Extensions 1→N→G→Q→1 with N=C₉ and Q=C₃₀

Direct product G=N×Q with N=C₉ and Q=C₃₀

		d	ρ	Label	ID
C₃×C₉₀		270		C3xC90	270,20

Semidirect products G=N:Q with N=C₉ and Q=C₃₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₉⋊C₃₀ = C₅×C₉⋊C₆	φ: C₃₀/C₅ → C₆ ⊆ Aut C₉	45	6	C9:C30	270,11
C₉⋊₂C₃₀ = C₁₀×3_-¹⁺²	φ: C₃₀/C₁₀ → C₃ ⊆ Aut C₉	90	3	C9:2C30	270,22
C₉⋊₃C₃₀ = C₁₅×D₉	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₉	90	2	C9:3C30	270,8

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁