Alien management center is a colony structure in Master of Orion.
The Alien Management Centre is used to control the alien population of an occupied colony improving the assimilation rate.
If you have unassimilated populations, you will have an icon of an alien face with an asterisk (*) over it's head and a number. The number represents how many turns until the next assimilation.
Once all of the population have been assimilated, the Alien Management Centre disappears.