Extensions 1→N→G→Q→1 with N=D₁₀ and Q=Dic₆

Direct product G=N×Q with N=D₁₀ and Q=Dic₆

		d	ρ	Label	ID
C₂×D₅×Dic₆		240		C2xD5xDic6	480,1073

Semidirect products G=N:Q with N=D₁₀ and Q=Dic₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀⋊₁Dic₆ = D₁₀⋊₁Dic₆	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₁₀	240		D10:1Dic6	480,497
D₁₀⋊₂Dic₆ = D₁₀⋊₂Dic₆	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₁₀	240		D10:2Dic6	480,498
D₁₀⋊₃Dic₆ = Dic₁₅.D₄	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₁₀	240		D10:3Dic6	480,506
D₁₀⋊₄Dic₆ = D₁₀⋊₄Dic₆	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₁₀	240		D10:4Dic6	480,507
D₁₀⋊₅Dic₆ = D₁₀⋊Dic₆	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₁₀	240		D10:5Dic6	480,425
D₁₀⋊₆Dic₆ = C₆₀.₆₇D₄	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₁₀	240		D10:6Dic6	480,435
D₁₀⋊₇Dic₆ = C₆₀.₆₈D₄	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₁₀	240		D10:7Dic6	480,436

Non-split extensions G=N.Q with N=D₁₀ and Q=Dic₆

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀.₁Dic₆ = D₁₀.Dic₆	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₁₀	240	8	D10.1Dic6	480,237
D₁₀.₂Dic₆ = D₁₀.₂Dic₆	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₁₀	240	8	D10.2Dic6	480,238
D₁₀.₃Dic₆ = D₁₀.₂₀D₁₂	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₁₀	120		D10.3Dic6	480,243
D₁₀.₄Dic₆ = C₂×Dic₃⋊F₅	φ: Dic₆/Dic₃ → C₂ ⊆ Out D₁₀	120		D10.4Dic6	480,1001
D₁₀.₅Dic₆ = C₄₀.Dic₃	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₁₀	240	4	D10.5Dic6	480,300
D₁₀.₆Dic₆ = C₂₄.₁F₅	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₁₀	240	4	D10.6Dic6	480,301
D₁₀.₇Dic₆ = D₁₀.₁₀D₁₂	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₁₀	120		D10.7Dic6	480,311
D₁₀.₈Dic₆ = C₂×C₆₀⋊C₄	φ: Dic₆/C₁₂ → C₂ ⊆ Out D₁₀	120		D10.8Dic6	480,1064
D₁₀.₉Dic₆ = D₅×Dic₃⋊C₄	φ: trivial image	240		D10.9Dic6	480,468
D₁₀.₁₀Dic₆ = D₅×C₄⋊Dic₃	φ: trivial image	240		D10.10Dic6	480,488

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁