During the events of Distemporal Blues, Drake, Siara and their fellows visited the planet; the Matriarch intended to kill them, but a Cloudan fleet attacked the satellite; in the ensuring chaos one of the slave soldiers freed the team and killed the Matriarch. Ultimately the remains of the empire collapsed but not before they could defeat the Cloudan forces.
The Matriarchy was a theocratic, feudalistic nation living under the reign of the Matriarch, an unnamed woman claimed to be a goddess. Their society was based on the dominance of the female gender, as in they were the only ones entitled for roles in politics and were also the leader of each family.
Rumors say Galarian women used supernatural techniques to seduce males, forcing them to keep women in a preferred position, and thus, stabilizing an otherwise fragile societal structure. This power can most likely be traced back to the Matriarch, as it was revealed during the fall.
The Galarian Matriarchy kept a cold war-like status with every human superpower, claiming they are “patriarchic dictatorships” - their only close ally were the Sun Serpents.