Extensions 1→N→G→Q→1 with N=C₅₀ and Q=D₅

Direct product G=N×Q with N=C₅₀ and Q=D₅

		d	ρ	Label	ID
D₅×C₅₀		100	2	D5xC50	500,29

Semidirect products G=N:Q with N=C₅₀ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀⋊D₅ = C₂×C₂₅⋊D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅₀	250		C50:D5	500,32

Non-split extensions G=N.Q with N=C₅₀ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀.₁D₅ = Dic₁₂₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅₀	500	2-	C50.1D5	500,1
C₅₀.₂D₅ = D₂₅₀	φ: D₅/C₅ → C₂ ⊆ Aut C₅₀	250	2+	C50.2D5	500,4
C₅₀.₃D₅ = C₅₀.D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅₀	500		C50.3D5	500,10
C₅₀.₄D₅ = Dic₅×C₂₅	central extension (φ=1)	100	2	C50.4D5	500,7

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Extensions 1→N→G→Q→1 with N=C50 and Q=D5