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Aliases
Subgroups
106 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 167 points:
(1,2)(3,14)(4,10)(5,21)(6,27)(7,30)(8,13)(9,16)(11,24)(12,23)(15,41)(17,46)(18,43)(19,48)(20,40)(22,39)(25,57)(26,52)(28,37)(29,59)(31,42)(32,44)(33,49)(34,53)(35,45)(36,50)(38,56)(47,63)(51,55)(54,61)(58,62)(60,64)(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);(1,3)(2,9)(4,15)(5,22)(6,28)(7,31)(8,18)(10,32)(11,37)(12,39)(13,35)(14,21)(16,24)(17,23)(19,49)(20,47)(25,58)(26,54)(27,33)(29,60)(30,34)(36,63)(38,64)(40,61)(41,48)(42,57)(43,52)(44,50)(45,56)(46,51)(53,55)(59,62);(1,4,8,7)(2,10,13,30)(3,15,18,31)(5,19,26,25)(6,20,29,23)(9,32,35,34)(11,36,38,51)(12,27,40,59)(14,41,43,42)(16,44,45,53)(17,28,47,60)(21,48,52,57)(22,49,54,58)(24,50,56,55)(33,61,62,39)(37,63,64,46)
Conjugacy classes & character table
3914 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13184, 994);
Finite Group Databasebeta