Extensions 1→N→G→Q→1 with N=Dic₁₅ and Q=S₃

Direct product G=N×Q with N=Dic₁₅ and Q=S₃

		d	ρ	Label	ID
S₃×Dic₁₅		120	4-	S3xDic15	360,78

Semidirect products G=N:Q with N=Dic₁₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₅⋊₁S₃ = D₆⋊₂D₁₅	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₅	60	4+	Dic15:1S3	360,82
Dic₁₅⋊₂S₃ = D₃₀.S₃	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₅	120	4	Dic15:2S3	360,84
Dic₁₅⋊₃S₃ = Dic₁₅⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₅	60	4	Dic15:3S3	360,85
Dic₁₅⋊₄S₃ = D₃₀⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₅	60	4	Dic15:4S3	360,86
Dic₁₅⋊₅S₃ = C₆.D₃₀	φ: trivial image	60	4+	Dic15:5S3	360,79

Non-split extensions G=N.Q with N=Dic₁₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₅.₁S₃ = C₃⋊Dic₃₀	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₅	120	4-	Dic15.1S3	360,83
Dic₁₅.₂S₃ = C₃²⋊₃Dic₁₀	φ: S₃/C₃ → C₂ ⊆ Out Dic₁₅	120	4	Dic15.2S3	360,88

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁