Extensions 1→N→G→Q→1 with N=A₄×C₂₀ and Q=C₂

Direct product G=N×Q with N=A₄×C₂₀ and Q=C₂

		d	ρ	Label	ID
A₄×C₂×C₂₀		120		A4xC2xC20	480,1126

Semidirect products G=N:Q with N=A₄×C₂₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(A₄×C₂₀)⋊₁C₂ = C₂₀⋊S₄	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	60	6+	(A4xC20):1C2	480,1026
(A₄×C₂₀)⋊₂C₂ = C₄×C₅⋊S₄	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	60	6	(A4xC20):2C2	480,1025
(A₄×C₂₀)⋊₃C₂ = A₄×D₂₀	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	60	6+	(A4xC20):3C2	480,1037
(A₄×C₂₀)⋊₄C₂ = C₅×C₄⋊S₄	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	60	6	(A4xC20):4C2	480,1015
(A₄×C₂₀)⋊₅C₂ = C₄×D₅×A₄	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	60	6	(A4xC20):5C2	480,1036
(A₄×C₂₀)⋊₆C₂ = C₂₀×S₄	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	60	3	(A4xC20):6C2	480,1014
(A₄×C₂₀)⋊₇C₂ = C₅×D₄×A₄	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	60	6	(A4xC20):7C2	480,1127

Non-split extensions G=N.Q with N=A₄×C₂₀ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(A₄×C₂₀).₁C₂ = C₂₀.₁S₄	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	120	6-	(A4xC20).1C2	480,1024
(A₄×C₂₀).₂C₂ = C₂₀.S₄	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	120	6	(A4xC20).2C2	480,259
(A₄×C₂₀).₃C₂ = A₄×Dic₁₀	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	120	6-	(A4xC20).3C2	480,1035
(A₄×C₂₀).₄C₂ = C₅×A₄⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	120	6	(A4xC20).4C2	480,1013
(A₄×C₂₀).₅C₂ = A₄×C₅⋊₂C₈	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	120	6	(A4xC20).5C2	480,265
(A₄×C₂₀).₆C₂ = C₅×A₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	120	3	(A4xC20).6C2	480,255
(A₄×C₂₀).₇C₂ = C₅×Q₈×A₄	φ: C₂/C₁ → C₂ ⊆ Out A₄×C₂₀	120	6	(A4xC20).7C2	480,1129
(A₄×C₂₀).₈C₂ = A₄×C₄₀	φ: trivial image	120	3	(A4xC20).8C2	480,659

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