Extensions 1→N→G→Q→1 with N=D₁₀ and Q=C₆

Direct product G=N×Q with N=D₁₀ and Q=C₆

		d	ρ	Label	ID
D₅×C₂×C₆		60		D5xC2xC6	120,44

Semidirect products G=N:Q with N=D₁₀ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀⋊₁C₆ = C₃×D₂₀	φ: C₆/C₃ → C₂ ⊆ Out D₁₀	60	2	D10:1C6	120,18
D₁₀⋊₂C₆ = C₃×C₅⋊D₄	φ: C₆/C₃ → C₂ ⊆ Out D₁₀	60	2	D10:2C6	120,20

Non-split extensions G=N.Q with N=D₁₀ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀.C₆ = C₆×F₅	φ: C₆/C₃ → C₂ ⊆ Out D₁₀	30	4	D10.C6	120,40
D₁₀.₂C₆ = D₅×C₁₂	φ: trivial image	60	2	D10.2C6	120,17

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=D10 and Q=C6