Colonial Capitals are XL sized ships that consist of Battlestars and Carrier support ships. The Battlestars are the last remaining Battlestars of the Twelve Colonies.
The Brimir is a Carrier class ship that can carry a number of Strike class ships and support them in combat.
The Carriers were reworked in June, 2014. The previous version of the Brimir can be found here:
Battlestar Pegasus can be commanded temporarily by asking Admiral Adama in exchange for a large sum of Merits.
Battlestar Galactica resides is Alpha Ceti in order to protect the vulnerable Colonial Fleet and can not be used in any way by players.