← Prev (#31773737) Next (#31773739) →
Dic4336 #31773738
Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 335 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);(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)(66,335)(67,334)(68,333)(69,332)(70,331)(71,330)(72,329)(73,328)(74,327)(75,326)(76,325)(77,324)(78,323)(79,322)(80,321)(81,320)(82,319)(83,318)(84,317)(85,316)(86,315)(87,314)(88,313)(89,312)(90,311)(91,310)(92,309)(93,308)(94,307)(95,306)(96,305)(97,304)(98,303)(99,302)(100,301)(101,300)(102,299)(103,298)(104,297)(105,296)(106,295)(107,294)(108,293)(109,292)(110,291)(111,290)(112,289)(113,288)(114,287)(115,286)(116,285)(117,284)(118,283)(119,282)(120,281)(121,280)(122,279)(123,278)(124,277)(125,276)(126,275)(127,274)(128,273)(129,272)(130,271)(131,270)(132,269)(133,268)(134,267)(135,266)(136,265)(137,264)(138,263)(139,262)(140,261)(141,260)(142,259)(143,258)(144,257)(145,256)(146,255)(147,254)(148,253)(149,252)(150,251)(151,250)(152,249)(153,248)(154,247)(155,246)(156,245)(157,244)(158,243)(159,242)(160,241)(161,240)(162,239)(163,238)(164,237)(165,236)(166,235)(167,234)(168,233)(169,232)(170,231)(171,230)(172,229)(173,228)(174,227)(175,226)(176,225)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)(183,218)(184,217)(185,216)(186,215)(187,214)(188,213)(189,212)(190,211)(191,210)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)(198,203)(199,202)(200,201)
Polycyclic presentation:
2^6,271|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^270,c^b=cd,d^b=de,e^b=ef,g^b=g^270
Conjugacy classes & character table
4339 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17344, 390);
Finite Group Databasebeta