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# Repsn

## A GAP4 Package
for constructing representations of finite groups

Version 2.1

February 2007

Vahid Dabbaghian-Abdoly
e-mail: vdabbagh@sfu.ca
WWW: http://www.sfu.ca/~vdabbagh
Address:
Department of Mathematics,
Simon Fraser University,
Burnaby, British Columbia,
V5A 1S6 Canada.

### Copyright

(C) 2004 Vahid Dabbaghian-Abdoly.

### Acknowledgements

This package was obtained during my Ph.D. studies at Carleton University. I would like to express deep gratitude to my supervisor Professor John D. Dixon whose guidance and support were crucial for the successful completion of this project. I also thank Professor Charles Wright and referees for pointing out some important comments to improve Repsn.

This documentation was prepared with the GAPDoc package by Frank Lübeck and Max Neunhöffer.

### Contents

1. Introduction
2. Irreducible Representations
2.1 Constructing Representations
2.1-1 IrreducibleAffordingRepresentation
2.1-2 IsAffordingRepresentation
2.2 Induction
2.2-1 InducedSubgroupRepresentation
2.3 Extension
2.3-1 ExtendedRepresentation
2.3-2 ExtendedRepresentationNormal
2.4 Character Subgroups
2.4-1 CharacterSubgroupRepresentation
2.4-2 IsCharacterSubgroup
2.4-3 AllCharacterPSubgroups
2.4-4 AllCharacterStandardSubgroups
2.4-5 AllCharacterSubgroups
2.5 Equivalent Representation
2.5-1 EquivalentRepresentation
3. Reducible Representations
3.1 Constituents of Representations
3.1-1 ConstituentsOfRepresentation
3.1-2 IsReducibleRepresentation
3.2 Block Representations
3.2-1 EquivalentBlockRepresentation

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