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Aliases
Subgroups
448 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 169 points:
(1,2,7,13)(3,14,18,29)(4,10,20,28)(5,12,6,11)(8,21,25,17)(9,22,26,19)(15,23,32,24)(16,30,31,27)(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);(1,3,7,18)(2,8,13,25)(4,15,20,32)(5,21,6,17)(9,23,26,24)(10,27,28,30)(11,29,12,14)(16,22,31,19);(1,4)(2,9)(3,15)(5,19)(6,22)(7,20)(8,23)(10,11)(12,28)(13,26)(14,30)(16,21)(17,31)(18,32)(24,25)(27,29);(1,4)(2,10)(3,16)(5,22)(6,19)(7,20)(8,24)(9,11)(12,26)(13,28)(14,30)(15,21)(17,32)(18,31)(23,25)(27,29)
Conjugacy classes & character table
3562 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2021);
Finite Group Databasebeta