← Prev (#14523118) Next (#14523120) →
Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 173 points:
(1,2)(6,8,13)(7,11,21)(9,16,31)(10,19,38)(12,24,48)(14,27,25)(15,30,42)(17,34,67)(18,36,57)(20,41,82)(22,44,26)(23,47,43)(28,55,61)(29,58,75)(32,63,51)(33,66,85)(35,70,121)(37,74,127)(39,77,52)(40,80,86)(45,90,62)(46,92,76)(49,81,53)(50,96,87)(54,59,88)(56,101,116)(60,93,89)(64,110,106)(65,113,129)(68,117,97)(69,120,139)(71,91,144)(72,112,98)(73,125,140)(78,133,107)(79,134,130)(83,136,99)(84,111,141)(94,126,108)(95,138,131)(100,114,115)(102,148,163)(103,135,142)(104,143,109)(105,145,132)(118,158,151)(119,161,166)(122,154,169)(123,160,152)(124,164,167)(128,165,146)(137,159,168)(147,162,157)(149,150,170)(153,156,155)(171,172,173);(3,4)(5,141,85,44,137,31,126,72,112,69,121,104,58,7,93,140,89,161,62,74,124,149,111,68,150,103,12,6,55,139,88,108,61,158,123,38,119,163,136,11,10,100,92,142,66,107,128,164,76,154,118,70,23,20,9,8,169,115,90,106,63,131,75,160,122,48,22,18,15,145,127,114,152,109,80,130,172,159,24,46,37,17,14,101,157,143,151,13,168,129,77,50,67,45,19,29,147,144,156,113,26,135,167,132,96,49,91,40,35,28,16,173,155,53,25,110,166,21,95,116,81,39,57,33,170,165,30,52,153,134,43,120,94,41,79,71,56,32,148,60,99,51,27,87,42,133,84,117,78,36,65,171,82,59,98,54,47,86,162,138,83,125,73,102,64,34,105,146,97)
Conjugacy classes & character table
236 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2028, 13);
Finite Group Databasebeta