A cluster tilting module for a representation-infinite block of a group algebra

Abstract Let G = S L ( 2 , 5 ) be the special linear group of 2 × 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.