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The Group Theory term for what is known to physicists as the Trace. All members of the same Conjugacy Class in the same representation have the same character. Members of other Conjugacy Classes may also have the same character, however. An (abstract) Group can be uniquely identified by a listing of the characters of its various representations, known as a Character Table. Some of the Schönflies Symbols denote different sets of symmetry operations but correspond to the same abstract Group and so have the same Character Tables.