Extensions 1→N→G→Q→1 with N=C₂xC₁₀ and Q=S₄

Direct product G=NxQ with N=C₂xC₁₀ and Q=S₄

		d	ρ	Label	ID
C₂xC₁₀xS₄		60		C2xC10xS4	480,1198

Semidirect products G=N:Q with N=C₂xC₁₀ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₁₀):₁S₄ = C₅xC₂²:S₄	φ: S₄/C₂² → S₃ ⊆ Aut C₂xC₁₀	40	6	(C2xC10):1S4	480,1200
(C₂xC₁₀):₂S₄ = C₂⁴:₄D₁₅	φ: S₄/C₂² → S₃ ⊆ Aut C₂xC₁₀	40	6	(C2xC10):2S4	480,1201
(C₂xC₁₀):₃S₄ = C₅xA₄:D₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂xC₁₀	60	6	(C2xC10):3S4	480,1023
(C₂xC₁₀):₄S₄ = C₂⁴:₂D₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂xC₁₀	60	6	(C2xC10):4S4	480,1034
(C₂xC₁₀):₅S₄ = C₂²xC₅:S₄	φ: S₄/A₄ → C₂ ⊆ Aut C₂xC₁₀	60		(C2xC10):5S4	480,1199

Non-split extensions G=N.Q with N=C₂xC₁₀ and Q=S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₁₀).₁S₄ = C₅xC₄²:S₃	φ: S₄/C₂² → S₃ ⊆ Aut C₂xC₁₀	60	3	(C2xC10).1S4	480,254
(C₂xC₁₀).₂S₄ = C₄²:D₁₅	φ: S₄/C₂² → S₃ ⊆ Aut C₂xC₁₀	60	6+	(C2xC10).2S4	480,258
(C₂xC₁₀).₃S₄ = C₅xQ₈.D₆	φ: S₄/A₄ → C₂ ⊆ Aut C₂xC₁₀	80	4	(C2xC10).3S4	480,1018
(C₂xC₁₀).₄S₄ = Q₈:Dic₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂xC₁₀	160		(C2xC10).4S4	480,260
(C₂xC₁₀).₅S₄ = C₂xQ₈.D₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂xC₁₀	160		(C2xC10).5S4	480,1027
(C₂xC₁₀).₆S₄ = C₂xQ₈:D₁₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂xC₁₀	80		(C2xC10).6S4	480,1028
(C₂xC₁₀).₇S₄ = Q₈.D₃₀	φ: S₄/A₄ → C₂ ⊆ Aut C₂xC₁₀	80	4	(C2xC10).7S4	480,1029
(C₂xC₁₀).₈S₄ = C₂xA₄:Dic₅	φ: S₄/A₄ → C₂ ⊆ Aut C₂xC₁₀	120		(C2xC10).8S4	480,1033
(C₂xC₁₀).₉S₄ = C₅xQ₈:Dic₃	central extension (φ=1)	160		(C2xC10).9S4	480,256
(C₂xC₁₀).₁₀S₄ = C₁₀xCSU₂(F₃)	central extension (φ=1)	160		(C2xC10).10S4	480,1016
(C₂xC₁₀).₁₁S₄ = C₁₀xGL₂(F₃)	central extension (φ=1)	80		(C2xC10).11S4	480,1017
(C₂xC₁₀).₁₂S₄ = C₁₀xA₄:C₄	central extension (φ=1)	120		(C2xC10).12S4	480,1022

׿

x

:

Z

F

o

wr

Q

<