  We provide algorithms to compute a complete irredundant set of extremely
strong Shoda pairs of a finite group $G$ and the set of the primitive central
idempotents of the rational group algebra $\mathbb{Q}[G]$ realized by them.
These algorithms are also extended to write new algorithms for computing a
complete irredundant set of strong Shoda pairs of $G$ and the set of the
primitive central idempotents of $\mathbb{Q}[G]$ realized by them. Another
algorithm to check whether a finite group $G$ is normally monomial or not is
also described.
