Obtaining representations from characters in GAP

Question

Given a character $\xi$ in GAP of degree $n$, is there a way to obtain a corresponding representation with this character in the form that for every group element (not just generators of the group) one obtains an $n \times n$-matrix?

Answer 1

You can use IrreducibleRepresentationsDixon(<group>,<character>), which will return a representation (over $\mathbb{C}$) as homomorphism.

Note that the method requires some random-based searching, so runtime can be inconsistent. Also the representation is not necessarily given over a minimal field, or in any particular nice way.