<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SmallClassNrGroup</code>( <var class="Arg">k</var>, <var class="Arg">i</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: the <var class="Arg">i</var>-th finite group of class number <var class="Arg">k</var> in the library.</p>
<p>Alternatively, the pair <code class="code">[ <var class="Arg">k</var>, <var class="Arg">i</var> ]</code> can be given as a single argument <var class="Arg">id</var>. If the group is solvable, it is given as a PcGroup whose Pcgs is a SpecialPcgs. If the group is not solvable, it will be given as a permutation group of minimal permutation degree and with a minimal generating set.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">G := SmallClassNrGroup( 6, 4 );</span>
<pc group of size 18 with 3 generators>
<span class="GAPprompt">gap></span> <span class="GAPinput">NrConjugacyClasses( G );</span>
6
<span class="GAPprompt">gap></span> <span class="GAPinput">IsDihedralGroup( G );</span>
true
</pre></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SmallClassNrGroupsAvailable</code>( <var class="Arg">k</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: <code class="keyw">true</code> if the finite groups of class number <var class="Arg">k</var> are available in the library, and <code class="keyw">false</code> otherwise.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AllSmallClassNrGroups</code>( <var class="Arg">arg</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: all finite groups with certain properties as specified by <var class="Arg">arg</var>.</p>
<p>The arguments must come in pairs consisting of a function and a value (or list of possible values). At least one of the functions must be <code class="keyw">NrConjugacyClasses</code>. Missing functions will be interpreted as <code class="keyw">NrConjugacyClasses</code>, missing values as <code class="keyw">true</code>.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">L1 := AllSmallClassNrGroups( [3..5], IsNilpotent );</span>
[ <pc group of size 3 with 1 generator>,
<pc group of size 4 with 2 generators>,
<pc group of size 4 with 2 generators>,
<pc group of size 5 with 1 generator>,
<pc group of size 8 with 3 generators>,
<pc group of size 8 with 3 generators> ]
<span class="GAPprompt">gap></span> <span class="GAPinput">List( L1, NrConjugacyClasses );</span>
[ 3, 4, 4, 5, 5, 5 ]
<span class="GAPprompt">gap></span> <span class="GAPinput">L2 := AllSmallClassNrGroups( IsSolvable, true, NrConjugacyClasses, 6 );</span>
[ <pc group of size 6 with 2 generators>,
<pc group of size 12 with 3 generators>,
<pc group of size 12 with 3 generators>,
<pc group of size 18 with 3 generators>,
<pc group of size 18 with 3 generators>,
<pc group of size 36 with 4 generators>,
<pc group of size 72 with 5 generators> ]
<span class="GAPprompt">gap></span> <span class="GAPinput">ForAll( L2, G -> IsSolvable( G ) and NrConjugacyClasses( G ) = 6 );</span>
true
</pre></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ OneSmallClassNrGroup</code>( <var class="Arg">arg</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: one finite group with certain properties as specified by <var class="Arg">arg</var>.</p>
<p>The arguments must come in pairs consisting of a function and a value (or list of possible values). At least one of the functions must be <code class="code">NrConjugacyClasses</code>. Missing functions will be interpreted as <code class="code">NrConjugacyClasses</code>, missing values as <code class="keyw">true</code>.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">H := OneSmallClassNrGroup( 6, IsAbelian );</span>
<pc group of size 6 with 2 generators>
<span class="GAPprompt">gap></span> <span class="GAPinput">IsCyclic( H );</span>
true
<span class="GAPprompt">gap></span> <span class="GAPinput">K := OneSmallClassNrGroup( 10, IsSolvable, true, IsNilpotent, false );</span>
<pc group of size 28 with 3 generators>
<span class="GAPprompt">gap></span> <span class="GAPinput">NrConjugacyClasses( K ) = 10 and IsSolvable( K ) and not IsNilpotent( K );</span>
true
</pre></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ NrSmallClassNrGroups</code>( <var class="Arg">arg</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: the number of finite groups with certain properties as specified by <var class="Arg">arg</var>.</p>
<p>The arguments must come in pairs consisting of a function and a value (or list of possible values). At least one of the functions must be <code class="code">NrConjugacyClasses</code>. Missing functions will be interpreted as <code class="code">NrConjugacyClasses</code>, missing values as <code class="keyw">true</code>.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IteratorSmallClassNrGroups</code>( <var class="Arg">arg</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>Returns: an iterator that iterates over the finite groups with properties as specified by <varclass="Arg">arg</var>. The arguments must come in pairs consisting of a function and a value (or list of possible values). At least one of the functions must be <code class="code">NrConjugacyClasses</code>. Missing functions will be interpreted as <code class="code">NrConjugacyClasses</code>, missing values as <code class="keyw">true</code>.</p>
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">iter := IteratorSmallClassNrGroups( IsSolvable, false, 11 );</span>
<iterator>
<span class="GAPprompt">gap></span> <span class="GAPinput">for G in iter do Print( Size( G ), "\n" ); od;</span>
336
720
720
1344
1344
1512
2448
29120
</pre></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ IdClassNr</code>( <var class="Arg">G</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: the <strong class="pkg">SmallClassNr</strong> ID of <var class="Arg">G</var>, i.e. a pair <code class="code">[ <var class="Arg">k</var>, <var class="Arg">i</var> ]</code> such that <var class="Arg">G</var> is isomorphic to <code class="code">SmallClassNrGroup( <var class="Arg">k</var>, <var class="Arg">i</var> )</code>.</p>
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