Extensions 1→N→G→Q→1 with N=C₂₀ and Q=S₄

Direct product G=N×Q with N=C₂₀ and Q=S₄

		d	ρ	Label	ID
C₂₀×S₄		60	3	C20xS4	480,1014

Semidirect products G=N:Q with N=C₂₀ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀⋊₁S₄ = C₂₀⋊S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	60	6+	C20:1S4	480,1026
C₂₀⋊₂S₄ = C₄×C₅⋊S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	60	6	C20:2S4	480,1025
C₂₀⋊₃S₄ = C₅×C₄⋊S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	60	6	C20:3S4	480,1015

Non-split extensions G=N.Q with N=C₂₀ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁S₄ = C₂₀.₁S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	120	6-	C20.1S4	480,1024
C₂₀.₂S₄ = C₂₀.₂S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	160	4-	C20.2S4	480,1030
C₂₀.₃S₄ = C₂₀.₃S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	80	4+	C20.3S4	480,1032
C₂₀.₄S₄ = C₂₀.S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	120	6	C20.4S4	480,259
C₂₀.₅S₄ = C₅⋊₂U₂(𝔽₃)	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	120	4	C20.5S4	480,261
C₂₀.₆S₄ = C₂₀.₆S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	80	4	C20.6S4	480,1031
C₂₀.₇S₄ = C₅×A₄⋊Q₈	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	120	6	C20.7S4	480,1013
C₂₀.₈S₄ = C₅×C₄.S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	160	4	C20.8S4	480,1019
C₂₀.₉S₄ = C₅×C₄.₃S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂₀	80	4	C20.9S4	480,1021
C₂₀.₁₀S₄ = C₅×A₄⋊C₈	central extension (φ=1)	120	3	C20.10S4	480,255
C₂₀.₁₁S₄ = C₅×U₂(𝔽₃)	central extension (φ=1)	120	2	C20.11S4	480,257
C₂₀.₁₂S₄ = C₅×C₄.₆S₄	central extension (φ=1)	80	2	C20.12S4	480,1020

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁