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 S<sub>6</sub> (which exist for no other S<sub>n</sub>), and the existence of non-standard differentiable structures on R<sup>4</sup> (but for no other R<sup>n</sup>).