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Aliases
Subgroups
454 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 169 points:
(1,2)(3,12)(4,9)(5,22)(6,11)(7,15)(8,20)(10,23)(13,25)(14,31)(16,27)(17,26)(18,24)(19,29)(21,28)(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)(2,7)(4,18)(5,16)(6,17)(8,25)(9,30)(10,26)(11,27)(12,22)(13,21)(14,19)(15,23)(20,32)(24,29)(28,31);(1,4)(2,8)(3,13)(5,19)(6,21)(7,24)(9,22)(10,28)(11,29)(12,31)(14,15)(16,32)(17,18)(20,23)(25,27)(26,30);(1,4)(2,9)(3,14)(5,20)(6,21)(7,25)(8,22)(10,29)(11,28)(12,31)(13,15)(16,18)(17,32)(19,23)(24,27)(26,30)
Conjugacy classes & character table
3973 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2022);
Finite Group Databasebeta