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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 160 points:
(1,2,3,4,5)(7,8,9,11)(10,13,14,20)(12,17,18,16)(15,22,23,33)(19,26,27,29)(21,30,31,25)(24,35,36,50)(28,39,40,46)(32,43,44,42)(34,47,48,38)(37,52,53,71)(41,56,57,67)(45,60,61,63)(49,64,65,59)(51,68,69,55)(54,73,74,96)(58,77,78,92)(62,81,82,88)(66,85,86,84)(70,89,90,80)(72,93,94,76)(75,98,99,125)(79,102,103,121)(83,106,107,117)(87,110,111,113)(91,114,115,109)(95,118,119,105)(97,122,123,101)(100,127,128,150)(104,131,132,148)(108,135,136,146)(112,139,140,144)(116,143,141,142)(120,145,137,138)(124,147,133,134)(126,149,129,130)(151,153,154,152)(155,156)(157,158,159,160);(6,7,10,15,24,37,54,75,100,129,125,148,145,114,85,60,39,22,34,49,66,87,112,141,115,90,69,50,67,88,113,142,135,102,73,97,124,132,103,78,57,40,27,18,11,16,25,38,55,76,101,130,152,154,150,147,118,89,64,43,26,13,21,32,45,62,83,108,137,119,94,71,92,117,144,139,106,77,52,72,95,120,136,107,82,61,44,31,20,29,42,59,80,105,134,127,151,153,149,122,93,68,47,30,17,8,12,19,28,41,58,79,104,133,123,96,121,146,143,110,81,56,35,51,70,91,116,140,111,86,65,48,33,46,63,84,109,138,131,98,126,128,99,74,53,36,23,14,9)(155,157,159)(156,160,158)
Conjugacy classes & character table
1695 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26820, 51);
Finite Group Databasebeta