Extensions 1→N→G→Q→1 with N=C₂³×C₁₀ and Q=S₃

Direct product G=N×Q with N=C₂³×C₁₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₂³×C₁₀		240		S3xC2^3xC10	480,1211

Semidirect products G=N:Q with N=C₂³×C₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₁₀)⋊₁S₃ = C₅×A₄⋊D₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³×C₁₀	60	6	(C2^3xC10):1S3	480,1023
(C₂³×C₁₀)⋊₂S₃ = C₂×C₁₀×S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³×C₁₀	60		(C2^3xC10):2S3	480,1198
(C₂³×C₁₀)⋊₃S₃ = C₅×C₂²⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³×C₁₀	40	6	(C2^3xC10):3S3	480,1200
(C₂³×C₁₀)⋊₄S₃ = C₂⁴⋊₂D₁₅	φ: S₃/C₁ → S₃ ⊆ Aut C₂³×C₁₀	60	6	(C2^3xC10):4S3	480,1034
(C₂³×C₁₀)⋊₅S₃ = C₂²×C₅⋊S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³×C₁₀	60		(C2^3xC10):5S3	480,1199
(C₂³×C₁₀)⋊₆S₃ = C₂⁴⋊₄D₁₅	φ: S₃/C₁ → S₃ ⊆ Aut C₂³×C₁₀	40	6	(C2^3xC10):6S3	480,1201
(C₂³×C₁₀)⋊₇S₃ = C₅×C₂⁴⋊₄S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂³×C₁₀	120		(C2^3xC10):7S3	480,832
(C₂³×C₁₀)⋊₈S₃ = C₂×C₁₀×C₃⋊D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³×C₁₀	240		(C2^3xC10):8S3	480,1164
(C₂³×C₁₀)⋊₉S₃ = C₂⁴⋊₅D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂³×C₁₀	120		(C2^3xC10):9S3	480,918
(C₂³×C₁₀)⋊₁₀S₃ = C₂²×C₁₅⋊₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³×C₁₀	240		(C2^3xC10):10S3	480,1179
(C₂³×C₁₀)⋊₁₁S₃ = C₂⁴×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂³×C₁₀	240		(C2^3xC10):11S3	480,1212

Non-split extensions G=N.Q with N=C₂³×C₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³×C₁₀).₁S₃ = C₁₀×A₄⋊C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³×C₁₀	120		(C2^3xC10).1S3	480,1022
(C₂³×C₁₀).₂S₃ = C₂×A₄⋊Dic₅	φ: S₃/C₁ → S₃ ⊆ Aut C₂³×C₁₀	120		(C2^3xC10).2S3	480,1033
(C₂³×C₁₀).₃S₃ = C₁₀×C₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³×C₁₀	240		(C2^3xC10).3S3	480,831
(C₂³×C₁₀).₄S₃ = C₂×C₃₀.₃₈D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³×C₁₀	240		(C2^3xC10).4S3	480,917
(C₂³×C₁₀).₅S₃ = C₂³×Dic₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂³×C₁₀	480		(C2^3xC10).5S3	480,1178
(C₂³×C₁₀).₆S₃ = Dic₃×C₂²×C₁₀	central extension (φ=1)	480		(C2^3xC10).6S3	480,1163

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