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Groups and FieldsHardConjugacy and the Class Equation

Conjugacy and the Class Equation · Hard problem

A nonabelian group of order 21=3⋅721 = 3 \cdot 7 has class equation 21=1+3+3+7+721 = 1 + 3 + 3 + 7 + 7 (one central element and four noncentral classes). How many elements of order 33 does such a group have?