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

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

		d	ρ	Label	ID
C₃²×C₆		54		C3^2xC6	54,15

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊C₆ = C₃²⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₃²	9	6+	C3^2:C6	54,5
C₃²⋊₂C₆ = C₂×He₃	φ: C₆/C₂ → C₃ ⊆ Aut C₃²	18	3	C3^2:2C6	54,10
C₃²⋊₃C₆ = S₃×C₃²	φ: C₆/C₃ → C₂ ⊆ Aut C₃²	18		C3^2:3C6	54,12
C₃²⋊₄C₆ = C₃×C₃⋊S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₃²	18		C3^2:4C6	54,13

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².C₆ = C₂×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Aut C₃²	18	3	C3^2.C6	54,11
C₃².₂C₆ = S₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₃²	18	2	C3^2.2C6	54,4

⋊

ℤ

𝔽

○

≀

ℚ

◁

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