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

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

		d	ρ	Label	ID
C₃⁵		243		C3^5	243,67

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³⋊₁C₃² = C₃²⋊He₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	27		C3^3:1C3^2	243,37
C₃³⋊₂C₃² = C₃³⋊C₃²	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	27	9	C3^3:2C3^2	243,56
C₃³⋊₃C₃² = 3₊¹⁺⁴	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	27	9	C3^3:3C3^2	243,65
C₃³⋊₄C₃² = C₃×C₃≀C₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	27		C3^3:4C3^2	243,51
C₃³⋊₅C₃² = C₃²×He₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3:5C3^2	243,62

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³.₁C₃² = C₃².₂₄He₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.1C3^2	243,3
C₃³.₂C₃² = C₃³.C₃²	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.2C3^2	243,4
C₃³.₃C₃² = C₃³.₃C₃²	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.3C3^2	243,5
C₃³.₄C₃² = C₃².₂₇He₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.4C3^2	243,6
C₃³.₅C₃² = C₃².₂₈He₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.5C3^2	243,7
C₃³.₆C₃² = C₃².₂₉He₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.6C3^2	243,8
C₃³.₇C₃² = C₃³.₇C₃²	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.7C3^2	243,9
C₃³.₈C₃² = C₉²⋊₇C₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.8C3^2	243,43
C₃³.₉C₃² = C₉²⋊₄C₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.9C3^2	243,44
C₃³.₁₀C₃² = C₉²⋊₅C₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.10C3^2	243,45
C₃³.₁₁C₃² = C₉²⋊₈C₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.11C3^2	243,46
C₃³.₁₂C₃² = C₉²⋊₉C₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	81		C3^3.12C3^2	243,47
C₃³.₁₃C₃² = He₃.C₃²	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	27	9	C3^3.13C3^2	243,57
C₃³.₁₄C₃² = He₃⋊C₃²	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	27	9	C3^3.14C3^2	243,58
C₃³.₁₅C₃² = C₃².C₃³	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	27	9	C3^3.15C3^2	243,59
C₃³.₁₆C₃² = C₉.₂He₃	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	27	9	C3^3.16C3^2	243,60
C₃³.₁₇C₃² = 3_-¹⁺⁴	φ: C₃²/C₁ → C₃² ⊆ Aut C₃³	27	9	C3^3.17C3^2	243,66
C₃³.₁₈C₃² = C₃³⋊C₉	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	27		C3^3.18C3^2	243,13
C₃³.₁₉C₃² = C₃².₁₉He₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.19C3^2	243,14
C₃³.₂₀C₃² = C₃².₂₀He₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.20C3^2	243,15
C₃³.₂₁C₃² = He₃⋊C₉	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.21C3^2	243,17
C₃³.₂₂C₃² = 3_-¹⁺²⋊C₉	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.22C3^2	243,18
C₃³.₂₃C₃² = C₃×C₃²⋊C₉	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.23C3^2	243,32
C₃³.₂₄C₃² = C₉²⋊₃C₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.24C3^2	243,34
C₃³.₂₅C₃² = C₉×He₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.25C3^2	243,35
C₃³.₂₆C₃² = C₉×3_-¹⁺²	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.26C3^2	243,36
C₃³.₂₇C₃² = C₃⁴.C₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	27		C3^3.27C3^2	243,38
C₃³.₂₈C₃² = C₉⋊He₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.28C3^2	243,39
C₃³.₂₉C₃² = C₃².₂₃C₃³	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.29C3^2	243,40
C₃³.₃₀C₃² = C₉⋊3_-¹⁺²	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.30C3^2	243,41
C₃³.₃₁C₃² = C₃³.₃₁C₃²	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.31C3^2	243,42
C₃³.₃₂C₃² = C₃×He₃.C₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.32C3^2	243,52
C₃³.₃₃C₃² = C₃×He₃⋊C₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.33C3^2	243,53
C₃³.₃₄C₃² = C₃×C₃.He₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.34C3^2	243,54
C₃³.₃₅C₃² = C₉.He₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	27	3	C3^3.35C3^2	243,55
C₃³.₃₆C₃² = C₃²×3_-¹⁺²	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.36C3^2	243,63
C₃³.₃₇C₃² = C₃×C₉○He₃	φ: C₃²/C₃ → C₃ ⊆ Aut C₃³	81		C3^3.37C3^2	243,64
C₃³.₃₈C₃² = C₃.C₉²	central extension (φ=1)	243		C3^3.38C3^2	243,2
C₃³.₃₉C₃² = C₃×C₉⋊C₉	central extension (φ=1)	243		C3^3.39C3^2	243,33

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

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