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Aliases
Splittings
Subgroups
42 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 144 points:
(1,3,7,13,22,34,49,67,33,47,39,55,73,92,110,115,106,64,83,104,97,116,127,134,138,137,124,93,54,45,19,29,43,60,80,101,118,128,109,70,35,2,5,9,16,27,41,58,78,99,87,21,32,25,38,53,71,90,108,85,105,66,86,76,96,114,125,132,133,113,74,63,31,44,61,81,102,119,129,135,122,91,52,23,18,4,8,15,26,40,57,77,98,68,12,20,14,24,36,51,69,88,107,121,48,65,56,75,94,112,123,126,95,84,46,62,82,103,120,130,136,139,131,111,72,37,30,10,17,28,42,59,79,100,117,89,50,6,11)(140,141,142,143,144);(1,2,4)(3,6,10)(7,12,19)(8,14,23)(9,11,18)(13,21,31)(15,25,37)(16,20,30)(17,24,35)(22,33,46)(26,39,54)(27,32,45)(28,38,52)(29,36,50)(34,48,64)(40,56,74)(41,47,63)(42,55,72)(43,53,70)(44,51,68)(49,66,85)(57,76,95)(58,65,84)(59,75,93)(60,73,91)(61,71,89)(62,69,87)(67,83,88)(77,97,115)(78,86,106)(79,96,113)(80,94,111)(81,92,109)(82,90,98)(99,104,108)(100,116,126)(101,114,124)(102,112,122)(103,110,117)(105,107,121)(118,127,133)(119,125,131)(120,123,128)(129,134,137)(130,132,135)(136,138,139)(140,143,141,142,144)
Conjugacy classes & character table
245 conjugacy classes — view the full character table.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25020, 131);
Finite Group Databasebeta