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Aliases
Subgroups
106 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 213 points:
(1,2,4,9,5,10,17,27,6,11,18,28,20,30,39,49,7,12,19,29,21,31,40,50,22,32,41,51,42,52,57,62)(3,8,14,24,15,25,36,46,16,26,37,47,38,48,56,61,13,23,33,43,34,44,53,58,35,45,54,59,55,60,63,64)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213);(1,3)(2,8)(4,14)(5,15)(6,16)(7,13)(9,24)(10,25)(11,26)(12,23)(17,36)(18,37)(19,33)(20,38)(21,34)(22,35)(27,46)(28,47)(29,43)(30,48)(31,44)(32,45)(39,56)(40,53)(41,54)(42,55)(49,61)(50,58)(51,59)(52,60)(57,63)(62,64);(3,13)(8,23)(14,33)(15,34)(16,35)(24,43)(25,44)(26,45)(36,53)(37,54)(38,55)(46,58)(47,59)(48,60)(56,63)(61,64)
Conjugacy classes & character table
11920 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19072, 990);
Finite Group Databasebeta