Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃²⋊D₉

Direct product G=N×Q with N=C₃ and Q=C₃²⋊D₉

		d	ρ	Label	ID
C₃×C₃²⋊D₉		54		C3xC3^2:D9	486,94

Semidirect products G=N:Q with N=C₃ and Q=C₃²⋊D₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃²⋊D₉) = C₃³⋊D₉	φ: C₃²⋊D₉/C₃²⋊C₉ → C₂ ⊆ Aut C₃	81		C3:(C3^2:D9)	486,137

Non-split extensions G=N.Q with N=C₃ and Q=C₃²⋊D₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃²⋊D₉) = C₃²⋊D₂₇	φ: C₃²⋊D₉/C₃²⋊C₉ → C₂ ⊆ Aut C₃	81		C3.1(C3^2:D9)	486,17
C₃.₂(C₃²⋊D₉) = He₃⋊D₉	φ: C₃²⋊D₉/C₃²⋊C₉ → C₂ ⊆ Aut C₃	81		C3.2(C3^2:D9)	486,25
C₃.₃(C₃²⋊D₉) = He₃.D₉	φ: C₃²⋊D₉/C₃²⋊C₉ → C₂ ⊆ Aut C₃	81	6+	C3.3(C3^2:D9)	486,27
C₃.₄(C₃²⋊D₉) = He₃.₂D₉	φ: C₃²⋊D₉/C₃²⋊C₉ → C₂ ⊆ Aut C₃	81	6+	C3.4(C3^2:D9)	486,29
C₃.₅(C₃²⋊D₉) = C₉⋊S₃⋊C₉	central extension (φ=1)	54		C3.5(C3^2:D9)	486,3
C₃.₆(C₃²⋊D₉) = C₃³⋊₁D₉	central stem extension (φ=1)	18	6	C3.6(C3^2:D9)	486,19
C₃.₇(C₃²⋊D₉) = (C₃×C₉)⋊D₉	central stem extension (φ=1)	54	6	C3.7(C3^2:D9)	486,21
C₃.₈(C₃²⋊D₉) = (C₃×C₉)⋊₃D₉	central stem extension (φ=1)	54	6	C3.8(C3^2:D9)	486,23

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁