The Artifical Slave Center is a Super Project just like the Hyperion Shrinker so each race is allowed to build one.
The ASC is kind of funky in that it's bonus is a hard coded 50% bonus to each planets *base* military production. What this means is that the ASC does more than just stack (i.e. is additive) it actually multiplies all other source of production bonus that you have.
Another aspect of this is that the benefit of the ASC is not shown in the Civilization Manager under your abilities as all other global bonuses are shown. The only real way to notice the effect is to see how much more military production each planet has when producing a ship versus social production when producing a building.
Regretably having two or more ASC's does nothing, you either get the 50% base production boost if you have one (or more) ASC's or you don't if you have none.