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Dic7811 #44530373
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 184 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77)(78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184);(1,3,2,4)(6,77)(7,76)(8,75)(9,74)(10,73)(11,72)(12,71)(13,70)(14,69)(15,68)(16,67)(17,66)(18,65)(19,64)(20,63)(21,62)(22,61)(23,60)(24,59)(25,58)(26,57)(27,56)(28,55)(29,54)(30,53)(31,52)(32,51)(33,50)(34,49)(35,48)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)(79,184)(80,183)(81,182)(82,181)(83,180)(84,179)(85,178)(86,177)(87,176)(88,175)(89,174)(90,173)(91,172)(92,171)(93,170)(94,169)(95,168)(96,167)(97,166)(98,165)(99,164)(100,163)(101,162)(102,161)(103,160)(104,159)(105,158)(106,157)(107,156)(108,155)(109,154)(110,153)(111,152)(112,151)(113,150)(114,149)(115,148)(116,147)(117,146)(118,145)(119,144)(120,143)(121,142)(122,141)(123,140)(124,139)(125,138)(126,137)(127,136)(128,135)(129,134)(130,133)(131,132)
Polycyclic presentation:
2,73,107,2|a^2=d,b^a=b^72,c^a=c^106
Conjugacy classes & character table
7814 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31244, 4);
Finite Group Databasebeta