Extensions 1→N→G→Q→1 with N=C₆₀ and Q=S₃

Direct product G=N×Q with N=C₆₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₆₀		120	2	S3xC60	360,96

Semidirect products G=N:Q with N=C₆₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₀⋊₁S₃ = C₆₀⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	180		C60:1S3	360,112
C₆₀⋊₂S₃ = C₄×C₃⋊D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	180		C60:2S3	360,111
C₆₀⋊₃S₃ = C₃×D₆₀	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	120	2	C60:3S3	360,102
C₆₀⋊₄S₃ = C₅×C₁₂⋊S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	180		C60:4S3	360,107
C₆₀⋊₅S₃ = C₁₂×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	120	2	C60:5S3	360,101
C₆₀⋊₆S₃ = C₃⋊S₃×C₂₀	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	180		C60:6S3	360,106
C₆₀⋊₇S₃ = C₁₅×D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	120	2	C60:7S3	360,97

Non-split extensions G=N.Q with N=C₆₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆₀.₁S₃ = Dic₉₀	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	360	2-	C60.1S3	360,25
C₆₀.₂S₃ = D₁₈₀	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	180	2+	C60.2S3	360,27
C₆₀.₃S₃ = C₁₂.D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	360		C60.3S3	360,110
C₆₀.₄S₃ = C₄₅⋊₃C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	360	2	C60.4S3	360,3
C₆₀.₅S₃ = C₄×D₄₅	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	180	2	C60.5S3	360,26
C₆₀.₆S₃ = C₆₀.S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	360		C60.6S3	360,37
C₆₀.₇S₃ = C₃×Dic₃₀	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	120	2	C60.7S3	360,100
C₆₀.₈S₃ = C₅×Dic₁₈	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	360	2	C60.8S3	360,20
C₆₀.₉S₃ = C₅×D₃₆	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	180	2	C60.9S3	360,22
C₆₀.₁₀S₃ = C₅×C₃²⋊₄Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	360		C60.10S3	360,105
C₆₀.₁₁S₃ = C₃×C₁₅⋊₃C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	120	2	C60.11S3	360,35
C₆₀.₁₂S₃ = C₅×C₉⋊C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	360	2	C60.12S3	360,1
C₆₀.₁₃S₃ = D₉×C₂₀	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	180	2	C60.13S3	360,21
C₆₀.₁₄S₃ = C₅×C₃²⋊₄C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	360		C60.14S3	360,36
C₆₀.₁₅S₃ = C₁₅×Dic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₆₀	120	2	C60.15S3	360,95
C₆₀.₁₆S₃ = C₁₅×C₃⋊C₈	central extension (φ=1)	120	2	C60.16S3	360,34

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