Extensions 1→N→G→Q→1 with N=C₃² and Q=C₃₀

Direct product G=N×Q with N=C₃² and Q=C₃₀

		d	ρ	Label	ID
C₃²×C₃₀		270		C3^2xC30	270,30

Semidirect products G=N:Q with N=C₃² and Q=C₃₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃²⋊C₃₀ = C₅×C₃²⋊C₆	φ: C₃₀/C₅ → C₆ ⊆ Aut C₃²	45	6	C3^2:C30	270,10
C₃²⋊₂C₃₀ = C₁₀×He₃	φ: C₃₀/C₁₀ → C₃ ⊆ Aut C₃²	90	3	C3^2:2C30	270,21
C₃²⋊₃C₃₀ = S₃×C₃×C₁₅	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₃²	90		C3^2:3C30	270,24
C₃²⋊₄C₃₀ = C₁₅×C₃⋊S₃	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₃²	90		C3^2:4C30	270,26

Non-split extensions G=N.Q with N=C₃² and Q=C₃₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃².C₃₀ = C₁₀×3_-¹⁺²	φ: C₃₀/C₁₀ → C₃ ⊆ Aut C₃²	90	3	C3^2.C30	270,22
C₃².₂C₃₀ = S₃×C₄₅	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₃²	90	2	C3^2.2C30	270,9

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