← Prev (#31778594) Next (#31778596) →
Aliases
Subgroups
1424 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 169 points:
(1,2)(3,12)(4,9)(5,10)(6,19)(7,11)(8,14)(13,26)(15,22)(16,24)(17,25)(18,29)(20,23)(21,28)(27,32)(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)(2,8)(4,13)(5,14)(6,20)(7,15)(9,21)(10,22)(11,23)(12,19)(16,27)(17,28)(18,30)(24,31)(25,32)(26,29);(1,4)(2,9)(3,13)(5,17)(6,18)(7,16)(8,21)(10,25)(11,24)(12,26)(14,28)(15,27)(19,29)(20,30)(22,32)(23,31);(4,16)(9,24)(13,27)(17,18)(21,31)(25,29)(26,32)(28,30);(1,5,7,6)(2,10,11,19)(3,14,15,20)(4,17,16,18)(8,22,23,12)(9,25,24,29)(13,28,27,30)(21,32,31,26)
Conjugacy classes & character table
6028 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2316);
Finite Group Databasebeta