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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 206 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)(75,98)(76,100)(78,102)(80,104)(82,106)(84,108)(86,110)(93,111)(94,115)(95,114)(96,113)(97,112)(99,120)(101,122)(103,124)(105,126)(107,128)(109,130)(116,131)(117,134)(118,133)(119,132)(121,138)(123,140)(125,142)(127,144)(129,146)(135,147)(136,149)(137,148)(139,152)(141,154)(143,156)(145,158)(150,159)(151,160)(153,162)(155,164)(157,166)(161,167)(163,168)(165,169)(170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206);(1,6,24,58,105,143,165,164,142,104,57,23,4,3,14,40,82,127,157,168,154,124,79,37,10,9,8,26,60,107,145,167,162,140,102,55,20,19,18,17,42,84,129,159,160,152,122,77,34,33,32,31,30,62,109,147,149,148,138,100,52,51,50,49,48,47,86,131,134,133,132,120,74,73,72,71,70,69,68,111,115,114,113,112,98,75,97,96,95,94,93,92,91,90,89,88,87,53,99,119,118,117,116,110,67,66,65,64,63,35,76,121,137,136,135,130,85,46,45,44,43,21,54,101,139,151,150,146,108,61,29,28,27,11,36,78,123,153,161,158,128,83,41,16,15,5,22,56,103,141,163,166,144,106,59,25,7,2,12,38,80,125,155,169,156,126,81,39,13)
Conjugacy classes & character table
3182 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12506, 2);
Finite Group Databasebeta