| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/GAP/pkg/sglppow/etc/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 20.2.2024 mit Größe 1 kB |
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The groups of order 3^8
We give a complete list of the groups of order 3^8. The groups are given by their SmallGroup codes, which are understood by both GAP and Magma. If c is the code for one of the groups, then to obtain the corresponding group in Magma enter SmallGroupDecoding(c,3^8) and in GAP enter PcGroupCode(c,3^8). The codes are given in a set of files, each file of the same form. For example the file "rank7class2" contains the codes for the ten seven generator groups of class two and order 3^8. The codes are given as a sequence "codes": codes:=[ 34359738432, 34359738496, 225468603171008, 225468603170945, 225468604219520, 1479299539764510912, 1479299539764510849, 1479299540301381760, 9705684280422972784832, 9705684280422972784769]; There are 22 files in all, each of the form "rankmclassn", where m is the rank of G/(G^3.[G,G]) and n is the p-class of G. (The classification of finite p-groups uses the lower exponent p central series G = G_1 > G_2 > G_3 > ... > G_n > G_{n+1} = {1}, where, for i > 1, G_i = G_{i-1}^3.[G_{i-1},G].) The number of groups of rank m and class n is given below as the n-th entry in the m-th row. [ [ 0, 0, 0, 0, 0, 0, 0, 1 ], [ 0, 0, 58, 486, 1343, 330, 9, 0 ], [ 0, 4, 216747, 40521, 2163, 24, 0, 0 ], [ 0, 23361, 494666, 22343, 51, 0, 0, 0 ], [ 0, 578478, 14796, 80, 0, 0, 0, 0 ], [ 0, 566, 39, 0, 0, 0, 0, 0 ], [ 0, 10, 0, 0, 0, 0, 0, 0 ], [ 1, 0, 0, 0, 0, 0, 0, 0 ] ] The total number of groups of order 3^8 is 1396077. ¤ Dauer der Verarbeitung: 0.12 Sekunden (vorverarbeitet) ¤*© Formatika GbR, Deutschland |
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2026-03-28