Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×C₃³⋊C₂

Direct product G=N×Q with N=C₃ and Q=C₃×C₃³⋊C₂

		d	ρ	Label	ID
C₃²×C₃³⋊C₂		54		C3^2xC3^3:C2	486,258

Semidirect products G=N:Q with N=C₃ and Q=C₃×C₃³⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃×C₃³⋊C₂) = C₃×C₃⁴⋊C₂	φ: C₃×C₃³⋊C₂/C₃⁴ → C₂ ⊆ Aut C₃	162		C3:(C3xC3^3:C2)	486,259

Non-split extensions G=N.Q with N=C₃ and Q=C₃×C₃³⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×C₃³⋊C₂) = C₃×C₃²⋊₄D₉	φ: C₃×C₃³⋊C₂/C₃⁴ → C₂ ⊆ Aut C₃	162		C3.1(C3xC3^3:C2)	486,240
C₃.₂(C₃×C₃³⋊C₂) = C₃⁴⋊₁₀C₆	φ: C₃×C₃³⋊C₂/C₃⁴ → C₂ ⊆ Aut C₃	81		C3.2(C3xC3^3:C2)	486,242
C₃.₃(C₃×C₃³⋊C₂) = C₃⁴.₁₁S₃	φ: C₃×C₃³⋊C₂/C₃⁴ → C₂ ⊆ Aut C₃	81		C3.3(C3xC3^3:C2)	486,244
C₃.₄(C₃×C₃³⋊C₂) = C₉○He₃⋊₃S₃	φ: C₃×C₃³⋊C₂/C₃⁴ → C₂ ⊆ Aut C₃	81		C3.4(C3xC3^3:C2)	486,245
C₃.₅(C₃×C₃³⋊C₂) = C₉×C₃³⋊C₂	central extension (φ=1)	162		C3.5(C3xC3^3:C2)	486,241
C₃.₆(C₃×C₃³⋊C₂) = C₃×He₃⋊₅S₃	central stem extension (φ=1)	54		C3.6(C3xC3^3:C2)	486,243
C₃.₇(C₃×C₃³⋊C₂) = C₉○He₃⋊₄S₃	central stem extension (φ=1)	54	6	C3.7(C3xC3^3:C2)	486,246

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁