<div="">pre dt class0/></>
<dd><p>the remaining groups of; group 60 4 >
</dd>
<dt><strong class="Mark">(11)</strong></dt>
<><> remaining order"\^\<> for < class"">( ,,71)/>.
</dd>
</dl>
<p>span>&;/> ="> =SmallGroup(78 100)
<p&; group size6 with>
<> libraryhas been constructed Hans Besche Eick E. A. Brien on an can <a chapBib_mj#biBBEO01<a.Further the inin href.biBNew77]/>< =.#"[OB90<,< =chapBib_mjhtmljava.lang.StringIndexOutOfBoundsException: Range [443, 442) out of bounds for length 1448
<p>As of version 1.4 of this library, the arrangement of groups is the same as in Magma, Version 2.23. In earlier releases of this library, the arrangement in orders <span class="SimpleMath">\(p^7\)</span>, <span class="SimpleMath">\(p=3,5,7,11\)</span> disagreed. An attempt to fix this was
<p>In version 1.5, the number of groups of order 1024 was corrected. For more information, refer to <a href="chapBib_mj.html#biBBurrell2021">[Bur21]</a>.</p>
tdright;>>t>/>
<div allwith as < class"arg/>. If< class="Arg>argv> is < class>(\<span this returns groups <span=SimpleMath(\/> , alsotake whichmust organizedin<codeclass=">function/code> nd value. In this case the function must be func<code< =./../doc/chap30_mj first of a list thenit consideredlistpossible valuesincludefunctionreturns groups specifiedspecified orders having those properties specified by the remaining functions andvalues>
<p>returns the <var class="Arg">i</var>-th group of order <var class="Arg">order
<div class="example"><pre>
<span class="GAPprompt">gap></span> <span class="GAPinput">G := SmallGroup( 60, 4 );</span>
torsjava.lang.StringIndexOutOfBoundsException: Index 45 out of bounds for length 45
<span class<pan="GAPprompt">>><panGAPinput ;/> "C60"
<span class=lt of 6 with> java.lang.StringIndexOutOfBoundsException: Index 48 out of bounds for length 48
Group123,4,), 12)]
<span class="GAPprompt">gap></span> <span;pcof6 4 &;, "A5"
< =""gap>< class>: ( 6,100);/pan
<pc group of size 76java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
s class>>spanGAPinput( 6,000];span
<pc group of size 768 with 9 generators>
</pre></div>
/>/table<>
<p>returns <code class="code">true</code> if the library of groups of order <var class="Arg">order</var> is installed, and <code class="code">false</code> otherwise.</p>
<
> all with properties by=""<>If" number < class"">(\<> this function all oforder < class=">n\/>., function take then organized <code=code</> < =""value>. n this the mustcode="">Size>< href/../.docchap30_mj#>span class=RefLink: Size></> thefirst an or range . If isa list it is a list possible values to. The returns of specified having propertiesspecified bythe functionsand their.</pjava.lang.StringIndexOutOfBoundsException: Range [882, 883) out of bounds for length 882
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SmallGroupsInformation</code>( <var class="Arg">order</var> )</td><td class="tdright">( function )</td></tr></table></div>
<p>prints information on the groups of the specified order.</p>
There are 51 groups of order 32.
They are sorted by their ranks.
1 is cyclic.
2 - 20 have rank 2.
21 - 44 have rank 3.
45 - 50 have rank 4.
51 is elementary abelian.
For the selection functions the values of the following attributes
are precomputed and stored:
IsAbelian, PClassPGroup, RankPGroup, FrattinifactorSize and
FrattinifactorId.
This size belongs to layer 2 of the SmallGroups library.
IdSmallGroup is available for this size.
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ UnloadSmallGroupsData</code>( )</td><td class="tdright">( function )</td></tr></table></div>
<p><strong class="pkg">GAP</strong> loads all necessary data from the library automatically, but it does not delete the data from the workspace again. Usually, this will be not necessary, since the data is stored in a compressed format. However, if a large number of groups from the library have been loaded, then the user might wish to remove the data from the workspace and this can be done by the above function call.</p>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ SMALL_GROUPS_OLD_ORDER</code></td><td class="tdright">( global variable )</td></tr></table></div>
<p>If set to <code class="code">true</code>, then groups of order <span class="SimpleMath">\(3^7\)</span>, <span class="SimpleMath">\(5^7\)</span>, <span class="SimpleMath">\(7^7\)</span>, and <span class="SimpleMath">\(11^7\)</span> are ordered in the way they were ordered up to version 1.0 of the package. If this variable is set to <code class="code">false</code>, which is the default as of version 1.4, then a different ordering, that agrees with the one in Magma version 2.23, is used. The functions <code class="code">SMALLGP_PERM</code><span class="SimpleMath">\(x\)</span>, with <span class="SimpleMath">\(x=3,5,7,11\)</span>, give the old index position corresponding to a new index position. In releases 1.1-1.3 a misunderstood ordering, based on the old ordering and the permutations <span class="SimpleMath">\((2,30083)(3,30084)(4,30085)(5,30086)\)</span>, <span class="SimpleMath">\((2,104599)(3,104600)(4,104601)(5,104602)\)</span>, and <spanclass="SimpleMath">\((2,721053)(3,721054)(4,721055)(5,721059)\)</span> respectively were used.</p>
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