| Precise formulas and estimates for the number of finite p-groups up to isomorphism are known, but much less is known about the number of non-isomorphic character tables of such groups. Two character tables of finite groups are isomorphic if there exist a bijection for the irreducible characters and a bijection for the conjugacy classes that preserve all the character values. We give necessary and sufficient conditions for two finite groups to have isomorphic character tables. In the case of finite p-groups with derived subgroup of order p , we classify up to isomorphism their irreducible character tables, and estimate their number. The number of such character tables turns out to be considerably fewer than the corresponding number of groups. |
