It is unknown if the Aurek Company designation existed in the Galactic Empire, prior to the reactivation of the 501st by the Empire of the Hand, but the unit had certainly existed for at least six years prior to the liberation of Kariek, and it continued to function as of the Outbound Flight mission in 22 ABY.
Before the Battle of Endor, most company-strength units in the Imperial Army and Stormtrooper Corps had consisted of around 150-200 troops divided into four platoons. Aurek Company, however, consisted of just forty men, divided into ten squads of four troopers each.
These component units were capable of extended commando missions on their own, using four-man shuttles and serving, for example, as commandos and bodyguards—two roles both performed by Unit Aurek-Seven when they were sent to escort Commander Chak Fel as the Imperial representative on Chaf Envoys journey to Outbound Flight.