Extensions 1→N→G→Q→1 with N=D₆.D₁₀ and Q=C₂

Direct product G=N×Q with N=D₆.D₁₀ and Q=C₂

		d	ρ	Label	ID
C₂×D₆.D₁₀		240		C2xD6.D10	480,1083

Semidirect products G=N:Q with N=D₆.D₁₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₆.D₁₀⋊₁C₂ = C₁₅⋊2_-¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	240	8-	D6.D10:1C2	480,1096
D₆.D₁₀⋊₂C₂ = D₂₀⋊₁₃D₆	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	120	8-	D6.D10:2C2	480,1101
D₆.D₁₀⋊₃C₂ = D₂₀⋊₁₄D₆	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	120	8+	D6.D10:3C2	480,1102
D₆.D₁₀⋊₄C₂ = D₁₂⋊₁₄D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	120	8+	D6.D10:4C2	480,1103
D₆.D₁₀⋊₅C₂ = D₂₀.₂₉D₆	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	240	8-	D6.D10:5C2	480,1104
D₆.D₁₀⋊₆C₂ = C₃₀.₃₃C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	240	8+	D6.D10:6C2	480,1105
D₆.D₁₀⋊₇C₂ = D₁₂.₂₉D₁₀	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	240	8-	D6.D10:7C2	480,1106
D₆.D₁₀⋊₈C₂ = D₂₀⋊₁₇D₆	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	120	8+	D6.D10:8C2	480,1111
D₆.D₁₀⋊₉C₂ = D₅×C₄○D₁₂	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	120	4	D6.D10:9C2	480,1090
D₆.D₁₀⋊₁₀C₂ = S₃×C₄○D₂₀	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	120	4	D6.D10:10C2	480,1091
D₆.D₁₀⋊₁₁C₂ = D₂₀⋊₂₄D₆	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	120	4	D6.D10:11C2	480,1092

Non-split extensions G=N.Q with N=D₆.D₁₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
D₆.D₁₀.₁C₂ = C₄₀.₃₄D₆	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	240	4	D6.D10.1C2	480,342
D₆.D₁₀.₂C₂ = C₄₀.₅₅D₆	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	240	4	D6.D10.2C2	480,343
D₆.D₁₀.₃C₂ = C₄₀.₃₅D₆	φ: C₂/C₁ → C₂ ⊆ Out D₆.D₁₀	240	4	D6.D10.3C2	480,344
D₆.D₁₀.₄C₂ = C₄₀.₅₄D₆	φ: trivial image	240	4	D6.D10.4C2	480,341

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁