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Aliases
Subgroups
72 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 171 points:
(1,2,5,10,7,13,26,12)(3,14,16,43,19,44,18,50)(4,20,23,51,25,53,58,52)(6,27,22,11,29,39,57,41)(8,30,31,46,33,45,42,15)(9,34,36,59,38,61,37,24)(17,48,47,62,49,63,28,35)(21,40,54,60,56,64,55,32)(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)(2,8)(4,21)(5,16)(6,28)(7,19)(9,35)(10,31)(11,40)(12,42)(13,33)(14,20)(15,24)(17,22)(18,26)(23,54)(25,56)(27,32)(29,47)(30,34)(36,48)(37,63)(38,62)(39,60)(41,64)(43,51)(44,53)(45,61)(46,59)(49,57)(50,52)(55,58)
Conjugacy classes & character table
4066 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13696, 149);
Finite Group Databasebeta