Extensions 1→N→G→Q→1 with N=C₃² and Q=C₃³

Direct product G=N×Q with N=C₃² and Q=C₃³

		d	ρ	Label	ID
C₃⁵		243		C3^5	243,67

Semidirect products G=N:Q with N=C₃² and Q=C₃³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊C₃³ = C₃²×He₃	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	81		C3^2:C3^3	243,62

Non-split extensions G=N.Q with N=C₃² and Q=C₃³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².₁C₃³ = C₃×C₃≀C₃	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	27		C3^2.1C3^3	243,51
C₃².₂C₃³ = C₃×He₃.C₃	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.2C3^3	243,52
C₃².₃C₃³ = C₃×He₃⋊C₃	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.3C3^3	243,53
C₃².₄C₃³ = C₃×C₃.He₃	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.4C3^3	243,54
C₃².₅C₃³ = C₉.He₃	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	27	3	C3^2.5C3^3	243,55
C₃².₆C₃³ = C₃³⋊C₃²	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.6C3^3	243,56
C₃².₇C₃³ = He₃.C₃²	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.7C3^3	243,57
C₃².₈C₃³ = He₃⋊C₃²	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.8C3^3	243,58
C₃².₉C₃³ = C₃².C₃³	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.9C3^3	243,59
C₃².₁₀C₃³ = C₉.₂He₃	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.10C3^3	243,60
C₃².₁₁C₃³ = C₃²×3_-¹⁺²	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.11C3^3	243,63
C₃².₁₂C₃³ = C₃×C₉○He₃	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.12C3^3	243,64
C₃².₁₃C₃³ = 3₊¹⁺⁴	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.13C3^3	243,65
C₃².₁₄C₃³ = 3_-¹⁺⁴	φ: C₃³/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.14C3^3	243,66
C₃².₁₅C₃³ = C₃×C₃²⋊C₉	central extension (φ=1)	81		C3^2.15C3^3	243,32
C₃².₁₆C₃³ = C₃×C₉⋊C₉	central extension (φ=1)	243		C3^2.16C3^3	243,33
C₃².₁₇C₃³ = C₉²⋊₃C₃	central extension (φ=1)	81		C3^2.17C3^3	243,34
C₃².₁₈C₃³ = C₉×He₃	central extension (φ=1)	81		C3^2.18C3^3	243,35
C₃².₁₉C₃³ = C₉×3_-¹⁺²	central extension (φ=1)	81		C3^2.19C3^3	243,36
C₃².₂₀C₃³ = C₃²⋊He₃	central stem extension (φ=1)	27		C3^2.20C3^3	243,37
C₃².₂₁C₃³ = C₃⁴.C₃	central stem extension (φ=1)	27		C3^2.21C3^3	243,38
C₃².₂₂C₃³ = C₉⋊He₃	central stem extension (φ=1)	81		C3^2.22C3^3	243,39
C₃².₂₃C₃³ = C₃².₂₃C₃³	central stem extension (φ=1)	81		C3^2.23C3^3	243,40
C₃².₂₄C₃³ = C₉⋊3_-¹⁺²	central stem extension (φ=1)	81		C3^2.24C3^3	243,41
C₃².₂₅C₃³ = C₃³.₃₁C₃²	central stem extension (φ=1)	81		C3^2.25C3^3	243,42
C₃².₂₆C₃³ = C₉²⋊₇C₃	central stem extension (φ=1)	81		C3^2.26C3^3	243,43
C₃².₂₇C₃³ = C₉²⋊₄C₃	central stem extension (φ=1)	81		C3^2.27C3^3	243,44
C₃².₂₈C₃³ = C₉²⋊₅C₃	central stem extension (φ=1)	81		C3^2.28C3^3	243,45
C₃².₂₉C₃³ = C₉²⋊₈C₃	central stem extension (φ=1)	81		C3^2.29C3^3	243,46
C₃².₃₀C₃³ = C₉²⋊₉C₃	central stem extension (φ=1)	81		C3^2.30C3^3	243,47

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Extensions 1→N→G→Q→1 with N=C32 and Q=C33

Extensions 1→N→G→Q→1 with N=C₃² and Q=C₃³