Extensions 1→N→G→Q→1 with N=C₂²×C₁₀ and Q=S₃

Direct product G=N×Q with N=C₂²×C₁₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₂²×C₁₀		120		S3xC2^2xC10	240,206

Semidirect products G=N:Q with N=C₂²×C₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₁₀)⋊₁S₃ = C₁₀×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₁₀	30	3	(C2^2xC10):1S3	240,196
(C₂²×C₁₀)⋊₂S₃ = C₂×C₅⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₁₀	30	6+	(C2^2xC10):2S3	240,197
(C₂²×C₁₀)⋊₃S₃ = C₁₀×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₀	120		(C2^2xC10):3S3	240,174
(C₂²×C₁₀)⋊₄S₃ = C₂×C₁₅⋊₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₀	120		(C2^2xC10):4S3	240,184
(C₂²×C₁₀)⋊₅S₃ = C₂³×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₀	120		(C2^2xC10):5S3	240,207

Non-split extensions G=N.Q with N=C₂²×C₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₁₀).₁S₃ = C₅×A₄⋊C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₁₀	60	3	(C2^2xC10).1S3	240,104
(C₂²×C₁₀).₂S₃ = A₄⋊Dic₅	φ: S₃/C₁ → S₃ ⊆ Aut C₂²×C₁₀	60	6-	(C2^2xC10).2S3	240,107
(C₂²×C₁₀).₃S₃ = C₅×C₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₀	120		(C2^2xC10).3S3	240,64
(C₂²×C₁₀).₄S₃ = C₃₀.₃₈D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₀	120		(C2^2xC10).4S3	240,80
(C₂²×C₁₀).₅S₃ = C₂²×Dic₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂²×C₁₀	240		(C2^2xC10).5S3	240,183
(C₂²×C₁₀).₆S₃ = Dic₃×C₂×C₁₀	central extension (φ=1)	240		(C2^2xC10).6S3	240,173

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