Extensions 1→N→G→Q→1 with N=C₃ and Q=S₃×C₂₀

Direct product G=N×Q with N=C₃ and Q=S₃×C₂₀

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

Semidirect products G=N:Q with N=C₃ and Q=S₃×C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(S₃×C₂₀) = C₅×C₆.D₆	φ: S₃×C₂₀/C₅×Dic₃ → C₂ ⊆ Aut C₃	60	4	C3:1(S3xC20)	360,73
C₃⋊₂(S₃×C₂₀) = C₃⋊S₃×C₂₀	φ: S₃×C₂₀/C₆₀ → C₂ ⊆ Aut C₃	180		C3:2(S3xC20)	360,106
C₃⋊₃(S₃×C₂₀) = C₅×S₃×Dic₃	φ: S₃×C₂₀/S₃×C₁₀ → C₂ ⊆ Aut C₃	120	4	C3:3(S3xC20)	360,72

Non-split extensions G=N.Q with N=C₃ and Q=S₃×C₂₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(S₃×C₂₀) = D₉×C₂₀	φ: S₃×C₂₀/C₆₀ → C₂ ⊆ Aut C₃	180	2	C3.(S3xC20)	360,21

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C3 and Q=S3×C20