From what I understand, the word fascism is one the vaguest of terms in modern political terminology and there is no universally excepted definition. I believe fascism to be akin to a secular religion. I see fascism as a sister movement to progressivism. Socialism as a movement is international whereas fascism is a national movement similiar to socialism in many ways. Fascism is collectivist and seeks to move a nation towards an organic whole, in that sense it opposes individual rights and suborndinates them to the goals of the state. Fascism opposes free markets and supports state capitalism which is a form of socialism.
Although fascism has been commonly associated with the political right it has much more in common with the left if you consider what the left and right stand for in America. In America the right stands strong on individual liberty, free markets and limited government, all these things fascists oppose. The left in America are the hiers of the progressives, who seek to expand government powers, subjugate individual frreedom to group rights and tightly control the private sector, all these factors are supported by the fascists.