Extensions 1→N→G→Q→1 with N=Q₈⋊₂D₅ and Q=C₆

Direct product G=N×Q with N=Q₈⋊₂D₅ and Q=C₆

		d	ρ	Label	ID
C₆×Q₈⋊₂D₅		240		C6xQ8:2D5	480,1143

Semidirect products G=N:Q with N=Q₈⋊₂D₅ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊₂D₅⋊C₆ = SL₂(𝔽₃).₁₁D₁₀	φ: C₆/C₁ → C₆ ⊆ Out Q₈⋊₂D₅	80	4	Q8:2D5:C6	480,1040
Q₈⋊₂D₅⋊₂C₆ = C₂×Dic₅.A₄	φ: C₆/C₂ → C₃ ⊆ Out Q₈⋊₂D₅	160		Q8:2D5:2C6	480,1038
Q₈⋊₂D₅⋊₃C₆ = D₅×C₄.A₄	φ: C₆/C₂ → C₃ ⊆ Out Q₈⋊₂D₅	80	4	Q8:2D5:3C6	480,1042
Q₈⋊₂D₅⋊₄C₆ = C₃×D₄₀⋊C₂	φ: C₆/C₃ → C₂ ⊆ Out Q₈⋊₂D₅	120	4	Q8:2D5:4C6	480,707
Q₈⋊₂D₅⋊₅C₆ = C₃×SD₁₆⋊₃D₅	φ: C₆/C₃ → C₂ ⊆ Out Q₈⋊₂D₅	240	4	Q8:2D5:5C6	480,709
Q₈⋊₂D₅⋊₆C₆ = C₃×Q₈.D₁₀	φ: C₆/C₃ → C₂ ⊆ Out Q₈⋊₂D₅	240	4	Q8:2D5:6C6	480,712
Q₈⋊₂D₅⋊₇C₆ = C₃×Q₈.₁₀D₁₀	φ: C₆/C₃ → C₂ ⊆ Out Q₈⋊₂D₅	240	4	Q8:2D5:7C6	480,1144
Q₈⋊₂D₅⋊₈C₆ = C₃×D₄⋊₈D₁₀	φ: C₆/C₃ → C₂ ⊆ Out Q₈⋊₂D₅	120	4	Q8:2D5:8C6	480,1146
Q₈⋊₂D₅⋊₉C₆ = C₃×D₅×C₄○D₄	φ: trivial image	120	4	Q8:2D5:9C6	480,1145

Non-split extensions G=N.Q with N=Q₈⋊₂D₅ and Q=C₆

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊₂D₅.₁C₆ = Dic₁₀.A₄	φ: C₆/C₁ → C₆ ⊆ Out Q₈⋊₂D₅	120	4+	Q8:2D5.1C6	480,1041
Q₈⋊₂D₅.₂C₆ = SL₂(𝔽₃).F₅	φ: C₆/C₁ → C₆ ⊆ Out Q₈⋊₂D₅	160	8+	Q8:2D5.2C6	480,964
Q₈⋊₂D₅.₃C₆ = C₃×Q₁₆⋊D₅	φ: C₆/C₃ → C₂ ⊆ Out Q₈⋊₂D₅	240	4	Q8:2D5.3C6	480,711
Q₈⋊₂D₅.₄C₆ = C₃×Q₈⋊₂F₅	φ: C₆/C₃ → C₂ ⊆ Out Q₈⋊₂D₅	120	8	Q8:2D5.4C6	480,290
Q₈⋊₂D₅.₅C₆ = C₃×Q₈.F₅	φ: C₆/C₃ → C₂ ⊆ Out Q₈⋊₂D₅	240	8	Q8:2D5.5C6	480,1055

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁