It's very hard to estimate how large the public sector is. Low-ball estimates would put it at around 30% which is a tad more than most in the socialism-leaning Europe. That is when you only count enterprises that are officially state owned. If you loosen it up 50% or even 60% isn't unreasonable (check out work of Derek Scissors).

The communism vs fascism question is always though. Soviet Russia can easily be described as both communist and strongly fascistic.