Extremely strong Shoda pairs with GAP

We provide algorithms to compute a complete irredundant set of extremely strong Shoda pairs of a finite group G and the set of primitive central idempotents of the rational group algebra 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 primitive central idempotents of Q[G] realized by them. Another algorithm to check whether a finite group G is normally monomial or not is also described.