Did you know you can make a carrier with 108 assault fighters?
Because you can make a carrier with 108 assault fighters (36 x 3 = 108).
Here's a view from the shipyard:
So for 10 logistics points, you can field a fleet worth 216 logistics points. Put six of these together, and that's a total of 648(!!!) fighters. Good luck finding a force that can beat that. To make this ship, I did need a Dense +2 race, a Hyperion Shrinker boosted by Caverns, a +2 Military resource, a Labor Oracle (+4), Preparedness center (+2) and 3 other +1 military buildings, along with all the space-increasing techs, several +5% miniturization resources, and the -30% support modules mass tech (the carrier mass reduction tech does nothing right now). It's base cost is also in the range of 7000 production (the cost shown is after ship cost reduction techs are applied). But still, this ship is just the extreme end of the spectrum - lesser ships could still outclass nearly all opposition.
Unfortunately, the older save I made this on has all the races stuck in peace, so I can show any combat pictures/videos 
UPDATE:
I've managed to tech up to this supercarrier in a new game on the latest Beta 5 version, and unleashed it on some hapless pirates. Here's the video:
And here are some selected pictures:
To be fair, the Assault Fighter module had its mass increased from 25 to 70, making it significantly less overpowered relative to endgame weaponry, at least in terms of DPS. However, fighters still replenish faster, are harder to hit, and can split their fire between multiple targets. I'll be checking in on Beta 6 to see how things balance out.