The Mothership: In the military sense, the hyperdreadnoughts, the directional Supremacy-class bases, and probably most of the other classes that qualify as The Battlestar, or just plain old carrier classes, and fleet carriers. Also their obvious civilian counterparts, the fleet carrier equivalents that ferry freighters and other civilian vessels around relativistically that don’t themselves have relativistic capability.
In a pure-mass sense, a large number of wandering city-ships, both Imperial and those used by nomadic species such as the londian, and in a specifically Imperial sense, the Empire Ships – essentially, flying city-states-cum-endless-parties whose job is to travel endlessly looped courses with one end in the Imperial Core passing through the hundreds of ecumenical colonies and exclaves out in the far reaches of the stargate plexus to keep the culture thoroughly mixed and stirred, and not turning into anything weird out there in the fringes.
And, of course, the Embassy Ships and the All Good Things skymalls, which are similar, except act as cultural bombs ambassadors to foreign star nations, where they turn up for memetic warfare goodwill visits, spreading intimidation peace and good will, their decadent ways happiness, propaganda cultural interchange, ethically bankrupt perversions of science technological advancement, and the wonders of hypercapitalist exploitation free trade and disobedience, insolence, selfishness, libertinism, etc., etc. actual freedom to everyone.