Extensions 1→N→G→Q→1 with N=C₃² and Q=C₃×D₅

Direct product G=N×Q with N=C₃² and Q=C₃×D₅

		d	ρ	Label	ID
D₅×C₃³		135		D5xC3^3	270,23

Semidirect products G=N:Q with N=C₃² and Q=C₃×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊(C₃×D₅) = He₃⋊D₅	φ: C₃×D₅/C₅ → C₆ ⊆ Aut C₃²	45	6+	C3^2:(C3xD5)	270,14
C₃²⋊₂(C₃×D₅) = D₅×He₃	φ: C₃×D₅/D₅ → C₃ ⊆ Aut C₃²	45	6	C3^2:2(C3xD5)	270,6
C₃²⋊₃(C₃×D₅) = C₃²×D₁₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₃²	90		C3^2:3(C3xD5)	270,25
C₃²⋊₄(C₃×D₅) = C₃×C₃⋊D₁₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₃²	90		C3^2:4(C3xD5)	270,27

Non-split extensions G=N.Q with N=C₃² and Q=C₃×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².(C₃×D₅) = D₅×3_-¹⁺²	φ: C₃×D₅/D₅ → C₃ ⊆ Aut C₃²	45	6	C3^2.(C3xD5)	270,7
C₃².₂(C₃×D₅) = C₉×D₁₅	φ: C₃×D₅/C₁₅ → C₂ ⊆ Aut C₃²	90	2	C3^2.2(C3xD5)	270,13
C₃².₃(C₃×D₅) = D₅×C₃×C₉	central extension (φ=1)	135		C3^2.3(C3xD5)	270,5

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