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Aliases
Subgroups
202 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 169 points:
(1,2,4,8,5,7,13,15)(3,9,10,16,11,6,12,14)(17,18)(19,26)(20,24)(21,29)(22,25)(23,27)(28,31)(30,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169);(1,3,5,11)(2,6,7,9)(4,12,13,10)(8,16,15,14)(17,19,22,28)(18,23,25,32)(20,27,21,30)(24,31,29,26);(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26)
Conjugacy classes & character table
5206 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 276);
Finite Group Databasebeta