Extensions 1→N→G→Q→1 with N=C₉ and Q=C₉⋊C₆

Direct product G=N×Q with N=C₉ and Q=C₉⋊C₆

		d	ρ	Label	ID
C₉×C₉⋊C₆		54	6	C9xC9:C6	486,100

Semidirect products G=N:Q with N=C₉ and Q=C₉⋊C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉⋊₁(C₉⋊C₆) = C₉²⋊₁₀C₆	φ: C₉⋊C₆/C₉ → C₆ ⊆ Aut C₉	81		C9:1(C9:C6)	486,154
C₉⋊₂(C₉⋊C₆) = C₉²⋊₁₂C₆	φ: C₉⋊C₆/C₉ → C₆ ⊆ Aut C₉	81		C9:2(C9:C6)	486,159
C₉⋊₃(C₉⋊C₆) = C₉²⋊₇C₆	φ: C₉⋊C₆/D₉ → C₃ ⊆ Aut C₉	54	6	C9:3(C9:C6)	486,109
C₉⋊₄(C₉⋊C₆) = C₉²⋊₈C₆	φ: C₉⋊C₆/D₉ → C₃ ⊆ Aut C₉	18	6	C9:4(C9:C6)	486,110
C₉⋊₅(C₉⋊C₆) = C₉²⋊₉C₆	φ: C₉⋊C₆/3_-¹⁺² → C₂ ⊆ Aut C₉	81		C9:5(C9:C6)	486,144

Non-split extensions G=N.Q with N=C₉ and Q=C₉⋊C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉.₁(C₉⋊C₆) = He₃.D₉	φ: C₉⋊C₆/C₉ → C₆ ⊆ Aut C₉	81	6+	C9.1(C9:C6)	486,27
C₉.₂(C₉⋊C₆) = He₃.₂D₉	φ: C₉⋊C₆/C₉ → C₆ ⊆ Aut C₉	81	6+	C9.2(C9:C6)	486,29
C₉.₃(C₉⋊C₆) = C₉²⋊₁₁C₆	φ: C₉⋊C₆/C₉ → C₆ ⊆ Aut C₉	81		C9.3(C9:C6)	486,158
C₉.₄(C₉⋊C₆) = C₃²⋊D₂₇	φ: C₉⋊C₆/3_-¹⁺² → C₂ ⊆ Aut C₉	81		C9.4(C9:C6)	486,17
C₉.₅(C₉⋊C₆) = C₉⋊C₅₄	central extension (φ=1)	54	6	C9.5(C9:C6)	486,30

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁