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Computing character tables of groups of type M.G.A

  • Thomas Breuer (a1)

Abstract

We describe a method for constructing the character table of a group of type M.G.A from the character tables of the subgroup M.G and the factor group G.A, provided that A acts suitably on M.G. This simplifies and generalizes a recently published method.

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References

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[1]An, J. and O’Brien, E. A., ‘Conjectures on the character degrees of the Harada–Norton simple group HN’, Israel J. Math. 137 (2003) 157181.
[2]Barraclough, R. W., ‘The character table of a group of the shape (2×2.G):2’, LMS J. Comput. Math. 13 (2010) 8289.
[3]Breuer, T., ‘The GAP character table library, version 1.1’, GAP package (2003) available fromhttp://www.math.rwth-aachen.de/∼Thomas.Breuer/ctbllib.
[4]Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A. and Wilson, R. A., Atlas of finite groups: maximal subgroups and ordinary characters for simple groups, with computational assistance from J. G. Thackray (Oxford University Press, Eynsham, 1985).
[5]Feit, W., The representation theory of finite groups, North-Holland Mathematical Library 25 (North-Holland, Amsterdam, 1982).
[6]Fischer, B., ‘Clifford-matrices’, Representation theory of finite groups and finite-dimensional algebras (Bielefeld, 1991), Progress in Mathematics 95 (Birkhäuser, Basel, 1991) 116.
[7]Gagola, S. M. Jr, ‘Formal character tables’, Michigan Math. J. 33 (1986) 310.
[8] The GAP group, ‘GAP–groups, algorithms, and programming, version 4.4.2’ (2004), available for download from http://www.gap-system.org.
[9]Isaacs, I. M., Character theory of finite groups, Pure and Applied Mathematics 69 (Academic Press, New York, NY, 1976).
[10]Jansen, C., Lux, K., Parker, R. and Wilson, R., An atlas of Brauer characters, London Mathematical Society Monographs, New Series, 11 (The Clarendon Press, Oxford University Press, New York, NY, 1995) Appendix 2 by T. Breuer and S. Norton.
[11]Lux, K., Noeske, F. and Ryba, A. J. E., ‘The 5-modular characters of the sporadic simple Harada–Norton group HN and its automorphism group HN.2’, J. Algebra 319 (2008) no. 1, 320335.
[12]Lux, K. and Pahlings, H., Representations of groups: a computational approach, Cambridge Studies in Advanced Mathematics 124 (Cambridge University Press, New York, NY, 2010).
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LMS Journal of Computation and Mathematics
  • ISSN: -
  • EISSN: 1461-1570
  • URL: /core/journals/lms-journal-of-computation-and-mathematics
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