Yes, the Astral is the big high-tech capital class carrier. Like any ship you can can hop into the captain's chair if it's on your side. You get one in the Coral Nebula mission, and I guess could get one in the random battles.
It is, in my opinion at least, less fun to pilot than most other ships, just because it's big, slow, fragile compared to anything comparable, and way under gunned compared to anything comparable. That and the mission where you get it puts you up against a bunch of pretty tough cruisers that it can't really go toe to toe with. It's still pretty awesome of course, I'd just rather be driving something zippier instead.