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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 163 points:
(2,3,4,8,5,9,12,22,6,10,13,23,15,25,33,52)(7,17,18,46,19,47,21,45,20,48,39,84,49,83,51,68)(11,28,29,66,30,38,69,75,31,67,70,76,72,14,36,37)(16,41,42,87,43,54,88,89,44,32,26,60,40,74,61,94)(24,55,56,86,35,81,82,50,57,85,34,77,78,59,79,80)(27,62,63,73,64,58,92,53,65,90,96,71,97,93,95,91)(100,101,102,107,103,108,112,122,104,109,113,123,116,126,132,142,105,110,114,124,117,127,133,143,119,129,135,145,138,148,152,157,106,111,115,125,118,128,134,144,120,130,136,146,139,149,153,158,121,131,137,147,140,150,154,159,141,151,155,160,156,161,162,163);(1,2,7,21,30,73,70,65,3,11,32,75,22,53,61,94,17,42,25,59,77,43,5,16,45,67,74,8,24,58,55,18,38,13,35,36,83,63,92,87,64,62,82,84,19,50,56,33,76,66,12,34,80,49,46,79,90,97,60,95,96,47,69,78,4,14,39,85,93,57,23,54,28,68,44,15,40,86,81,9,26,48,89,88,91,52,37,41,31,10,27,29,71,72,51,20,6)(98,99)
Conjugacy classes & character table
176 conjugacy classes — view the full character table.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21791);
Finite Group Databasebeta