Extensions 1→N→G→Q→1 with N=C₈₀ and Q=S₃

Direct product G=N×Q with N=C₈₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₈₀		240	2	S3xC80	480,116

Semidirect products G=N:Q with N=C₈₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₀⋊₁S₃ = D₂₄₀	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	240	2+	C80:1S3	480,159
C₈₀⋊₂S₃ = C₄₈⋊D₅	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:2S3	480,160
C₈₀⋊₃S₃ = C₅×D₄₈	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:3S3	480,118
C₈₀⋊₄S₃ = C₁₆×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:4S3	480,157
C₈₀⋊₅S₃ = C₈₀⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:5S3	480,158
C₈₀⋊₆S₃ = C₅×C₄₈⋊C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:6S3	480,119
C₈₀⋊₇S₃ = C₅×D₆.C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	240	2	C80:7S3	480,117

Non-split extensions G=N.Q with N=C₈₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₀.₁S₃ = Dic₁₂₀	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	480	2-	C80.1S3	480,161
C₈₀.₂S₃ = C₅×Dic₂₄	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	480	2	C80.2S3	480,120
C₈₀.₃S₃ = C₁₅⋊₃C₃₂	φ: S₃/C₃ → C₂ ⊆ Aut C₈₀	480	2	C80.3S3	480,3
C₈₀.₄S₃ = C₅×C₃⋊C₃₂	central extension (φ=1)	480	2	C80.4S3	480,1

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