₃²×C₉	φ: trivial image	162	(S3xC3^3).3C3	486,221

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=S3×C33 and Q=C3