<p>The <em>class number</em> <span class="Math">k(G)</span> of a group <span class="Math">G</span> is the number of conjugacy classes of <span class="Math">G</span>. In 1903, Landau proved in <a href="chapBib.html#biBland03-a">[Lan03]</a> that for every <span class="Math">n \in \mathbb{N}</span>, there are only finitely many finite groups with exactly <span class="Math">n</span> conjugacy classes. The <strong class="pkg">SmallClassNr</strong> package provides access to the finite groups with class number at most <span class="Math">14</span>.</p>
<p>These groups were classified in the following papers:</p>
<ul>
<li><p><span class="Math">k(G) \leq 5</span>, by Miller in <a href="chapBib.html#biBmill11-a">[Mil11]</a> and independently by Burnside in <a href="chapBib.html#biBburn11-a">[Bur11]</a></p>
</li>
<li><p><span class="Math">k(G) = 6,7</span>, by Poland in <a href="chapBib.html#biBpola68-a">[Pol68]</a></p>
</li>
<li><p><span class="Math">k(G) = 8</span>, by Kosvintsev in <a href="chapBib.html#biBkosv74-a">[Kos74]</a></p>
</li>
<li><p><span class="Math">k(G) = 9</span>, by Odincov and Starostin in <a href="chapBib.html#biBos76-a">[OS76]</a></p>
</li>
<li><p><span class="Math">k(G) = 10,11</span>, by Vera López and Vera López in <a href="chapBib.html#biBll85-a">[VLVL85]</a> (1)</p>
</li>
<li><p><span class="Math">k(G) = 12</span>, by Vera López and Vera López in <a href="chapBib.html#biBll86-a">[VLVL86]</a> (2)</p>
</li>
<li><p><span class="Math">k(G) = 13, 14</span>, by Vera López and Sangroniz in <a href="chapBib.html#biBvs07-a">[VLS07]</a></p>
</li>
</ul>
<p>(1) In <a href="chapBib.html#biBll85-a">[VLVL85]</a>, three distinct groups of the form <span class="Math">(C_5 \times C_5) \rtimes C_4</span> order <span class="Math">100</span> with class number <span class="Math">10</span> are given. However, only two such groups exist, being the ones with <code class="code">IdClassNr</code> equal to <code class="code">[10,25]</code> and <code class="code">[10,26]</code>.</p>
<p>(2) In <a href="chapBib.html#biBll86-a">[VLVL86]</a>, only 48 groups with class number 12 are listed. The three missing groups are provided in the appendix of <a href="chapBib.html#biBvs07-a">[VLS07]</a>. These are the groups with <code class="code">IdClassNr</code> equal to <code class="code">[12,13]</code>, <code class="code">[12,16]</code> and <code class="code">[12,39]</code>.</p>
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