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<html><head><title>[sglppow] 2 Accessing the data</title></head>
<body text="#000000" bgcolor="#ffffff"> [<a href = "chapters.htm">Up</a>] [<a href ="CHAP001.htm">Previous</a>] [<a href ="CHAP003.htm">Nex <h1>2 Accessing the data</h1><p> <p> When this package is loaded, then the groups of order 3<sup>8</sup> and <i>p</i><sup>7</sup> for primes <i>p</i> > 11 are additionally available via the SmallGroups library. As a result, all groups of order <i>p</i><sup><i>n</i></sup> with <i>p</i>=2 and <i>n</i> ≤ 9 and <i>p</i>=3 and <i>n</i> ≤ 8 and <i>p</i> an arbitrary prime and <i>n</i> ≤ 7 are then available via the small groups library. The corresponding information can be obtained via <p> <a name = ""></a> <li><code>SmallGroup(size, number)</code> <p> <a name = ""></a> <li><code>NumberSmallGroups(size)</code> <p> <a name = ""></a> <li><code>SmallGroupsInformation(size)</code> <p> See Section 50.7 in the GAP manual for background on these functions. Note that there is no IdGroup function available for this extension of the small groups library. <p> WARNING: The user should be aware that there are there are 1,396,077 groups of order 3<sup>8</sup>, 1,600,573 groups of order 13<sup>7</sup>, and 5,546,909 groups of order 17<sup>7</sup>. For general <i>p</i> the number of groups of order <i>p</i><sup>7</sup> is a PORC polynomial in <i>p</i> with leading term 3<i>p</i><sup>5</sup>. Furthermore, as the prime <i>p</i> increases, the time taken to generate a complete list of the groups of order <i>p</i><sup>7</sup> grows rapidly. Experimentally the time seems to be proportional to <i>p</i><sup>6·2</sup>. For <i>p</i>=13 it takes several hours to generate the complete list. For primes <i>p</i> ≤ 11 the groups are precomputed, and their SmallGroup codes are stored in the SmallGroups database. For primes <i>p</i> > 11 the Lie rings have to be generated from 4773 parametrized presentations in the LiePRing database, and then converted into groups using the Baker-Campbell-Hausdorff formula. A complete list of power commutator presentations for the groups of order 13<sup>7</sup> takes over 11 gb of memory. <p> <pre> gap> NumberSmallGroups(3^8); 1396077 gap> SmallGroup(3^8, 1000000); <pc group of size 6561 with 8 generators> gap> NumberSmallGroups(17^7); 5546909 gap> SmallGroup(17^7, 5000); constructing a batch of 1156 groups ... this may take a while <pc group of size 410338673 with 7 generators> gap> NumberSmallGroups(101^7); 32826263845 </pre> <p> <p> [<a href = "chapters.htm">Up</a>] [<a href ="CHAP001.htm">Previous</a>] [<a href ="CHAP003.htm">Nex <P> <address>sglppow manual<br>March 2024 </address></body></html> ¤ Dauer der Verarbeitung: 0.12 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28