Extensions 1→N→G→Q→1 with N=C₃⁴ and Q=C₃

Direct product G=N×Q with N=C₃⁴ and Q=C₃

		d	ρ	Label	ID
C₃⁵		243		C3^5	243,67

Semidirect products G=N:Q with N=C₃⁴ and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⁴⋊₁C₃ = C₃²⋊He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃⁴	27		C3^4:1C3	243,37
C₃⁴⋊₂C₃ = C₃×C₃≀C₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃⁴	27		C3^4:2C3	243,51
C₃⁴⋊₃C₃ = C₃²×He₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃⁴	81		C3^4:3C3	243,62

Non-split extensions G=N.Q with N=C₃⁴ and Q=C₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⁴.₁C₃ = C₃³⋊C₉	φ: C₃/C₁ → C₃ ⊆ Aut C₃⁴	27		C3^4.1C3	243,13
C₃⁴.₂C₃ = C₃×C₃²⋊C₉	φ: C₃/C₁ → C₃ ⊆ Aut C₃⁴	81		C3^4.2C3	243,32
C₃⁴.₃C₃ = C₃⁴.C₃	φ: C₃/C₁ → C₃ ⊆ Aut C₃⁴	27		C3^4.3C3	243,38
C₃⁴.₄C₃ = C₃²×3_-¹⁺²	φ: C₃/C₁ → C₃ ⊆ Aut C₃⁴	81		C3^4.4C3	243,63

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁