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Aliases
Subgroups
104 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 171 points:
(1,2)(3,13)(4,18)(5,24)(6,28)(7,9)(8,14)(10,21)(11,20)(12,26)(15,45)(16,48)(17,40)(19,37)(22,56)(23,39)(25,35)(27,58)(29,41)(30,44)(31,52)(32,51)(33,42)(34,46)(36,63)(38,43)(47,64)(49,54)(50,55)(53,62)(57,60)(59,61)(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);(1,3,7,17)(2,8,9,30)(4,19,23,53)(5,25,27,59)(6,29,26,16)(10,35,33,61)(11,37,34,62)(12,38,28,32)(13,39,40,18)(14,42,44,21)(15,46,47,20)(22,57,55,52)(24,31,58,60)(36,64,49,45)(41,50,48,56)(43,54,51,63);(2,9)(8,30)(10,33)(11,34)(12,28)(13,40)(18,39)(24,58)(31,60)(32,38)(35,61)(36,49)(37,62)(41,48)(45,64)(50,56)
Conjugacy classes & character table
2782 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13696, 996);
Finite Group Databasebeta