Extensions 1→N→G→Q→1 with N=Dic₁₀ and Q=C₁₀

Direct product G=N×Q with N=Dic₁₀ and Q=C₁₀

		d	ρ	Label	ID
C₁₀×Dic₁₀		80		C10xDic10	400,181

Semidirect products G=N:Q with N=Dic₁₀ and Q=C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₀⋊₁C₁₀ = C₅×C₄₀⋊C₂	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₀	80	2	Dic10:1C10	400,78
Dic₁₀⋊₂C₁₀ = C₅×D₄.D₅	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₀	40	4	Dic10:2C10	400,88
Dic₁₀⋊₃C₁₀ = C₅×D₄⋊₂D₅	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₀	40	4	Dic10:3C10	400,186
Dic₁₀⋊₄C₁₀ = C₅×Q₈×D₅	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₀	80	4	Dic10:4C10	400,187
Dic₁₀⋊₅C₁₀ = C₅×C₄○D₂₀	φ: trivial image	40	2	Dic10:5C10	400,184

Non-split extensions G=N.Q with N=Dic₁₀ and Q=C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₀.₁C₁₀ = C₅×Dic₂₀	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₀	80	2	Dic10.1C10	400,80
Dic₁₀.₂C₁₀ = C₅×C₅⋊Q₁₆	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₀	80	4	Dic10.2C10	400,90

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁