Extensions 1→N→G→Q→1 with N=C₂₀ and Q=C₆

Direct product G=N×Q with N=C₂₀ and Q=C₆

		d	ρ	Label	ID
C₂×C₆₀		120		C2xC60	120,31

Semidirect products G=N:Q with N=C₂₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀⋊₁C₆ = C₃×D₂₀	φ: C₆/C₃ → C₂ ⊆ Aut C₂₀	60	2	C20:1C6	120,18
C₂₀⋊₂C₆ = D₅×C₁₂	φ: C₆/C₃ → C₂ ⊆ Aut C₂₀	60	2	C20:2C6	120,17
C₂₀⋊₃C₆ = D₄×C₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₂₀	60	2	C20:3C6	120,32

Non-split extensions G=N.Q with N=C₂₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁C₆ = C₃×Dic₁₀	φ: C₆/C₃ → C₂ ⊆ Aut C₂₀	120	2	C20.1C6	120,16
C₂₀.₂C₆ = C₃×C₅⋊₂C₈	φ: C₆/C₃ → C₂ ⊆ Aut C₂₀	120	2	C20.2C6	120,2
C₂₀.₃C₆ = Q₈×C₁₅	φ: C₆/C₃ → C₂ ⊆ Aut C₂₀	120	2	C20.3C6	120,33

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C20 and Q=C6