Extensions 1→N→G→Q→1 with N=3_-¹⁺² and Q=C₁₅

Direct product G=N×Q with N=3_-¹⁺² and Q=C₁₅

		d	ρ	Label	ID
C₁₅×3_-¹⁺²		135		C15xES-(3,1)	405,13

Semidirect products G=N:Q with N=3_-¹⁺² and Q=C₁₅

extension	φ:Q→Out N	d	ρ	Label	ID
3_-¹⁺²⋊₁C₁₅ = C₅×C₃≀C₃	φ: C₁₅/C₅ → C₃ ⊆ Out 3_-¹⁺²	45	3	ES-(3,1):1C15	405,7
3_-¹⁺²⋊₂C₁₅ = C₅×He₃.C₃	φ: C₁₅/C₅ → C₃ ⊆ Out 3_-¹⁺²	135	3	ES-(3,1):2C15	405,8
3_-¹⁺²⋊₃C₁₅ = C₅×C₉○He₃	φ: trivial image	135	3	ES-(3,1):3C15	405,14

Non-split extensions G=N.Q with N=3_-¹⁺² and Q=C₁₅

extension	φ:Q→Out N	d	ρ	Label	ID
3_-¹⁺².C₁₅ = C₅×C₃.He₃	φ: C₁₅/C₅ → C₃ ⊆ Out 3_-¹⁺²	135	3	ES-(3,1).C15	405,10

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=3- 1+2 and Q=C15