I agree entirely with you that you didn't know the most rudimental aspects of Nazism and fascism as they were based on purely national chauvinism, that opportunistically clothes itself in nationalist rhetoric much like American exceptionalism, in a mishmash convenient towards that and only that end where, the ends justifies the means, without a international character as does socialism.
The first Nazism being the artificial construct that was devised by a paid agent of the German military high commend, much like the political parties of Europe and Japan which financed and reestablished through the assistance of the US Army as a bulwark during what become the Cold War that they launched against the Soviet Union as otherwise they were defeated in Europe at the end of World War II.
There are several forms of fascists, Nazism, and Neo-Nazism being only three categories. But consistently throughout analysis they all exhibit extreme forms of national chauvinism which would be the forms described in what preceded the official use of the name "fascist" that arose with its introduction by the Mussolini fascists of Italy.
Though there is some argument relating to this matter as it regards socialists and even anarchists real socialist bases what they premise philosophically on nationalism rather than socialism.
As the main error of the Second International during World War I was that they sided as revisionists with their respective countries rather than the working class. As did many used their socialist labels so as to bind workers to reformist forms of capitalism (Great Society of Lyndon Johnson) and split the working class.