Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂xC₃²:C₆

Direct product G=NxQ with N=C₃ and Q=C₂xC₃²:C₆

		d	ρ	Label	ID
C₆xC₃²:C₆		36	6	C6xC3^2:C6	324,138

Semidirect products G=N:Q with N=C₃ and Q=C₂xC₃²:C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃:₁(C₂xC₃²:C₆) = S₃xC₃²:C₆	φ: C₂xC₃²:C₆/C₃²:C₆ → C₂ ⊆ Aut C₃	18	12+	C3:1(C2xC3^2:C6)	324,116
C₃:₂(C₂xC₃²:C₆) = C₂xHe₃:₄S₃	φ: C₂xC₃²:C₆/C₂xHe₃ → C₂ ⊆ Aut C₃	54		C3:2(C2xC3^2:C6)	324,144

Non-split extensions G=N.Q with N=C₃ and Q=C₂xC₃²:C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₂xC₃²:C₆) = C₂xC₃²:D₉	φ: C₂xC₃²:C₆/C₂xHe₃ → C₂ ⊆ Aut C₃	54		C3.1(C2xC3^2:C6)	324,63
C₃.₂(C₂xC₃²:C₆) = C₂xC₃³:C₆	φ: C₂xC₃²:C₆/C₂xHe₃ → C₂ ⊆ Aut C₃	18	6+	C3.2(C2xC3^2:C6)	324,69
C₃.₃(C₂xC₃²:C₆) = C₂xHe₃.S₃	φ: C₂xC₃²:C₆/C₂xHe₃ → C₂ ⊆ Aut C₃	54	6+	C3.3(C2xC3^2:C6)	324,71
C₃.₄(C₂xC₃²:C₆) = C₂xHe₃.₂S₃	φ: C₂xC₃²:C₆/C₂xHe₃ → C₂ ⊆ Aut C₃	54	6+	C3.4(C2xC3^2:C6)	324,73
C₃.₅(C₂xC₃²:C₆) = C₂xC₃²:C₁₈	central extension (φ=1)	36	6	C3.5(C2xC3^2:C6)	324,62
C₃.₆(C₂xC₃²:C₆) = C₂xC₃wrS₃	central stem extension (φ=1)	18	3	C3.6(C2xC3^2:C6)	324,68
C₃.₇(C₂xC₃²:C₆) = C₂xHe₃.C₆	central stem extension (φ=1)	54	3	C3.7(C2xC3^2:C6)	324,70
C₃.₈(C₂xC₃²:C₆) = C₂xHe₃.₂C₆	central stem extension (φ=1)	54	3	C3.8(C2xC3^2:C6)	324,72

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