  Let $G=SL(2,5)$ be the special linear group of $2 \times 2$-matrices with
coefficients in the field with $5$ elements. We show that the principal block
over a splitting field $K$ of characteristic two of the group algebra $KG$ has
a $3$-cluster tilting module. This gives the first example of a
representation-infinite block of a group algebra having a cluster tilting
module and answers a question by Erdmann and Holm.
