A character table is a tool used in group theory, specifically in the study of finite groups. It is a table that displays information about the irreducible representations of a group, which are essential for understanding the group's structure and properties. Each row of the character table corresponds to an irreducible representation of the group, and each column corresponds to a conjugacy class of the group. The values in the table are the characters, which are functions that map group elements to complex numbers and provide information about how the irreducible representations transform under group operations. Character tables are used in many areas of mathematics and physics, such as in the classification of finite groups, the study of group representations, and in quantum mechanics.