Extensions 1→N→G→Q→1 with N=D₂₀ and Q=S₃

Direct product G=N×Q with N=D₂₀ and Q=S₃

		d	ρ	Label	ID
S₃×D₂₀		60	4+	S3xD20	240,137

Semidirect products G=N:Q with N=D₂₀ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
D₂₀⋊₁S₃ = C₃⋊D₄₀	φ: S₃/C₃ → C₂ ⊆ Out D₂₀	120	4+	D20:1S3	240,14
D₂₀⋊₂S₃ = C₁₅⋊D₈	φ: S₃/C₃ → C₂ ⊆ Out D₂₀	120	4	D20:2S3	240,13
D₂₀⋊₃S₃ = D₂₀⋊S₃	φ: S₃/C₃ → C₂ ⊆ Out D₂₀	120	4	D20:3S3	240,127
D₂₀⋊₄S₃ = C₂₀⋊D₆	φ: S₃/C₃ → C₂ ⊆ Out D₂₀	60	4	D20:4S3	240,138
D₂₀⋊₅S₃ = D₂₀⋊₅S₃	φ: trivial image	120	4-	D20:5S3	240,126

Non-split extensions G=N.Q with N=D₂₀ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
D₂₀.₁S₃ = C₆.D₂₀	φ: S₃/C₃ → C₂ ⊆ Out D₂₀	120	4-	D20.1S3	240,18
D₂₀.₂S₃ = C₃₀.D₄	φ: S₃/C₃ → C₂ ⊆ Out D₂₀	120	4	D20.2S3	240,16

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁