  It is well known that the adjacency algebra of an association scheme has the
standard character. In this paper we first define the concept of standard
character for C-algebras and we say that a C-algebra has the {\it standard
character condition} if it has the standard character. Then we investigate some
properties of C-algebras which have the standard character condition and prove
that under some conditions a C-algebra has an adjacency algebra homomorphic
image. In particular, we obtain a necessary and sufficient condition for which
a commutative table algebra comes from an association scheme.
