In the wild cardinals will school, but I would not expect that type of behavior in a tank that size. Mutlipe females may stick together or at least leave each other alone, but larger older females may be aggressvie towards each other. Males will most likely fight till someone dies. My juvi's school together until about 5 months old, then they have a tendency to go solo.
fwiw, it's going to be somewhat difficult to recreat what you are looking for with only a 150g tank. Most schooling species require sufficient room or they'll loose that behavoir, even with chromis.
I've heard you can keep smaller aggregates of blue assessors, mostly females from my understanding, or even a few yellow wrasses.