Computing matrix representations

Dabbaghian, Vahid; Dixon, John

doi:10.1090/S0025-5718-10-02330-6

Computing matrix representations
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by Vahid Dabbaghian and John D. Dixon;

Math. Comp. 79 (2010), 1801-1810

DOI: https://doi.org/10.1090/S0025-5718-10-02330-6

Published electronically: January 12, 2010

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Abstract:

Let $G$ be a finite group and $\chi$ a faithful irreducible character for $G$. Earlier papers by the first author describe techniques for computing a matrix representation for $G$ which affords $\chi$ whenever the degree $\chi (1)$ is less than $32$. In the present paper we introduce a new, fast method which can be applied in the important case where $G$ is perfect and the socle $soc(G/Z(G))$ of $G$ over its centre is abelian. In particular, this enables us to extend the general construction of representations to all cases where $\chi (1)\leq 100$. The improved algorithms have been implemented in the new version 3.0.1 of the GAP package REPSN by the first author.

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