← Prev (#31778250) Next (#31778252) →
Aliases
Subgroups
328 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 169 points:
(1,2)(3,9)(4,7)(5,8)(6,11)(10,15)(12,14)(13,16)(17,18)(19,27)(20,26)(21,23)(22,25)(24,28)(29,32)(30,31)(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)(2,6,8,9)(4,12,13,10)(7,15,16,14)(18,23)(24,31)(25,26)(27,32);(1,4,5,13)(2,7,8,16)(3,10,11,12)(6,14,9,15)(17,19,21,29)(18,24,23,31)(20,28,22,30)(25,27,26,32);(2,8)(6,9)(7,16)(14,15)(17,20,21,22)(18,25,23,26)(19,28,29,30)(24,27,31,32)
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, 1972);
Finite Group Databasebeta