Libertarianism is where the government stays out of everything in economic, fiscal and social aspects. Communism is where the government has control over all social and economic aspect of peoples lives and there is no private property.
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the original french Libertarians were anarcho-communist types.
The american marketfetishists that stole the name think of the "free" market as the pinnacle of freedom.
Communists and most anarchists consider the market as bad and coercive as any living/breathing dictator.
However, communists are willing to sacrifice the state for the good of the people. Fascists are willing to sacrifice humans for the good of the nation.
So real opposite extreme of Communism depends on what spectrum you are looking at