Computing subgroups of bounded index in a finite group

Authors:
John J. Cannon;Derek F. Holt;Michael Slattery;Allan K. Steel
Affiliations:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia;Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom;Department of Mathematics, Statistics, and Computer Science, Marquette University, Milwaukee, WI 53201-1881, USA;School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
Venue:
Journal of Symbolic Computation
Year:
2005

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Abstract

We describe a practical algorithm for computing representatives of the conjugacy classes of subgroups up to a given index in a finite group. This algorithm has been implemented in Magma, and we present some performance statistics.