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Dic5008 #34093993
Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 377 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)(33,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377);(1,33,17,49)(2,34,18,50)(3,35,19,51)(4,36,20,52)(5,37,21,53)(6,38,22,54)(7,39,23,55)(8,40,24,56)(9,41,25,57)(10,42,26,58)(11,43,27,59)(12,44,28,60)(13,45,29,61)(14,46,30,62)(15,47,31,63)(16,48,32,64)(66,377)(67,376)(68,375)(69,374)(70,373)(71,372)(72,371)(73,370)(74,369)(75,368)(76,367)(77,366)(78,365)(79,364)(80,363)(81,362)(82,361)(83,360)(84,359)(85,358)(86,357)(87,356)(88,355)(89,354)(90,353)(91,352)(92,351)(93,350)(94,349)(95,348)(96,347)(97,346)(98,345)(99,344)(100,343)(101,342)(102,341)(103,340)(104,339)(105,338)(106,337)(107,336)(108,335)(109,334)(110,333)(111,332)(112,331)(113,330)(114,329)(115,328)(116,327)(117,326)(118,325)(119,324)(120,323)(121,322)(122,321)(123,320)(124,319)(125,318)(126,317)(127,316)(128,315)(129,314)(130,313)(131,312)(132,311)(133,310)(134,309)(135,308)(136,307)(137,306)(138,305)(139,304)(140,303)(141,302)(142,301)(143,300)(144,299)(145,298)(146,297)(147,296)(148,295)(149,294)(150,293)(151,292)(152,291)(153,290)(154,289)(155,288)(156,287)(157,286)(158,285)(159,284)(160,283)(161,282)(162,281)(163,280)(164,279)(165,278)(166,277)(167,276)(168,275)(169,274)(170,273)(171,272)(172,271)(173,270)(174,269)(175,268)(176,267)(177,266)(178,265)(179,264)(180,263)(181,262)(182,261)(183,260)(184,259)(185,258)(186,257)(187,256)(188,255)(189,254)(190,253)(191,252)(192,251)(193,250)(194,249)(195,248)(196,247)(197,246)(198,245)(199,244)(200,243)(201,242)(202,241)(203,240)(204,239)(205,238)(206,237)(207,236)(208,235)(209,234)(210,233)(211,232)(212,231)(213,230)(214,229)(215,228)(216,227)(217,226)(218,225)(219,224)(220,223)(221,222)
Polycyclic presentation:
2^6,313|a^2=f,b^2=f,c^2=de,d^2=ef,e^2=f,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^312,c^b=cd,d^b=de,e^b=ef,g^b=g^312
Conjugacy classes & character table
5011 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20032, 390);
Finite Group Databasebeta