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Aliases
Splittings
Subgroups
60 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 183 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)(53,74)(54,77)(56,79)(58,81)(60,83)(62,85)(68,92)(69,91)(70,90)(71,89)(72,88)(73,87)(75,76)(78,100)(80,102)(82,104)(84,106)(86,108)(93,109)(94,114)(95,113)(96,112)(97,111)(98,110)(99,120)(101,122)(103,124)(105,126)(107,128)(115,129)(116,133)(117,132)(118,131)(119,130)(121,138)(123,140)(125,142)(127,144)(134,145)(135,148)(136,147)(137,146)(139,152)(141,154)(143,156)(149,157)(150,159)(151,158)(153,162)(155,164)(160,165)(161,166)(163,168)(167,169)(171,172)(173,174)(175,176)(177,178,179,180,181);(1,28,90,145,125,101,76,120,140,156,116,49,9,7,45,114,127,103,78,53,138,154,149,95,32,4,16,66,129,105,80,54,110,152,164,135,71,19,13,29,91,107,82,56,35,130,162,160,117,50,10,25,46,109,84,58,36,87,146,168,150,96,33,23,41,67,86,60,38,21,111,158,167,136,72,20,39,61,92,62,40,22,63,131,166,161,118,51,37,59,85,68,42,24,11,88,147,169,151,97,34,57,83,108,47,26,12,43,112,159,163,137,73,55,81,106,93,30,14,5,64,132,165,153,119,52,79,104,128,69,17,6,27,89,148,155,139,98,77,102,126,115,48,8,2,44,113,157,141,121,74,100,124,144,94,31,3,15,65,133,143,123,99,75,122,142,134,70,18)(170,171,173,175,176,174,172)(182,183)
Conjugacy classes & character table
5930 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23660, 31);
Finite Group Databasebeta