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Aliases
Subgroups
70 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 171 points:
(1,2,5,11,8,13,7,31)(3,14,16,45,19,47,18,54)(4,20,23,55,26,57,25,62)(6,27,22,43,30,38,29,12)(9,32,33,15,35,49,41,51)(10,36,39,61,40,60,56,24)(17,52,48,37,53,64,28,46)(21,42,58,63,50,44,59,34)(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);(1,3,8,19)(2,9,13,35)(4,21,26,50)(5,18,7,16)(6,28,30,48)(10,37,40,46)(11,41,31,33)(12,42,43,44)(14,20,47,57)(15,24,51,61)(17,22,53,29)(23,59,25,58)(27,34,38,63)(32,36,49,60)(39,52,56,64)(45,62,54,55)
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, 152);
Finite Group Databasebeta