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  "body": "\n## Summary\n\nThe character table of a finite group lists the values of its irreducible complex [[characters|RMWMYBY8TC]] on its [[conjugacy classes|0DEBXAJ5SA]].\nIt is a square matrix, because the number of irreducible characters equals the number of conjugacy classes.\nMuch information about the group can be read from it, such as its order, its normal subgroups and whether it is simple or abelian.\n\n## Explanations\n\n### L1 human\n\nA character table is a compact summary of all the ways a finite group can act by matrices.\nEach row belongs to one irreducible representation, each column to one class of conjugate elements, and each entry is a trace.\nFor the cyclic group of order $2$ the table has rows $(1, 1)$ and $(1, -1)$.\nChemists use character tables of symmetry groups of molecules to classify vibrations and orbitals.\n",
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