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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₃²×D₅) = C₃²×D₁₅	φ: C₃²×D₅/C₃×C₁₅ → C₂ ⊆ Aut C₃	90		C3:(C3^2xD5)	270,25

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃²×D₅) = D₅×C₃×C₉	central extension (φ=1)	135		C3.1(C3^2xD5)	270,5
C₃.₂(C₃²×D₅) = D₅×He₃	central stem extension (φ=1)	45	6	C3.2(C3^2xD5)	270,6
C₃.₃(C₃²×D₅) = D₅×3_-¹⁺²	central stem extension (φ=1)	45	6	C3.3(C3^2xD5)	270,7

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