Extensions 1→N→G→Q→1 with N=C₂×C₁₀ and Q=S₄

Direct product G=N×Q with N=C₂×C₁₀ and Q=S₄

		d	ρ	Label	ID
C₂×C₁₀×S₄		60		C2xC10xS4	480,1198

Semidirect products G=N:Q with N=C₂×C₁₀ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀)⋊₁S₄ = C₅×C₂²⋊S₄	φ: S₄/C₂² → S₃ ⊆ Aut C₂×C₁₀	40	6	(C2xC10):1S4	480,1200
(C₂×C₁₀)⋊₂S₄ = C₂⁴⋊₄D₁₅	φ: S₄/C₂² → S₃ ⊆ Aut C₂×C₁₀	40	6	(C2xC10):2S4	480,1201
(C₂×C₁₀)⋊₃S₄ = C₅×A₄⋊D₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂×C₁₀	60	6	(C2xC10):3S4	480,1023
(C₂×C₁₀)⋊₄S₄ = C₂⁴⋊₂D₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂×C₁₀	60	6	(C2xC10):4S4	480,1034
(C₂×C₁₀)⋊₅S₄ = C₂²×C₅⋊S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂×C₁₀	60		(C2xC10):5S4	480,1199

Non-split extensions G=N.Q with N=C₂×C₁₀ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀).₁S₄ = C₅×C₄²⋊S₃	φ: S₄/C₂² → S₃ ⊆ Aut C₂×C₁₀	60	3	(C2xC10).1S4	480,254
(C₂×C₁₀).₂S₄ = C₄²⋊D₁₅	φ: S₄/C₂² → S₃ ⊆ Aut C₂×C₁₀	60	6+	(C2xC10).2S4	480,258
(C₂×C₁₀).₃S₄ = C₅×Q₈.D₆	φ: S₄/A₄ → C₂ ⊆ Aut C₂×C₁₀	80	4	(C2xC10).3S4	480,1018
(C₂×C₁₀).₄S₄ = Q₈⋊Dic₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂×C₁₀	160		(C2xC10).4S4	480,260
(C₂×C₁₀).₅S₄ = C₂×Q₈.D₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂×C₁₀	160		(C2xC10).5S4	480,1027
(C₂×C₁₀).₆S₄ = C₂×Q₈⋊D₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10).6S4	480,1028
(C₂×C₁₀).₇S₄ = Q₈.D₃₀	φ: S₄/A₄ → C₂ ⊆ Aut C₂×C₁₀	80	4	(C2xC10).7S4	480,1029
(C₂×C₁₀).₈S₄ = C₂×A₄⋊Dic₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂×C₁₀	120		(C2xC10).8S4	480,1033
(C₂×C₁₀).₉S₄ = C₅×Q₈⋊Dic₃	central extension (φ=1)	160		(C2xC10).9S4	480,256
(C₂×C₁₀).₁₀S₄ = C₁₀×CSU₂(𝔽₃)	central extension (φ=1)	160		(C2xC10).10S4	480,1016
(C₂×C₁₀).₁₁S₄ = C₁₀×GL₂(𝔽₃)	central extension (φ=1)	80		(C2xC10).11S4	480,1017
(C₂×C₁₀).₁₂S₄ = C₁₀×A₄⋊C₄	central extension (φ=1)	120		(C2xC10).12S4	480,1022

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