It is the second ship from the left of all of the capital ship options. It is a special ability though and a point must be used to invest in the skill. Every capital ship gets a point to spend upon creation, so pick colonize as the first one .

I've only played through two small solo games, and don't have the game handy right now, but I do remember wormhole traversal to be a researchable tech.

I really enjoy SoaSE, and I have mixed feelings about the amount you have to learn about the game through trial-and-error. In general, I like games that don't spell out everything you need to know through the tutorials and game manual - sometimes it's fun the first few games to learn on your own. This is one place, however, where SoaSE falls just a little short, by leaving too many things for the player to learn on their own. These are definitely areas where solo campaign levels would have been a great addition - if only for the educational aspects of it.

Especially in the cases of "what are the different types of capital ships available, and why would I want to build an 'x' over a 'y'" questions, I did a lot of my learning at the end of solo games - when the CPU opponent is on the ropes, that's when I do some "playing" to see what higher levels of techs will accompilish (I still haven't reached the upper levels of tech yet), and especially, to kick the tires on the various larger support ships (and especially the capital ships), and to learn what kind of effort it takes to wipe out the pirates once and for all. It also gives me time to even sort out minor details like "wow, that's a neat glowing special-effect wrapped around my capital ship right now, but what is it and what does it mean? is it helping or hurting me?"

I usually build this type Cap Ship first and after researching it, set the automatic use of Colonize to Disable.

Too many times I've wondered into new systems for the Cap Ship to acquire a planet and use anti-matter instead of killing a Cruiser or two...

Once the system is clear I manually use the Colonize ability.

Actually, each race also has a special frigate (left-most in second row) that can colonize. It's cheaper than the cap ship!