generalship

noun

1. The position or office of a general.
2. The term of office of a military general.

   “George Washington's generalship was marked by both amazing victories and stunning blunders, neither of which would have happened to someone with more formal officer training.”

3. The skills or performance of a good general; military leadership, strategy.

   “General Polk stated, with all respect to General Bragg’s great abilities in the direction of organization and discipline, that he had been wanting in the higher elements of generalship in the conduct of the campaign; […]”

   “At the same time, awed by the brilliant and daring generalship which had enabled the Russian to capture their city with so small a force, the elders gave him the honorific title of ‘Lion of Tashkent’.”

   “Virtually the whole of the region fell to Saxe's ingenious generalship.”

4. By extension, leadership, good management.

   “Under my generalship my fine troop of brats picked up every scrap of litter in that lot.”