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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:
(2,3,4,9,5,10,14,29,6,11,15,30,18,32,42,70,7,12,16,31,19,33,37,73,21,35,43,74,34,75,78,77)(8,23,24,62,25,63,66,65,26,41,67,84,28,71,61,45,27,64,68,82,55,94,76,87,69,13,38,39,72,40,81,83)(17,46,47,56,48,88,90,86,49,89,54,22,57,58,95,59,50,85,91,60,92,80,79,96,93,97,20,52,36,51,53,44)(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);(1,2,8,28,49,94,92,83,4,17,51,95,42,40,86,89,24,59,43,74,73,60,6,22,61,91,88,14,3,13,9,25,54,19,11,36,38,82,39,85,87,64,32,76,26,70,10,34,79,90,18,33,77,69,66,75,23,65,46,84,62,67,57,35,5,20,55,31,41,12,37,80,47,81,52,21,56,29,30,15,44,68,97,96,71,78,53,58,50,16,45,48,63,93,72,27,7)(98,99)
Conjugacy classes & character table
140 conjugacy classes — view the full character table.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21813);
Finite Group Databasebeta