Extensions 1→N→G→Q→1 with N=D₅₀ and Q=C₄

Direct product G=N×Q with N=D₅₀ and Q=C₄

		d	ρ	Label	ID
C₂×C₄×D₂₅		200		C2xC4xD25	400,36

Semidirect products G=N:Q with N=D₅₀ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₀⋊₁C₄ = D₅₀⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out D₅₀	200		D50:1C4	400,14
D₅₀⋊₂C₄ = D₂₅.D₄	φ: C₄/C₂ → C₂ ⊆ Out D₅₀	100	4+	D50:2C4	400,34
D₅₀⋊₃C₄ = C₂²×C₂₅⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out D₅₀	100		D50:3C4	400,53

Non-split extensions G=N.Q with N=D₅₀ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₀.₁C₄ = C₈⋊D₂₅	φ: C₄/C₂ → C₂ ⊆ Out D₅₀	200	2	D50.1C4	400,6
D₅₀.₂C₄ = D₂₅⋊C₈	φ: C₄/C₂ → C₂ ⊆ Out D₅₀	200	4	D50.2C4	400,28
D₅₀.₃C₄ = C₁₀₀.C₄	φ: C₄/C₂ → C₂ ⊆ Out D₅₀	200	4	D50.3C4	400,29
D₅₀.₄C₄ = C₈×D₂₅	φ: trivial image	200	2	D50.4C4	400,5

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁