Extensions 1→N→G→Q→1 with N=C₅²⋊₄Q₈ and Q=C₂

Direct product G=N×Q with N=C₅²⋊₄Q₈ and Q=C₂

		d	ρ	Label	ID
C₂×C₅²⋊₄Q₈		400		C2xC5^2:4Q8	400,191

Semidirect products G=N:Q with N=C₅²⋊₄Q₈ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₅²⋊₄Q₈⋊₁C₂ = C₄₀⋊₂D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	200		C5^2:4Q8:1C2	400,94
C₅²⋊₄Q₈⋊₂C₂ = C₅²⋊₃SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	80	4-	C5^2:4Q8:2C2	400,67
C₅²⋊₄Q₈⋊₃C₂ = C₅²⋊₈SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	200		C5^2:4Q8:3C2	400,104
C₅²⋊₄Q₈⋊₄C₂ = D₅×Dic₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	80	4-	C5^2:4Q8:4C2	400,163
C₅²⋊₄Q₈⋊₅C₂ = D₂₀⋊₅D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	80	4-	C5^2:4Q8:5C2	400,164
C₅²⋊₄Q₈⋊₆C₂ = C₂₀.D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	200		C5^2:4Q8:6C2	400,196
C₅²⋊₄Q₈⋊₇C₂ = Q₈×C₅⋊D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	200		C5^2:4Q8:7C2	400,197
C₅²⋊₄Q₈⋊₈C₂ = C₂₀.₅₀D₁₀	φ: trivial image	200		C5^2:4Q8:8C2	400,194

Non-split extensions G=N.Q with N=C₅²⋊₄Q₈ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
C₅²⋊₄Q₈.₁C₂ = C₄₀.D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	400		C5^2:4Q8.1C2	400,96
C₅²⋊₄Q₈.₂C₂ = C₅²⋊₃Q₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	80	4-	C5^2:4Q8.2C2	400,70
C₅²⋊₄Q₈.₃C₂ = C₅²⋊₇Q₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₅²⋊₄Q₈	400		C5^2:4Q8.3C2	400,106

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁