Extensions 1→N→G→Q→1 with N=D₄ and Q=C₅₀

Direct product G=N×Q with N=D₄ and Q=C₅₀

		d	ρ	Label	ID
D₄×C₅₀		200		D4xC50	400,46

Semidirect products G=N:Q with N=D₄ and Q=C₅₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊C₅₀ = D₈×C₂₅	φ: C₅₀/C₂₅ → C₂ ⊆ Out D₄	200	2	D4:C50	400,25
D₄⋊₂C₅₀ = C₄○D₄×C₂₅	φ: trivial image	200	2	D4:2C50	400,48

Non-split extensions G=N.Q with N=D₄ and Q=C₅₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.C₅₀ = SD₁₆×C₂₅	φ: C₅₀/C₂₅ → C₂ ⊆ Out D₄	200	2	D4.C50	400,26

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Extensions 1→N→G→Q→1 with N=D4 and Q=C50