Extensions 1→N→G→Q→1 with N=C₅ and Q=S₃×C₁₀

Direct product G=N×Q with N=C₅ and Q=S₃×C₁₀

		d	ρ	Label	ID
S₃×C₅×C₁₀		150		S3xC5xC10	300,46

Semidirect products G=N:Q with N=C₅ and Q=S₃×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(S₃×C₁₀) = C₅×S₃×D₅	φ: S₃×C₁₀/C₅×S₃ → C₂ ⊆ Aut C₅	30	4	C5:1(S3xC10)	300,37
C₅⋊₂(S₃×C₁₀) = C₁₀×D₁₅	φ: S₃×C₁₀/C₃₀ → C₂ ⊆ Aut C₅	60	2	C5:2(S3xC10)	300,47

Non-split extensions G=N.Q with N=C₅ and Q=S₃×C₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(S₃×C₁₀) = S₃×C₅₀	central extension (φ=1)	150	2	C5.(S3xC10)	300,10

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Extensions 1→N→G→Q→1 with N=C5 and Q=S3×C10