Erdogan is clearly using the coup attempt to attack anyone he sees as a nuisance. The fact that all this is so immediate, does strengthen the hypothesis that the entire thing was staged. I'm usually quite skeptical towards allegations of false flag operations, but if this isn't one, Erdogan isn't doing a lot to make it clear that it isn't one.
The last thing I'd want to do in life is to sound like an Erdoğan apologist but this isn't true at all.
Erdoğan and the government has been ongoing a major crackdown on Gülenists in governmental institutions and other powerful positions for a while now. They have basically an entire list that covers just about every Gülenist there is. -Which shouldn't be surprise, because they're the ones that put Gülenists in those positions when they were allied together- Laying off civil servants from their jobs, forcing every dean and department president at unis to do a purge would probably be too radical of a move, even for Erdoğan. What is going is that the coup attempt gave them an incentive to be even harsher in their purges.
The arrests and lay offs might look out of nowhere for an outsider, but it hardly is for someone who's been following the conflict between Erdoğan and Gülen closely. According to reports so far, there's been nobody aside from a Gülenist affiliation that's been arrested or let go. -Erdoğan and AKP aren't really targeting anyone else anyway, their speeches have strictly been anti-Gülenist and not anti-opposition. The bans are more of a precautionary measure, to make sure Gülenists don't flee the country. -They have done so in the past, on the day of the coup 8 pro-coup officials fled to Greece, for example-
The nature of the coup attempt has very little to suggest that this was a false flag. I highly doubt Erdoğan would bomb the Parliament with not one but two of his ministers inside. It's probably more like the National Intelligence Service finding out that a coup attempt was supposed to happen, informing the officials to go into defense mode and the government having some time to prepare for the aftermath.
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Also worthy of adding: After the coup there has been a strong sense of solidarity in the Parliament. There hadn't been a single case where all parties of the parliament came together as one, until this one. The coup has been condemned unanimously by Islamist AKP, social democratic CHP, ultra-nationalist MHP and pro-Kurdish HDP. There has really been no opposition to the crackdown on Gülenists, either.