We show an exponential gap between communication complexity and information complexity, by giving an explicit example for a communication task (relation), with information complexity O(k), and distributional communication complexity 2k. This shows that a communication protocol cannot always be compressed to its internal information. By a result of Braverman, our gap is the largest possible. By a result of Braverman and Rao, our example shows a gap between communication complexity and amortized communication complexity, implying that a tight direct sum result for distributional communication complexity cannot hold.