Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×Dic₆

Direct product G=N×Q with N=C₃ and Q=C₃×Dic₆

		d	ρ	Label	ID
C₃²×Dic₆		72		C3^2xDic6	216,135

Semidirect products G=N:Q with N=C₃ and Q=C₃×Dic₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×Dic₆) = C₃×C₃²⋊₂Q₈	φ: C₃×Dic₆/C₃×Dic₃ → C₂ ⊆ Aut C₃	24	4	C3:1(C3xDic6)	216,123
C₃⋊₂(C₃×Dic₆) = C₃×C₃²⋊₄Q₈	φ: C₃×Dic₆/C₃×C₁₂ → C₂ ⊆ Aut C₃	72		C3:2(C3xDic6)	216,140

Non-split extensions G=N.Q with N=C₃ and Q=C₃×Dic₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×Dic₆) = C₃×Dic₁₈	φ: C₃×Dic₆/C₃×C₁₂ → C₂ ⊆ Aut C₃	72	2	C3.1(C3xDic6)	216,43
C₃.₂(C₃×Dic₆) = He₃⋊₃Q₈	φ: C₃×Dic₆/C₃×C₁₂ → C₂ ⊆ Aut C₃	72	6-	C3.2(C3xDic6)	216,49
C₃.₃(C₃×Dic₆) = C₃₆.C₆	φ: C₃×Dic₆/C₃×C₁₂ → C₂ ⊆ Aut C₃	72	6-	C3.3(C3xDic6)	216,52
C₃.₄(C₃×Dic₆) = C₉×Dic₆	central extension (φ=1)	72	2	C3.4(C3xDic6)	216,44

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