1. A collective affinity for a strongman as opposed to a constitutional set of principles and a blind, apolitical respect for the Law.
2. A reliance on black propaganda or "hard" propaganda with a plethora of lies to shape public opinion.
3. A denial of class struggle as an imperative that can drive politics, while allowing corporate interests to define policy and the state. Thus, W. Bush had said at some time that America was a society "without classes", turning around to the Carlisle Group in a recorded meeting or rally to call them "My base -- the Haves and Have Mores".
4. Use of the state's institutions to serve the political party and the strongman.
5. Use of force to defeat a political opposition and pursue the will of the strongman.
6. A politics of division, defining an "Other" as an enemy of the state to mobilize a base.
In Chile after the assassination and fall of Salvador Allende, Pinochet became a fascist leader, whose crimes were only less than Hitler's because of the smaller number of people exterminated.
You don't need extermination camps or a Gestapo to define a fascist state, but one should worry about those aspects as a developing possibility.
Oddly, I don't think that Fascism and Communism are disjoint. They both fall under a more general category of Totalitarianism or Authoritarianism, and they can co-exist. An example of that would be the DPRK or North Korea.
After the Korean War, South Korea shed the influences of Imperial Japan -- which occupied Korea even before WWII. North Korea seemed to continue or adopt Japanese Fascism.