According to the Adeptus Terra, Alyrium is the capital system of the Alyria Sub-sector. This isn't true in any practical sense, given the regular infighting that occurs between the systems in the region. Alyrium is a matrilineal matriarchy, the maintenance of which was Alyrium's condition for peacefully joining the Imperium, and so long as the Tithe is met the Imperium doesn't seem to care.
Alyrium is also the largest human-inhabited star system in the region, with five inhabited worlds orbiting its three stars. There are also numerous industrial ventures throughout the system, and an extensive system defence fleet to patrol it all. This wealth and strong defence has made Alyrium the strongest system in the region, although their relative lack of warp drive technology or navigators meant that they were unable to launch decisive invasions of the other systems, restricting the frequent fighting to skirmishes.