Extensions 1→N→G→Q→1 with N=C₃×C₉ and Q=D₉

Direct product G=N×Q with N=C₃×C₉ and Q=D₉

		d	ρ	Label	ID
D₉×C₃×C₉		54		D9xC3xC9	486,91

Semidirect products G=N:Q with N=C₃×C₉ and Q=D₉

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₉)⋊₁D₉ = C₉⋊S₃⋊C₉	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	54		(C3xC9):1D9	486,3
(C₃×C₉)⋊₂D₉ = (C₃×C₉)⋊D₉	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	54	6	(C3xC9):2D9	486,21
(C₃×C₉)⋊₃D₉ = (C₃×C₉)⋊₃D₉	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	54	6	(C3xC9):3D9	486,23
(C₃×C₉)⋊₄D₉ = C₃.₂(C₉⋊D₉)	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	162		(C3xC9):4D9	486,42
(C₃×C₉)⋊₅D₉ = (C₃×C₉)⋊₅D₉	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	81		(C3xC9):5D9	486,53
(C₃×C₉)⋊₆D₉ = (C₃×C₉)⋊₆D₉	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	81		(C3xC9):6D9	486,54
(C₃×C₉)⋊₇D₉ = C₉²⋊₃C₆	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	81		(C3xC9):7D9	486,141
(C₃×C₉)⋊₈D₉ = C₉²⋊₄S₃	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	54	6	(C3xC9):8D9	486,140
(C₃×C₉)⋊₉D₉ = C₉×C₉⋊S₃	φ: D₉/C₉ → C₂ ⊆ Aut C₃×C₉	54		(C3xC9):9D9	486,133
(C₃×C₉)⋊₁₀D₉ = C₃×C₉⋊D₉	φ: D₉/C₉ → C₂ ⊆ Aut C₃×C₉	162		(C3xC9):10D9	486,134
(C₃×C₉)⋊₁₁D₉ = C₉²⋊₈S₃	φ: D₉/C₉ → C₂ ⊆ Aut C₃×C₉	243		(C3xC9):11D9	486,180

Non-split extensions G=N.Q with N=C₃×C₉ and Q=D₉

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₉).₁D₉ = C₂₇⋊₃C₁₈	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	54	6	(C3xC9).1D9	486,15
(C₃×C₉).₂D₉ = C₃²⋊₂D₂₇	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	54	6	(C3xC9).2D9	486,51
(C₃×C₉).₃D₉ = C₃³.D₉	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	27	6+	(C3xC9).3D9	486,55
(C₃×C₉).₄D₉ = C₈₁⋊C₆	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	81	6+	(C3xC9).4D9	486,34
(C₃×C₉).₅D₉ = C₃³.₅D₉	φ: D₉/C₃ → S₃ ⊆ Aut C₃×C₉	81		(C3xC9).5D9	486,162
(C₃×C₉).₆D₉ = C₉×D₂₇	φ: D₉/C₉ → C₂ ⊆ Aut C₃×C₉	54	2	(C3xC9).6D9	486,13
(C₃×C₉).₇D₉ = C₃×D₈₁	φ: D₉/C₉ → C₂ ⊆ Aut C₃×C₉	162	2	(C3xC9).7D9	486,32
(C₃×C₉).₈D₉ = C₉⋊D₂₇	φ: D₉/C₉ → C₂ ⊆ Aut C₃×C₉	243		(C3xC9).8D9	486,50
(C₃×C₉).₉D₉ = C₈₁⋊S₃	φ: D₉/C₉ → C₂ ⊆ Aut C₃×C₉	243		(C3xC9).9D9	486,60
(C₃×C₉).₁₀D₉ = C₃×C₂₇⋊S₃	φ: D₉/C₉ → C₂ ⊆ Aut C₃×C₉	162		(C3xC9).10D9	486,160
(C₃×C₉).₁₁D₉ = C₃²⋊₄D₂₇	φ: D₉/C₉ → C₂ ⊆ Aut C₃×C₉	243		(C3xC9).11D9	486,184

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁