Extensions 1→N→G→Q→1 with N=Dic₁₂ and Q=C₁₀

Direct product G=N×Q with N=Dic₁₂ and Q=C₁₀

		d	ρ	Label	ID
C₁₀×Dic₁₂		480		C10xDic12	480,784

Semidirect products G=N:Q with N=Dic₁₂ and Q=C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₂⋊₁C₁₀ = C₅×C₄₈⋊C₂	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₂	240	2	Dic12:1C10	480,119
Dic₁₂⋊₂C₁₀ = C₅×C₈.D₆	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₂	240	4	Dic12:2C10	480,788
Dic₁₂⋊₃C₁₀ = C₅×D₈.S₃	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₂	240	4	Dic12:3C10	480,146
Dic₁₂⋊₄C₁₀ = C₅×D₈⋊₃S₃	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₂	240	4	Dic12:4C10	480,791
Dic₁₂⋊₅C₁₀ = C₅×S₃×Q₁₆	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₂	240	4	Dic12:5C10	480,796
Dic₁₂⋊₆C₁₀ = C₅×D₄.D₆	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₂	240	4	Dic12:6C10	480,794
Dic₁₂⋊₇C₁₀ = C₅×C₄○D₂₄	φ: trivial image	240	2	Dic12:7C10	480,783

Non-split extensions G=N.Q with N=Dic₁₂ and Q=C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₂.₁C₁₀ = C₅×Dic₂₄	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₂	480	2	Dic12.1C10	480,120
Dic₁₂.₂C₁₀ = C₅×C₃⋊Q₃₂	φ: C₁₀/C₅ → C₂ ⊆ Out Dic₁₂	480	4	Dic12.2C10	480,148

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁