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Aliases
Splittings
Subgroups
54 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 179 points:
(2,4,9)(3,7,17)(5,12,28)(6,15,35)(8,20,45)(10,23,21)(11,26,39)(13,31,43)(14,33,24)(16,38,78)(18,41,22)(19,44,40)(25,54,72)(27,58,88)(29,60,48)(30,63,81)(32,67,102)(34,71,120)(36,73,49)(37,76,82)(42,86,59)(46,77,50)(47,92,83)(51,56,84)(52,53,87)(55,100,127)(57,89,85)(61,94,69)(62,108,123)(64,111,137)(65,75,93)(66,91,131)(68,115,122)(70,74,124)(79,128,95)(80,130,132)(90,119,105)(96,103,125)(97,107,144)(98,139,155)(99,126,133)(101,135,106)(104,140,134)(109,150,160)(110,138,136)(112,118,117)(113,129,158)(114,146,161)(116,151,165)(121,156,141)(142,152,157)(143,162,163)(145,154,147)(148,166,168)(149,159,164)(153,167,169)(171,172,173)(174,176,175)(178,179);(1,46,138,37,133,74,155,62,108,35,95,169,23,20,89,137,85,36,120,30,157,61,50,162,94,100,44,88,115,15,84,98,122,29,147,130,49,166,93,45,132,87,41,55,110,12,121,142,22,146,48,128,83,43,124,27,161,53,71,97,106,104,21,145,114,19,82,42,131,25,63,52,154,167,9,103,159,99,40,18,81,11,129,24,119,153,60,58,126,160,67,7,39,34,80,10,105,116,118,150,76,127,152,54,17,16,165,4,79,68,70,164,117,78,113,144,73,8,140,14,38,32,59,136,69,156,66,102,112,96,92,6,139,13,125,151,33,135,148,57,65,101,158,3,91,5,77,163,28,86,109,149,31,56,123,51,47,2,90,134,75,111,64,168,107,26,72,141,143)(170,171,173,175,172,174,176)(177,178,179)
Conjugacy classes & character table
1191 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21294, 48);
Finite Group Databasebeta