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 $S_{6}$ (which exists for no other $S_{n}$), and the existence of non-standard differentiable structures on $\mathbb{R}^{4}$ (but no other $\mathbb{R}^{n}$).