Command centers can only be built by factions as HQs, and I believe the CC is further restricted to paramilitary groups. The facility is not open for public construction, or even other faction construction.
The CC is a restricted one time use Facil as I remember when I was in the TF. You get awarded one once you reach a certain member level. ANd then one for every other level reached. If you cant build it, it means one of the following: 1.) you dont have enough people. 2.) Someone already used it (if someone built it even for themselves, you lost it) 3.) You dont have the privs to build it
Again this was years and years ago so it may have changed