Extensions 1→N→G→Q→1 with N=C₃×C₂₇ and Q=S₃

Direct product G=N×Q with N=C₃×C₂₇ and Q=S₃

		d	ρ	Label	ID
S₃×C₃×C₂₇		162		S3xC3xC27	486,112

Semidirect products G=N:Q with N=C₃×C₂₇ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₂₇)⋊₁S₃ = C₃²⋊C₅₄	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	54	6	(C3xC27):1S3	486,16
(C₃×C₂₇)⋊₂S₃ = He₃.C₁₈	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	81	3	(C3xC27):2S3	486,26
(C₃×C₂₇)⋊₃S₃ = He₃.₂C₁₈	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	81	3	(C3xC27):3S3	486,28
(C₃×C₂₇)⋊₄S₃ = C₃²⋊₂D₂₇	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	54	6	(C3xC27):4S3	486,51
(C₃×C₂₇)⋊₅S₃ = He₃.₃D₉	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	81	6+	(C3xC27):5S3	486,58
(C₃×C₂₇)⋊₆S₃ = He₃.₄D₉	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	81	6+	(C3xC27):6S3	486,59
(C₃×C₂₇)⋊₇S₃ = He₃.₅D₉	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	81	6+	(C3xC27):7S3	486,163
(C₃×C₂₇)⋊₈S₃ = He₃.₅C₁₈	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	81	3	(C3xC27):8S3	486,164
(C₃×C₂₇)⋊₉S₃ = C₃⋊S₃×C₂₇	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₇	162		(C3xC27):9S3	486,161
(C₃×C₂₇)⋊₁₀S₃ = C₃×C₂₇⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₇	162		(C3xC27):10S3	486,160
(C₃×C₂₇)⋊₁₁S₃ = C₃²⋊₄D₂₇	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₇	243		(C3xC27):11S3	486,184

Non-split extensions G=N.Q with N=C₃×C₂₇ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₂₇).₁S₃ = C₉⋊C₅₄	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	54	6	(C3xC27).1S3	486,30
(C₃×C₂₇).₂S₃ = C₈₁⋊C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃×C₂₇	81	6+	(C3xC27).2S3	486,34
(C₃×C₂₇).₃S₃ = D₉×C₂₇	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₇	54	2	(C3xC27).3S3	486,14
(C₃×C₂₇).₄S₃ = C₃×D₈₁	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₇	162	2	(C3xC27).4S3	486,32
(C₃×C₂₇).₅S₃ = C₉⋊D₂₇	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₇	243		(C3xC27).5S3	486,50
(C₃×C₂₇).₆S₃ = C₈₁⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃×C₂₇	243		(C3xC27).6S3	486,60

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