A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is constant on a conjugacy class. Hence, the values of the characters can be written as an array, known as a character table. Typically, the rows are given by the irreducible representations and the columns are given the conjugacy classes. A character table often contains enough information to identify a given abstract group and distinguish it from others. However, there exist nonisomorphic groups which nevertheless have the same character table, for example D_4 (the symmetry group of the square) and Q_8 (the quaternion group).

conjugacy class | group | group character | group representation | irreducible representation | point groups