Extensions 1→N→G→Q→1 with N=D₁₀ and Q=Dic₃

Direct product G=N×Q with N=D₁₀ and Q=Dic₃

		d	ρ	Label	ID
C₂×D₅×Dic₃		120		C2xD5xDic3	240,139

Semidirect products G=N:Q with N=D₁₀ and Q=Dic₃

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀⋊₁Dic₃ = D₁₀⋊Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Out D₁₀	120		D10:1Dic3	240,26
D₁₀⋊₂Dic₃ = D₁₀.D₆	φ: Dic₃/C₆ → C₂ ⊆ Out D₁₀	60	4	D10:2Dic3	240,124
D₁₀⋊₃Dic₃ = C₂²×C₃⋊F₅	φ: Dic₃/C₆ → C₂ ⊆ Out D₁₀	60		D10:3Dic3	240,201

Non-split extensions G=N.Q with N=D₁₀ and Q=Dic₃

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀.₁Dic₃ = C₂₀.₃₂D₆	φ: Dic₃/C₆ → C₂ ⊆ Out D₁₀	120	4	D10.1Dic3	240,10
D₁₀.₂Dic₃ = C₆₀.C₄	φ: Dic₃/C₆ → C₂ ⊆ Out D₁₀	120	4	D10.2Dic3	240,118
D₁₀.₃Dic₃ = C₁₂.F₅	φ: Dic₃/C₆ → C₂ ⊆ Out D₁₀	120	4	D10.3Dic3	240,119
D₁₀.₄Dic₃ = D₅×C₃⋊C₈	φ: trivial image	120	4	D10.4Dic3	240,7

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁