While there is a great deal of economical resemblance between Hitler's fascism and Stalin's communism, these two share little commonality socially, in term of separation of church and state. On the other hand, the kind of fascism run by Mussolini is at the extreme opposite end to communism both socially and economically.
Fascism really doesn't have one definition but in general it is an authoritarian government that is very rigid in hierarchy and extrememly nationalistic. Fascist governments aren't really about government working for the community but they are always tied to populist-type dogma. Keep in mind also that true communism means an eventual erosion of the state after the working class has been empowered. Obviously this has not and will not happen in the real world so communist regimes have become fascistic or, if you prefer a more general term, authoritarian. Stalin and Mao were about as communist as Hitler was republican.
I wouldn't necessarily equate being Left or Right politically with being liberal or conservative. For instance while Nazi Germany was about as Right as you could get it practiced many liberal economic policies. While at the same time a Leftist state like North Korea acts very conservative. My understanding is generally politically Right means more nationalistic and focussed on one's country and prevailing social order whereas Left means more focussed on a wider society beyond one's country and challenging prevailing social orders. So while Fascism was Right in that it expressed extreme nationalism it also pushed very radical economic and social change to build up Germany and Italy.
Your political compass Economic Left/Right: -2.00 Social Libertarian/Authoritarian: -2.36 as I have said before...contrary to some claims that moderates are just people who are afraid to say what they stand for....we do exist.
From Dictionary.com LEFT: The people and groups who advocate liberal, often radical measures to effect change in the established order, especially in politics, usually to achieve the equality, freedom, and well-being of the common citizens of a state. Also called left wing. RIGHT: The people and groups who advocate the adoption of conservative or reactionary measures, especially in government and politics. Also called right wing. not very helpful Rocket RIver . . why am I listening to the MUZAK version of 'I like the way you Move' by OutKast
Your political compass Economic Left/Right: 4.00 Social Libertarian/Authoritarian: -1.90 The only example they have in the same quadrant as me is Friedman.