The Command Core is a Fleet's mobile Administration and Command Facility in times of War. This enables a Fleet to remain cohesive and reduces the chance of centralized command being severed. In peacetime, administration and command functions are done from a Fleet's Orbital Headquarters.
A single squadron of escorts and one Flagship is the entirety of the Command Core to reduce chance of notice. However, the Command Core often travels to systems with a large Abwehran military presence in order to reduce the chances of it being taken out.