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Dic5339 #36319481
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 304 points:
(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304);(1,3,2,4)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(25,304)(26,303)(27,302)(28,301)(29,300)(30,299)(31,298)(32,297)(33,296)(34,295)(35,294)(36,293)(37,292)(38,291)(39,290)(40,289)(41,288)(42,287)(43,286)(44,285)(45,284)(46,283)(47,282)(48,281)(49,280)(50,279)(51,278)(52,277)(53,276)(54,275)(55,274)(56,273)(57,272)(58,271)(59,270)(60,269)(61,268)(62,267)(63,266)(64,265)(65,264)(66,263)(67,262)(68,261)(69,260)(70,259)(71,258)(72,257)(73,256)(74,255)(75,254)(76,253)(77,252)(78,251)(79,250)(80,249)(81,248)(82,247)(83,246)(84,245)(85,244)(86,243)(87,242)(88,241)(89,240)(90,239)(91,238)(92,237)(93,236)(94,235)(95,234)(96,233)(97,232)(98,231)(99,230)(100,229)(101,228)(102,227)(103,226)(104,225)(105,224)(106,223)(107,222)(108,221)(109,220)(110,219)(111,218)(112,217)(113,216)(114,215)(115,214)(116,213)(117,212)(118,211)(119,210)(120,209)(121,208)(122,207)(123,206)(124,205)(125,204)(126,203)(127,202)(128,201)(129,200)(130,199)(131,198)(132,197)(133,196)(134,195)(135,194)(136,193)(137,192)(138,191)(139,190)(140,189)(141,188)(142,187)(143,186)(144,185)(145,184)(146,183)(147,182)(148,181)(149,180)(150,179)(151,178)(152,177)(153,176)(154,175)(155,174)(156,173)(157,172)(158,171)(159,170)(160,169)(161,168)(162,167)(163,166)(164,165)
Polycyclic presentation:
2,19,281,2|a^2=d,b^a=b^18,c^a=c^280
Conjugacy classes & character table
5342 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21356, 4);
Finite Group Databasebeta