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Mathematics of Computation

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Computing matrix representations

Authors: Vahid Dabbaghian and John D. Dixon
Journal: Math. Comp. 79 (2010), 1801-1810
MSC (2010): Primary 20C40; Secondary 20C15
Published electronically: January 12, 2010
MathSciNet review: 2630014
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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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Additional Information

Vahid Dabbaghian
Affiliation: MoCSSy Program, The IRMACS Centre, Simon Fraser University, Burnaby, BC V5A 1S6, Canada

John D. Dixon
Affiliation: School of Mathematics and Statistics, Carleton Unversity, Ottawa, ON K1S 5B6, Canada

Received by editor(s): November 12, 2008
Received by editor(s) in revised form: July 16, 2009
Published electronically: January 12, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.