Colloquially, this is what everyone understands when using the term fascist, but it's not quite in line with the history. 'Fascism' is a pejorative dog whistle, when people hear it they think "enemy" - because in WWII the Italian and German governments were fascist.

In fact, fascism, as I understand it, developed as a "third way" on the European continent. It was a rejection of capitalism as dominated by wealthy US, English interests, and of Communism. It's interesting that it developed in an area of Europe geographically juxtaposed in the middle of two powerful capitalist and communist fronts. Fascism was a reaction to domination by foreign power - so yes, naturally it's nationalistic. It also has a component of strong integration of nation and economy. The fasces is a binding together, metaphorically a combination of social, political, and economic institutions. Initially, it was an attempt to strengthen the nation, to reclaim power over the national destiny, and make good for the people of that country.

Of course, in hind site, we can see that some truly awful deeds were committed by some truly awful people, and we should be vigilant to prevent that from happening again. Unfortunately, it's a hard thing to predict, and even harder to prevent. It of course becomes harder if the name of fascism is misused in partisan political contexts because the nuance and history of the term is quickly lost.