Extensions 1→N→G→Q→1 with N=C₅₀ and Q=S₃

Direct product G=N×Q with N=C₅₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₅₀		150	2	S3xC50	300,10

Semidirect products G=N:Q with N=C₅₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀⋊S₃ = D₁₅₀	φ: S₃/C₃ → C₂ ⊆ Aut C₅₀	150	2+	C50:S3	300,11

Non-split extensions G=N.Q with N=C₅₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₀.S₃ = Dic₇₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅₀	300	2-	C50.S3	300,3
C₅₀.₂S₃ = Dic₃×C₂₅	central extension (φ=1)	300	2	C50.2S3	300,1

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Extensions 1→N→G→Q→1 with N=C50 and Q=S3