The Exodus Fleet is composed of several ships, called homesteaders, including the Oxomoco and the Asteria, orbiting around a star. The system in question is Ex-Aeluon who gave it to them while humans were still GC refugees. The Aeluons saw no benefit in the system as it has no planets that could be colonized.
The Exodus fleet is part of the Diaspora. If has had previously frigid relations with the Martian population. By the time of the events of Record of a Spaceborn Few, relations have improved. The All Stories Festival invited members from across the diaspora to Mars to celebrate human heritage. Martian president Kevin Liu unveiled a memorial out of solidarity for the Exodans after the Oxocomo disaster.
Human spacer captains can check Exodan fleet feeds on the linkings for information on the state of the entire diaspora, as they often contain news from the all over the human territories and events.