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# Repsn

## Constructing representations of finite groups

3.1.0

22 February 2019

Vahid Dabbaghian
Email: vdabbagh@sfu.ca
Homepage: http://www.sfu.ca/~vdabbagh
Address:
Vahid Dabbaghian
Department of Mathematics
Simon Fraser University
Burnaby, British Columbia
V5A 1S6 Canada

The GAP Team
Email: support@gap-system.org

### Acknowledgements

The first version of 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
References
Index
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