Summary: Character theory of finite groups have an important role in understanding the structure of finite groups. A number of previously unresolved problems related to the structure of finite groups have been solved with the development of representation and character theory. There are many articles in the literature on the relationships between the structure of finite groups and their irreducible characters. Today, many researchers continue to study these relationships. Our purpose in this paper is to prove that for determining some properties of the structure of a finite group \(G\), it is enough to consider only strongly monolithic characters of \(G\) instead of all irreducible characters of \(G\). We give relationships between the structure of \(G\) and the vanishing elements, co-degrees of strongly monolithic characters of \(G\).