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Dic7739 #44526302
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)(6,75)(7,74)(8,73)(9,72)(10,71)(11,70)(12,69)(13,68)(14,67)(15,66)(16,65)(17,64)(18,63)(19,62)(20,61)(21,60)(22,59)(23,58)(24,57)(25,56)(26,55)(27,54)(28,53)(29,52)(30,51)(31,50)(32,49)(33,48)(34,47)(35,46)(36,45)(37,44)(38,43)(39,42)(40,41)(77,184)(78,183)(79,182)(80,181)(81,180)(82,179)(83,178)(84,177)(85,176)(86,175)(87,174)(88,173)(89,172)(90,171)(91,170)(92,169)(93,168)(94,167)(95,166)(96,165)(97,164)(98,163)(99,162)(100,161)(101,160)(102,159)(103,158)(104,157)(105,156)(106,155)(107,154)(108,153)(109,152)(110,151)(111,150)(112,149)(113,148)(114,147)(115,146)(116,145)(117,144)(118,143)(119,142)(120,141)(121,140)(122,139)(123,138)(124,137)(125,136)(126,135)(127,134)(128,133)(129,132)(130,131)
Polycyclic presentation:
2,71,109,2|a^2=d,b^a=b^70,c^a=c^108
Conjugacy classes & character table
7742 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30956, 4);
Finite Group Databasebeta