The 1-, 2-, and 3-characters determine a group
  A set of invariants for a finite group is described. These arise naturally from Frobenius' early work on the group determinant and provide an answer to a question of Brauer. Whereas it is well known that the ordinary character table of a group does not determine the group uniquely, it is a consequence of the results presented here that a group is determined uniquely by its ``3-character'' table. 
Hans-J\"urgen Hoehnke, Kenneth W. Johnson