← Prev (#27134646) Next (#27134648) →
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 141 points:
(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,20)(12,23)(14,25)(17,29)(18,28)(19,27)(21,34)(22,37)(24,39)(26,41)(30,46)(31,45)(32,44)(33,43)(35,52)(36,55)(38,57)(40,59)(42,61)(47,67)(48,66)(49,65)(50,64)(51,63)(53,72)(54,74)(56,76)(58,78)(60,80)(62,82)(68,83)(69,86)(70,85)(71,84)(73,90)(75,92)(77,94)(79,96)(81,98)(87,99)(88,101)(89,100)(91,104)(93,106)(95,108)(97,110)(102,111)(103,112)(105,114)(107,116)(109,118)(113,119)(115,120)(117,121)(122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138)(139,140,141);(1,6,24,58,95,117,116,94,57,23,4,3,14,40,79,109,120,106,76,37,10,9,8,26,60,97,119,114,92,55,20,19,18,17,42,81,111,112,104,74,34,33,32,31,30,62,99,101,100,90,52,51,50,49,48,47,83,86,85,84,72,53,71,70,69,68,67,66,65,64,63,35,73,89,88,87,82,46,45,44,43,21,54,91,103,102,98,61,29,28,27,11,36,75,105,113,110,80,41,16,15,5,22,56,93,115,118,96,59,25,7,2,12,38,77,107,121,108,78,39,13)
Conjugacy classes & character table
3162 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12342, 3);
Finite Group Databasebeta