I briefly played around with that a while back. I eventually got it to work, as in show up in the game, by assigning the CAG commander 1 aircraft so there was an air class for the unit.
1 - Open the Guadalcanal scenario in the editor and save it in a slot below #25.
2 - Un-sink the Akagi (ship #017) and park it in Rabaul (base 990 something).
3 - Go to the air groups screen and find Akagi's groups, at slots 482-484.
4 - in blank slot 481 type CAG A1 in the name field, set it to formation 10, give it 1 Claude or something with a max size of 1 put it on the Akagi, and tick the boxes for CV trained, and air group.
---- I gave it nationality IJN, no HQ.
5. Go to each of the three squadrons and enter 481 in the parent field (or maybe you can just attach them in game anyway).
With a single button click you can transfer all three to Rabaul - but they stay attached to the group so it makes it easier to get them all back again.
None of this was mentioned in the manual, and having on occasion opened the other side of an AI game to look around, I have seen these groups, despite there being none in the scenario data.
I suspect the AI possibly gets to create these in-game to help it keep everything organised.
"You may find that having is not so nearly pleasing a thing as wanting. It is not logical, but it is often true."
- Cdr Spock