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<h1><strong class="pkg">PrimGrp</strong></h1>


<h2><strong class="pkg">GAP</strong> Primitive Permutation Groups Library</h2>

<p>Version 4.0.1</p>

<p>24 September 2025</p>

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<p><b>Alexander Hulpke
          
       
                  
  </b>
<br />Email: <span class="URL"><a href="mailto:hulpke@math.colostate.edu">hulpke@math.colostate.edu</a></span>
<br />Homepage: <span class="URL"><a href="https://www.math.colostate.edu/~hulpke/">https://www.math.colostate.edu/~hulpke/</a></span>
<br />Address: <br />Department of Mathematics<br /> Colorado State University<br /> Fort Collins, CO, 80523-1874, USA
</p><p><b>Colva Roney-Dougal
          
       
           
  </b>
<br />Email: <span class="URL"><a href="mailto:colva.roney-dougal@st-andrews.ac.uk">colva.roney-dougal@st-andrews.ac.uk</a></span>
<br />Homepage: <span class="URL"><a href="http://www-groups.mcs.st-and.ac.uk/~colva/">http://www-groups.mcs.st-and.ac.uk/~colva/</a></span>
<br />Address: <br />School of Mathematics and Statistics<br /> University of St Andrews<br /> North Haugh, St Andrews<br /> Fife, KY16 9SXS Scotland
</p><p><b>Christopher Russell
          
           
  </b>
<br />Email: <span class="URL"><a href="mailto:cr66@st-andrews.ac.uk">cr66@st-andrews.ac.uk</a></span>
<br />Address: <br />School of Mathematics and Statistics<br /> University of St Andrews<br /> North Haugh, St Andrews<br /> Fife, KY16 9SXS Scotland
</p>

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<h3>Abstract</h3>
<p>The <strong class="pkg">GAP</strong> package <strong class="pkg">PrimGrp</strong> 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.</p>

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<h3>Copyright</h3>
<p>© 2007-2025 by Alexander Hulpke and Colva Roney-Dougal</p>

<p><strong class="pkg">PrimGrp</strong> 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 <span class="URL"><a href="https://www.gnu.org/licenses/gpl.html">https://www.gnu.org/licenses/gpl.html</a></span>.</p>

<p>If you obtained <strong class="pkg">PrimGrp</strong>, we would be grateful for a short notification sent to one of the authors.</p>

<p>If you publish a result which was partially obtained with the usage of <strong class="pkg">PrimGrp</strong>, please cite it in the following form:</p>

<p>A. Hulpke, C. Roney-Dougal, C. Russell. <em>PrimGrp --- GAP Primitive Permutation Groups Library, Version 4.0.1;</em> 2025 (<span class="URL"><a href="https://gap-packages.github.io/primgrp/">https://gap-packages.github.io/primgrp/</a></span>).</p>

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<h3>Acknowledgements</h3>
<p>The conversion of the <strong class="pkg">GAP</strong> database of primitive permutation groups to a separate <strong class="pkg">GAP</strong> package has been supported by the EPSRC Collaborative Computational Project EP/M022641/1 CoDiMa (CCP in the area of Computational Discrete Mathematics), <span class="URL"><a href="https://www.codima.ac.uk/">https://www.codima.ac.uk/</a></span>.</p>

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<div class="contents">
<h3>Contents<a id="contents" name="contents"></a></h3>

<div class="ContChap"><a href="chap1_mj.html#X7AE00EA7791F2574">1 <span class="Heading">Primitive Permutation Groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7AE00EA7791F2574">1.1 <span class="Heading">Primitive Permutation Groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X81BDF8CA7CCBFC95">1.1-1 PrimitiveGroupsAvailable</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7BCEA0C57B6D9F42">1.1-2 PrimitiveGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X8564FECC8477F199">1.1-3 NrPrimitiveGroups</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X86EF380E8007D304">1.1-4 AllPrimitiveGroups</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X82870C177DB70470">1.1-5 OnePrimitiveGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X7B1D4C0483A7F444">1.1-6 PrimitiveGroupsIterator</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X81329B9B7F5FF8DE">1.1-7 COHORTS_PRIMITIVE_GROUPS</a></span>
</div></div>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap1_mj.html#X7DA239CC848F6CAE">1.2 <span class="Heading">Index numbers of primitive groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X870400597FD4E392">1.2-1 PrimitiveIdentification</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X790D50447ABDF7EE">1.2-2 SimsNo</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap1_mj.html#X784820DA86D0E6F4">1.2-3 PRIMITIVE_INDICES_MAGMA</a></span>
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<div class="ContChap"><a href="chap2_mj.html#X78C56BAA804A56A1">2 <span class="Heading">Irreducible Matrix Groups</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap2_mj.html#X82FD673384BF353B">2.1 <span class="Heading">Irreducible Solvable Matrix Groups</span></a>
</span>
<div class="ContSSBlock">
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7DF4B4D683A727E8">2.1-1 IrreducibleSolvableGroupMS</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X836AEF4A7E494724">2.1-2 NumberIrreducibleSolvableGroups</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X7DAC64F17C8B49A2">2.1-3 AllIrreducibleSolvableGroups</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X844E60B87FC48D1B">2.1-4 OneIrreducibleSolvableGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X81B11EE77EFA745E">2.1-5 PrimitiveIndexIrreducibleSolvableGroup</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap2_mj.html#X816FF4DD8267B4A7">2.1-6 IrreducibleSolvableGroup</a></span>
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</div>
<div class="ContChap"><a href="chapBib_mj.html"><span class="Heading">References</span></a></div>
<div class="ContChap"><a href="chapInd_mj.html"><span class="Heading">Index</span></a></div>
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