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Dic4688 #34035970
Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 357 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);(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)(66,357)(67,356)(68,355)(69,354)(70,353)(71,352)(72,351)(73,350)(74,349)(75,348)(76,347)(77,346)(78,345)(79,344)(80,343)(81,342)(82,341)(83,340)(84,339)(85,338)(86,337)(87,336)(88,335)(89,334)(90,333)(91,332)(92,331)(93,330)(94,329)(95,328)(96,327)(97,326)(98,325)(99,324)(100,323)(101,322)(102,321)(103,320)(104,319)(105,318)(106,317)(107,316)(108,315)(109,314)(110,313)(111,312)(112,311)(113,310)(114,309)(115,308)(116,307)(117,306)(118,305)(119,304)(120,303)(121,302)(122,301)(123,300)(124,299)(125,298)(126,297)(127,296)(128,295)(129,294)(130,293)(131,292)(132,291)(133,290)(134,289)(135,288)(136,287)(137,286)(138,285)(139,284)(140,283)(141,282)(142,281)(143,280)(144,279)(145,278)(146,277)(147,276)(148,275)(149,274)(150,273)(151,272)(152,271)(153,270)(154,269)(155,268)(156,267)(157,266)(158,265)(159,264)(160,263)(161,262)(162,261)(163,260)(164,259)(165,258)(166,257)(167,256)(168,255)(169,254)(170,253)(171,252)(172,251)(173,250)(174,249)(175,248)(176,247)(177,246)(178,245)(179,244)(180,243)(181,242)(182,241)(183,240)(184,239)(185,238)(186,237)(187,236)(188,235)(189,234)(190,233)(191,232)(192,231)(193,230)(194,229)(195,228)(196,227)(197,226)(198,225)(199,224)(200,223)(201,222)(202,221)(203,220)(204,219)(205,218)(206,217)(207,216)(208,215)(209,214)(210,213)(211,212)
Polycyclic presentation:
2^6,293|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^292,c^b=cd,d^b=de,e^b=ef,g^b=g^292
Conjugacy classes & character table
4691 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 390);
Finite Group Databasebeta