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# PrimGrp

## GAP Primitive Permutation Groups Library

Version 4.0.1

24 September 2025

Alexander Hulpke
Email: hulpke@math.colostate.edu
Homepage: https://www.math.colostate.edu/~hulpke/
Address:
Department of Mathematics
Colorado State University
Fort Collins, CO, 80523-1874, USA

Colva Roney-Dougal
Email: colva.roney-dougal@st-andrews.ac.uk
Homepage: http://www-groups.mcs.st-and.ac.uk/~colva/
Address:
School of Mathematics and Statistics
University of St Andrews
North Haugh, St Andrews
Fife, KY16 9SXS Scotland

Christopher Russell
Email: cr66@st-andrews.ac.uk
Address:
School of Mathematics and Statistics
University of St Andrews
North Haugh, St Andrews
Fife, KY16 9SXS Scotland

### Abstract

The GAP package PrimGrp provides the library of primitive permutation groups which includes, up to permutation isomorphism (i.e., up to conjugacy in the corresponding symmetric group), all primitive permutation groups of degree < 4096.

### Copyright

© 2007-2025 by Alexander Hulpke and Colva Roney-Dougal

PrimGrp is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. For details, see the FSF's own site https://www.gnu.org/licenses/gpl.html.

If you obtained PrimGrp, we would be grateful for a short notification sent to one of the authors.

If you publish a result which was partially obtained with the usage of PrimGrp, please cite it in the following form:

A. Hulpke, C. Roney-Dougal, C. Russell. PrimGrp --- GAP Primitive Permutation Groups Library, Version 4.0.1; 2025 (https://gap-packages.github.io/primgrp/).

### Acknowledgements

The conversion of the GAP database of primitive permutation groups to a separate GAP package has been supported by the EPSRC Collaborative Computational Project EP/M022641/1 CoDiMa (CCP in the area of Computational Discrete Mathematics), https://www.codima.ac.uk/.

### Contents

1 Primitive Permutation Groups
1.1 Primitive Permutation Groups
1.1-1 PrimitiveGroupsAvailable
1.1-2 PrimitiveGroup
1.1-3 NrPrimitiveGroups
1.1-4 AllPrimitiveGroups
1.1-5 OnePrimitiveGroup
1.1-6 PrimitiveGroupsIterator
1.1-7 COHORTS_PRIMITIVE_GROUPS
1.2 Index numbers of primitive groups
1.2-1 PrimitiveIdentification
1.2-2 SimsNo
1.2-3 PRIMITIVE_INDICES_MAGMA
2 Irreducible Matrix Groups
2.1 Irreducible Solvable Matrix Groups
2.1-1 IrreducibleSolvableGroupMS
2.1-2 NumberIrreducibleSolvableGroups
2.1-3 AllIrreducibleSolvableGroups
2.1-4 OneIrreducibleSolvableGroup
2.1-5 PrimitiveIndexIrreducibleSolvableGroup
2.1-6 IrreducibleSolvableGroup
References
Index
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