Extensions 1→N→G→Q→1 with N=C₉ and Q=C₃²⋊C₆

Direct product G=N×Q with N=C₉ and Q=C₃²⋊C₆

		d	ρ	Label	ID
C₉×C₃²⋊C₆		54	6	C9xC3^2:C6	486,98

Semidirect products G=N:Q with N=C₉ and Q=C₃²⋊C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉⋊(C₃²⋊C₆) = C₉⋊He₃⋊₂C₂	φ: C₃²⋊C₆/C₃² → C₆ ⊆ Aut C₉	81		C9:(C3^2:C6)	486,148
C₉⋊₂(C₃²⋊C₆) = C₉⋊He₃⋊C₂	φ: C₃²⋊C₆/C₃⋊S₃ → C₃ ⊆ Aut C₉	54	6	C9:2(C3^2:C6)	486,107
C₉⋊₃(C₃²⋊C₆) = He₃⋊₃D₉	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₉	81		C9:3(C3^2:C6)	486,142

Non-split extensions G=N.Q with N=C₉ and Q=C₃²⋊C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉.(C₃²⋊C₆) = C₃≀C₃.S₃	φ: C₃²⋊C₆/C₃² → C₆ ⊆ Aut C₉	27	6+	C9.(C3^2:C6)	486,175
C₉.₂(C₃²⋊C₆) = C₃≀C₃.C₆	φ: C₃²⋊C₆/C₃⋊S₃ → C₃ ⊆ Aut C₉	27	9	C9.2(C3^2:C6)	486,132
C₉.₃(C₃²⋊C₆) = C₃²⋊D₂₇	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₉	81		C9.3(C3^2:C6)	486,17
C₉.₄(C₃²⋊C₆) = He₃.D₉	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₉	81	6+	C9.4(C3^2:C6)	486,27
C₉.₅(C₃²⋊C₆) = He₃.₂D₉	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₉	81	6+	C9.5(C3^2:C6)	486,29
C₉.₆(C₃²⋊C₆) = C₃²⋊C₅₄	central extension (φ=1)	54	6	C9.6(C3^2:C6)	486,16
C₉.₇(C₃²⋊C₆) = He₃.C₁₈	central extension (φ=1)	81	3	C9.7(C3^2:C6)	486,26
C₉.₈(C₃²⋊C₆) = He₃.₂C₁₈	central extension (φ=1)	81	3	C9.8(C3^2:C6)	486,28
C₉.₉(C₃²⋊C₆) = C₃≀S₃⋊₃C₃	central extension (φ=1)	27	3	C9.9(C3^2:C6)	486,125

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁