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Dic4496 #31823304
Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 345 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);(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)(66,345)(67,344)(68,343)(69,342)(70,341)(71,340)(72,339)(73,338)(74,337)(75,336)(76,335)(77,334)(78,333)(79,332)(80,331)(81,330)(82,329)(83,328)(84,327)(85,326)(86,325)(87,324)(88,323)(89,322)(90,321)(91,320)(92,319)(93,318)(94,317)(95,316)(96,315)(97,314)(98,313)(99,312)(100,311)(101,310)(102,309)(103,308)(104,307)(105,306)(106,305)(107,304)(108,303)(109,302)(110,301)(111,300)(112,299)(113,298)(114,297)(115,296)(116,295)(117,294)(118,293)(119,292)(120,291)(121,290)(122,289)(123,288)(124,287)(125,286)(126,285)(127,284)(128,283)(129,282)(130,281)(131,280)(132,279)(133,278)(134,277)(135,276)(136,275)(137,274)(138,273)(139,272)(140,271)(141,270)(142,269)(143,268)(144,267)(145,266)(146,265)(147,264)(148,263)(149,262)(150,261)(151,260)(152,259)(153,258)(154,257)(155,256)(156,255)(157,254)(158,253)(159,252)(160,251)(161,250)(162,249)(163,248)(164,247)(165,246)(166,245)(167,244)(168,243)(169,242)(170,241)(171,240)(172,239)(173,238)(174,237)(175,236)(176,235)(177,234)(178,233)(179,232)(180,231)(181,230)(182,229)(183,228)(184,227)(185,226)(186,225)(187,224)(188,223)(189,222)(190,221)(191,220)(192,219)(193,218)(194,217)(195,216)(196,215)(197,214)(198,213)(199,212)(200,211)(201,210)(202,209)(203,208)(204,207)(205,206)
Polycyclic presentation:
2^6,281|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^280,c^b=cd,d^b=de,e^b=ef,g^b=g^280
Conjugacy classes & character table
4499 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 390);
Finite Group Databasebeta