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Dic6223 #38733513
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 180 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);(1,3,2,4)(6,53)(7,52)(8,51)(9,50)(10,49)(11,48)(12,47)(13,46)(14,45)(15,44)(16,43)(17,42)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(55,180)(56,179)(57,178)(58,177)(59,176)(60,175)(61,174)(62,173)(63,172)(64,171)(65,170)(66,169)(67,168)(68,167)(69,166)(70,165)(71,164)(72,163)(73,162)(74,161)(75,160)(76,159)(77,158)(78,157)(79,156)(80,155)(81,154)(82,153)(83,152)(84,151)(85,150)(86,149)(87,148)(88,147)(89,146)(90,145)(91,144)(92,143)(93,142)(94,141)(95,140)(96,139)(97,138)(98,137)(99,136)(100,135)(101,134)(102,133)(103,132)(104,131)(105,130)(106,129)(107,128)(108,127)(109,126)(110,125)(111,124)(112,123)(113,122)(114,121)(115,120)(116,119)(117,118)
Polycyclic presentation:
2,7,127,2,7|a^2=d,b^7=e^6,b^a=b^6e,c^a=c^126,e^a=e^6
Conjugacy classes & character table
6226 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24892, 6);
Finite Group Databasebeta