Let's say... about a hundred ships, varied.

And because of that, let's say that they were sucked into a tear-thingy-majig when moving to scout/settle/attack a bandit-occupied system, and ended up in the Milky Way? That way there is Draconian tech and ships, but it's not all entirely military.

Let's say... 4 Carriers, with 4 flights of fighters [and one flight of bombers] each, with, say, 12 Frigates, 8 Destroyers, and 4 Cruisers. If this is an unusually high number, then keep in mind that unless they capture other, already-established shipyards with mines and other resource input, then that's all they will have for quite a few years. The rest are colony ships, prefab-settlement deployments, cargo ships, mining ships, probe-launchers, etc.