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D10688 #36322351
Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 231 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)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231);(2,64)(3,63)(4,62)(5,61)(6,60)(7,59)(8,58)(9,57)(10,56)(11,55)(12,54)(13,53)(14,52)(15,51)(16,50)(17,49)(18,48)(19,47)(20,46)(21,45)(22,44)(23,43)(24,42)(25,41)(26,40)(27,39)(28,38)(29,37)(30,36)(31,35)(32,34)(66,231)(67,230)(68,229)(69,228)(70,227)(71,226)(72,225)(73,224)(74,223)(75,222)(76,221)(77,220)(78,219)(79,218)(80,217)(81,216)(82,215)(83,214)(84,213)(85,212)(86,211)(87,210)(88,209)(89,208)(90,207)(91,206)(92,205)(93,204)(94,203)(95,202)(96,201)(97,200)(98,199)(99,198)(100,197)(101,196)(102,195)(103,194)(104,193)(105,192)(106,191)(107,190)(108,189)(109,188)(110,187)(111,186)(112,185)(113,184)(114,183)(115,182)(116,181)(117,180)(118,179)(119,178)(120,177)(121,176)(122,175)(123,174)(124,173)(125,172)(126,171)(127,170)(128,169)(129,168)(130,167)(131,166)(132,165)(133,164)(134,163)(135,162)(136,161)(137,160)(138,159)(139,158)(140,157)(141,156)(142,155)(143,154)(144,153)(145,152)(146,151)(147,150)(148,149)
Polycyclic presentation:
2^7,167|c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,h^a=h^166,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^166
Conjugacy classes & character table
5347 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21376, 2723);
Finite Group Databasebeta