The number of nonlinear non-faithful irreducible character of p-group of maximal class
In This paper,we studied the number of nonlinear non-faithful irreducible characters of p-group G of maximal class,by using the properties of p-group of maximal class and character theory of finite groups.It is proved that the number of nonlinear non-faithful irreducible characters of p-group G of maximal class of order pn equal the number of nonlinear irreducible characters of p-group G/Z(G)of maximal class of order pn-1.In parti-cular,the properties of finite groups with exactly three nonlinear non-faithful irreducible characters are analyzed.
p-group of maximal classnonlinear irreducible characternon-faithful irreducible character
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