  Schur multiplier $M(G)$ of a finite group $G$ has been studied heavily. To
proceed further to the study of projective (or spin) representations of $G$ and
their characters (called spin characters), it is necessary to construct
explicitly a representation group $R(G)$ of $G$, a certain central extension of
$G$ by $M(G)$, since projective representations of $G$ correspond bijectively
to linear representations of $R(G)$. We propose here a practical method to
construct $R(G)$ by repetition of one-step efficient central extensions
according to a certain choice of a series of elements of $M(G)$. This method is
also helpful for constructing linear representations of $R(G)$ and accordingly
for calculating spin characters. Actually, we will apply this method to several
examples of $G$ with prime number 3 in $M(G)$.
