Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×C₃²⋊C₄

Direct product G=N×Q with N=C₃ and Q=C₃×C₃²⋊C₄

		d	ρ	Label	ID
C₃²×C₃²⋊C₄		36		C3^2xC3^2:C4	324,161

Semidirect products G=N:Q with N=C₃ and Q=C₃×C₃²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃×C₃²⋊C₄) = C₃×C₃³⋊C₄	φ: C₃×C₃²⋊C₄/C₃×C₃⋊S₃ → C₂ ⊆ Aut C₃	12	4	C3:(C3xC3^2:C4)	324,162

Non-split extensions G=N.Q with N=C₃ and Q=C₃×C₃²⋊C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×C₃²⋊C₄) = C₉×C₃²⋊C₄	central extension (φ=1)	36	4	C3.1(C3xC3^2:C4)	324,109
C₃.₂(C₃×C₃²⋊C₄) = C₃×He₃⋊C₄	central stem extension (φ=1)	54		C3.2(C3xC3^2:C4)	324,110
C₃.₃(C₃×C₃²⋊C₄) = He₃.₃C₁₂	central stem extension (φ=1)	54	3	C3.3(C3xC3^2:C4)	324,111

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Extensions 1→N→G→Q→1 with N=C3 and Q=C3×C32⋊C4