Extensions 1→N→G→Q→1 with N=C₅₀ and Q=C₁₀

Direct product G=N×Q with N=C₅₀ and Q=C₁₀

		d	ρ	Label	ID
C₁₀×C₅₀		500		C10xC50	500,34

Semidirect products G=N:Q with N=C₅₀ and Q=C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀⋊C₁₀ = C₂×C₂₅⋊C₁₀	φ: C₁₀/C₁ → C₁₀ ⊆ Aut C₅₀	50	10+	C50:C10	500,31
C₅₀⋊₂C₁₀ = C₂²×5_-¹⁺²	φ: C₁₀/C₂ → C₅ ⊆ Aut C₅₀	100		C50:2C10	500,36
C₅₀⋊₃C₁₀ = C₁₀×D₂₅	φ: C₁₀/C₅ → C₂ ⊆ Aut C₅₀	100	2	C50:3C10	500,28

Non-split extensions G=N.Q with N=C₅₀ and Q=C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀.C₁₀ = C₅₀.C₁₀	φ: C₁₀/C₁ → C₁₀ ⊆ Aut C₅₀	100	10-	C50.C10	500,9
C₅₀.₂C₁₀ = C₄×5_-¹⁺²	φ: C₁₀/C₂ → C₅ ⊆ Aut C₅₀	100	5	C50.2C10	500,14
C₅₀.₃C₁₀ = C₅×Dic₂₅	φ: C₁₀/C₅ → C₂ ⊆ Aut C₅₀	100	2	C50.3C10	500,6

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Extensions 1→N→G→Q→1 with N=C50 and Q=C10