Extensions 1→N→G→Q→1 with N=C₆ and Q=C₃²⋊C₆

Direct product G=N×Q with N=C₆ and Q=C₃²⋊C₆

		d	ρ	Label	ID
C₆×C₃²⋊C₆		36	6	C6xC3^2:C6	324,138

Semidirect products G=N:Q with N=C₆ and Q=C₃²⋊C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₃²⋊C₆) = C₂×He₃⋊₄S₃	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	54		C6:(C3^2:C6)	324,144

Non-split extensions G=N.Q with N=C₆ and Q=C₃²⋊C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₃²⋊C₆) = C₃²⋊Dic₉	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	108		C6.1(C3^2:C6)	324,8
C₆.₂(C₃²⋊C₆) = C₃³⋊C₁₂	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	36	6-	C6.2(C3^2:C6)	324,14
C₆.₃(C₃²⋊C₆) = He₃.Dic₃	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	108	6-	C6.3(C3^2:C6)	324,16
C₆.₄(C₃²⋊C₆) = He₃.₂Dic₃	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	108	6-	C6.4(C3^2:C6)	324,18
C₆.₅(C₃²⋊C₆) = C₂×C₃²⋊D₉	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	54		C6.5(C3^2:C6)	324,63
C₆.₆(C₃²⋊C₆) = C₂×C₃³⋊C₆	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	18	6+	C6.6(C3^2:C6)	324,69
C₆.₇(C₃²⋊C₆) = C₂×He₃.S₃	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	54	6+	C6.7(C3^2:C6)	324,71
C₆.₈(C₃²⋊C₆) = C₂×He₃.₂S₃	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	54	6+	C6.8(C3^2:C6)	324,73
C₆.₉(C₃²⋊C₆) = C₃³⋊₄C₁₂	φ: C₃²⋊C₆/He₃ → C₂ ⊆ Aut C₆	108		C6.9(C3^2:C6)	324,98
C₆.₁₀(C₃²⋊C₆) = C₃²⋊C₃₆	central extension (φ=1)	36	6	C6.10(C3^2:C6)	324,7
C₆.₁₁(C₃²⋊C₆) = He₃⋊C₁₂	central extension (φ=1)	36	3	C6.11(C3^2:C6)	324,13
C₆.₁₂(C₃²⋊C₆) = He₃.C₁₂	central extension (φ=1)	108	3	C6.12(C3^2:C6)	324,15
C₆.₁₃(C₃²⋊C₆) = He₃.₂C₁₂	central extension (φ=1)	108	3	C6.13(C3^2:C6)	324,17
C₆.₁₄(C₃²⋊C₆) = C₂×C₃²⋊C₁₈	central extension (φ=1)	36	6	C6.14(C3^2:C6)	324,62
C₆.₁₅(C₃²⋊C₆) = C₂×C₃≀S₃	central extension (φ=1)	18	3	C6.15(C3^2:C6)	324,68
C₆.₁₆(C₃²⋊C₆) = C₂×He₃.C₆	central extension (φ=1)	54	3	C6.16(C3^2:C6)	324,70
C₆.₁₇(C₃²⋊C₆) = C₂×He₃.₂C₆	central extension (φ=1)	54	3	C6.17(C3^2:C6)	324,72
C₆.₁₈(C₃²⋊C₆) = C₃×C₃²⋊C₁₂	central extension (φ=1)	36	6	C6.18(C3^2:C6)	324,92

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