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Dic334 #13050684
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 175 points:
(1,2,3,4)(5,8,7,6)(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);(1,5,3,7)(2,6,4,8)(10,175)(11,174)(12,173)(13,172)(14,171)(15,170)(16,169)(17,168)(18,167)(19,166)(20,165)(21,164)(22,163)(23,162)(24,161)(25,160)(26,159)(27,158)(28,157)(29,156)(30,155)(31,154)(32,153)(33,152)(34,151)(35,150)(36,149)(37,148)(38,147)(39,146)(40,145)(41,144)(42,143)(43,142)(44,141)(45,140)(46,139)(47,138)(48,137)(49,136)(50,135)(51,134)(52,133)(53,132)(54,131)(55,130)(56,129)(57,128)(58,127)(59,126)(60,125)(61,124)(62,123)(63,122)(64,121)(65,120)(66,119)(67,118)(68,117)(69,116)(70,115)(71,114)(72,113)(73,112)(74,111)(75,110)(76,109)(77,108)(78,107)(79,106)(80,105)(81,104)(82,103)(83,102)(84,101)(85,100)(86,99)(87,98)(88,97)(89,96)(90,95)(91,94)(92,93)
Polycyclic presentation:
2^3,167|a^2=c,b^2=c,b^a=bc,d^b=d^166
Conjugacy classes & character table
337 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1336, 11);
Finite Group Databasebeta