  Let $G$ be a finite solvable group. Then $G$ always has a useful
presentation, which we call a "long presentation". Using a "long presentation"
of $G$, we present an inductive method of constructing the irreducible
representations of $G$ over $\mathbb{C}$ and computing the primitive central
idempotents of the complex group algebra $\mathbb{C}[G]$. For a finite abelian
group, we present a systematic method of constructing the irreducible
representations over a field of characteristic either $0$ or prime to order of
the group and also a systematic method of computing the primitive central
idempotents of the semisimple abelian group algebra.
