What are examples of strikingly anomalous phenomena in mathematics, where just one or a rather small number of cases stand out because they don't fit a general pattern?

This is most interesting when the situation considered is very simple and basic, and where the exceptional cases are not merely the lowest-numbered ones.

For example, the outer automorphism of the symmetric group S₆ (which exists for no other S_n), and the existence of non-standard differentiable structures on ℝ⁴ (but no other ℝⁿ).