Extensions 1→N→G→Q→1 with N=C₃² and Q=3_-¹⁺²

Direct product G=N×Q with N=C₃² and Q=3_-¹⁺²

		d	ρ	Label	ID
C₃²×3_-¹⁺²		81		C3^2xES-(3,1)	243,63

Semidirect products G=N:Q with N=C₃² and Q=3_-¹⁺²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊₁3_-¹⁺² = C₉⋊He₃	φ: 3_-¹⁺²/C₉ → C₃ ⊆ Aut C₃²	81		C3^2:1ES-(3,1)	243,39
C₃²⋊₂3_-¹⁺² = C₃⁴.C₃	φ: 3_-¹⁺²/C₃² → C₃ ⊆ Aut C₃²	27		C3^2:2ES-(3,1)	243,38

Non-split extensions G=N.Q with N=C₃² and Q=3_-¹⁺²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².₁3_-¹⁺² = He₃⋊C₉	φ: 3_-¹⁺²/C₉ → C₃ ⊆ Aut C₃²	81		C3^2.1ES-(3,1)	243,17
C₃².₂3_-¹⁺² = 3_-¹⁺²⋊C₉	φ: 3_-¹⁺²/C₉ → C₃ ⊆ Aut C₃²	81		C3^2.2ES-(3,1)	243,18
C₃².₃3_-¹⁺² = C₉⋊3_-¹⁺²	φ: 3_-¹⁺²/C₉ → C₃ ⊆ Aut C₃²	81		C3^2.3ES-(3,1)	243,41
C₃².₄3_-¹⁺² = C₃³⋊C₉	φ: 3_-¹⁺²/C₃² → C₃ ⊆ Aut C₃²	27		C3^2.4ES-(3,1)	243,13
C₃².₅3_-¹⁺² = C₃².₁₉He₃	φ: 3_-¹⁺²/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.5ES-(3,1)	243,14
C₃².₆3_-¹⁺² = C₃².₂₀He₃	φ: 3_-¹⁺²/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.6ES-(3,1)	243,15
C₃².₇3_-¹⁺² = C₂₇⋊C₉	φ: 3_-¹⁺²/C₃² → C₃ ⊆ Aut C₃²	27	9	C3^2.7ES-(3,1)	243,22
C₃².₈3_-¹⁺² = C₃³.₃₁C₃²	φ: 3_-¹⁺²/C₃² → C₃ ⊆ Aut C₃²	81		C3^2.8ES-(3,1)	243,42
C₃².₉3_-¹⁺² = C₃.C₉²	central extension (φ=1)	243		C3^2.9ES-(3,1)	243,2
C₃².₁₀3_-¹⁺² = C₃×C₃²⋊C₉	central extension (φ=1)	81		C3^2.10ES-(3,1)	243,32
C₃².₁₁3_-¹⁺² = C₃×C₉⋊C₉	central extension (φ=1)	243		C3^2.11ES-(3,1)	243,33

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁