Extensions 1→N→G→Q→1 with N=C₃² and Q=C₃×C₉

Direct product G=N×Q with N=C₃² and Q=C₃×C₉

		d	ρ	Label	ID
C₃³×C₉		243		C3^3xC9	243,61

Semidirect products G=N:Q with N=C₃² and Q=C₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊₁(C₃×C₉) = C₉×He₃	φ: C₃×C₉/C₉ → C₃ ⊆ Aut C₃²	81		C3^2:1(C3xC9)	243,35
C₃²⋊₂(C₃×C₉) = C₃×C₃²⋊C₉	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₃²	81		C3^2:2(C3xC9)	243,32

Non-split extensions G=N.Q with N=C₃² and Q=C₃×C₉

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².₁(C₃×C₉) = He₃⋊C₉	φ: C₃×C₉/C₉ → C₃ ⊆ Aut C₃²	81		C3^2.1(C3xC9)	243,17
C₃².₂(C₃×C₉) = 3_-¹⁺²⋊C₉	φ: C₃×C₉/C₉ → C₃ ⊆ Aut C₃²	81		C3^2.2(C3xC9)	243,18
C₃².₃(C₃×C₉) = C₉.₅He₃	φ: C₃×C₉/C₉ → C₃ ⊆ Aut C₃²	81	3	C3^2.3(C3xC9)	243,19
C₃².₄(C₃×C₉) = C₉.₆He₃	φ: C₃×C₉/C₉ → C₃ ⊆ Aut C₃²	81	3	C3^2.4(C3xC9)	243,20
C₃².₅(C₃×C₉) = C₉×3_-¹⁺²	φ: C₃×C₉/C₉ → C₃ ⊆ Aut C₃²	81		C3^2.5(C3xC9)	243,36
C₃².₆(C₃×C₉) = C₂₇○He₃	φ: C₃×C₉/C₉ → C₃ ⊆ Aut C₃²	81	3	C3^2.6(C3xC9)	243,50
C₃².₇(C₃×C₉) = C₃³⋊C₉	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₃²	27		C3^2.7(C3xC9)	243,13
C₃².₈(C₃×C₉) = C₃².₁₉He₃	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.8(C3xC9)	243,14
C₃².₉(C₃×C₉) = C₃².₂₀He₃	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.9(C3xC9)	243,15
C₃².₁₀(C₃×C₉) = C₉.₄He₃	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₃²	27	3	C3^2.10(C3xC9)	243,16
C₃².₁₁(C₃×C₉) = C₉²⋊₃C₃	φ: C₃×C₉/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.11(C3xC9)	243,34
C₃².₁₂(C₃×C₉) = C₃.C₉²	central extension (φ=1)	243		C3^2.12(C3xC9)	243,2
C₃².₁₃(C₃×C₉) = C₂₇⋊₂C₉	central extension (φ=1)	243		C3^2.13(C3xC9)	243,11
C₃².₁₄(C₃×C₉) = C₃²⋊C₂₇	central extension (φ=1)	81		C3^2.14(C3xC9)	243,12
C₃².₁₅(C₃×C₉) = C₉⋊C₂₇	central extension (φ=1)	243		C3^2.15(C3xC9)	243,21
C₃².₁₆(C₃×C₉) = C₃×C₉⋊C₉	central extension (φ=1)	243		C3^2.16(C3xC9)	243,33
C₃².₁₇(C₃×C₉) = C₃×C₂₇⋊C₃	central extension (φ=1)	81		C3^2.17(C3xC9)	243,49

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