Exactly -- a Left-wing fascist authoritarian regime, despite modern-day historical revisionism. The "fasci" were Italian Leftist unionists who made up the first fascist party. Mussolini -- a socialist writer before he entered politics -- considered "fascism" to be the "right" or "perfected" form of socialism, differing only from his earlier views in that it placed the good of the state paramount, rather than socialism's good of the people.
As for Hitler's party, they weren't called National Socialism for nothing: high taxes on the rich, powerful central government, strong labor unions, tight regulation of corporations, bans on firearm ownership, laws against "unfair" profits, nationalization of major industries, restrictions on free speech, expanded access to abortion, free higher education for college students, and a slavish desire to categorize people by race, not as individuals.