Extensions 1→N→G→Q→1 with N=Dic₁₀ and Q=S₃

Direct product G=N×Q with N=Dic₁₀ and Q=S₃

		d	ρ	Label	ID
S₃×Dic₁₀		120	4-	S3xDic10	240,128

Semidirect products G=N:Q with N=Dic₁₀ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₀⋊₁S₃ = C₁₅⋊SD₁₆	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₀	120	4+	Dic10:1S3	240,19
Dic₁₀⋊₂S₃ = C₂₀.D₆	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₀	120	4	Dic10:2S3	240,17
Dic₁₀⋊₃S₃ = D₁₂⋊D₅	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₀	120	4	Dic10:3S3	240,129
Dic₁₀⋊₄S₃ = D₁₅⋊Q₈	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₀	120	4	Dic10:4S3	240,131
Dic₁₀⋊₅S₃ = D₆₀⋊C₂	φ: trivial image	120	4+	Dic10:5S3	240,130

Non-split extensions G=N.Q with N=Dic₁₀ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₀.₁S₃ = C₃⋊Dic₂₀	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₀	240	4-	Dic10.1S3	240,23
Dic₁₀.₂S₃ = C₁₅⋊Q₁₆	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₀	240	4	Dic10.2S3	240,22

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁