Mathematics, Department of


Date of this Version



Published in Proceedings of the Edinburgh Mathematical Society 43 (2000), pp 211-217.

doi 10.1017/S0013091500020824


Copyright 2000 Edinburgh Mathematical Society; published by Cambridge University Press. Used by permission.


An old question of Brauer asking how fast numbers of conjugacy classes grow is investigated by considering the least number cn of conjugacy classes in a group of order 2n. The numbers cn are computed for n ≤ 14 and a lower bound is given for c15. It is observed that cn grows very slowly except for occasional large jumps corresponding to an increase in coclass of the minimal groups Gn. Restricting to groups that are 2-generated or have coclass at most 3 allows us to extend these computations.