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D6527 #27189458
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 168 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61)(62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168);(2,61)(3,60)(4,59)(5,58)(6,57)(7,56)(8,55)(9,54)(10,53)(11,52)(12,51)(13,50)(14,49)(15,48)(16,47)(17,46)(18,45)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)(63,168)(64,167)(65,166)(66,165)(67,164)(68,163)(69,162)(70,161)(71,160)(72,159)(73,158)(74,157)(75,156)(76,155)(77,154)(78,153)(79,152)(80,151)(81,150)(82,149)(83,148)(84,147)(85,146)(86,145)(87,144)(88,143)(89,142)(90,141)(91,140)(92,139)(93,138)(94,137)(95,136)(96,135)(97,134)(98,133)(99,132)(100,131)(101,130)(102,129)(103,128)(104,127)(105,126)(106,125)(107,124)(108,123)(109,122)(110,121)(111,120)(112,119)(113,118)(114,117)(115,116)
Polycyclic presentation:
2,61,107|b^a=b^60,c^a=c^106
Conjugacy classes & character table
3265 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13054, 3);
Finite Group Databasebeta