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Dic4528 #31826306
Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 347 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);(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)(66,347)(67,346)(68,345)(69,344)(70,343)(71,342)(72,341)(73,340)(74,339)(75,338)(76,337)(77,336)(78,335)(79,334)(80,333)(81,332)(82,331)(83,330)(84,329)(85,328)(86,327)(87,326)(88,325)(89,324)(90,323)(91,322)(92,321)(93,320)(94,319)(95,318)(96,317)(97,316)(98,315)(99,314)(100,313)(101,312)(102,311)(103,310)(104,309)(105,308)(106,307)(107,306)(108,305)(109,304)(110,303)(111,302)(112,301)(113,300)(114,299)(115,298)(116,297)(117,296)(118,295)(119,294)(120,293)(121,292)(122,291)(123,290)(124,289)(125,288)(126,287)(127,286)(128,285)(129,284)(130,283)(131,282)(132,281)(133,280)(134,279)(135,278)(136,277)(137,276)(138,275)(139,274)(140,273)(141,272)(142,271)(143,270)(144,269)(145,268)(146,267)(147,266)(148,265)(149,264)(150,263)(151,262)(152,261)(153,260)(154,259)(155,258)(156,257)(157,256)(158,255)(159,254)(160,253)(161,252)(162,251)(163,250)(164,249)(165,248)(166,247)(167,246)(168,245)(169,244)(170,243)(171,242)(172,241)(173,240)(174,239)(175,238)(176,237)(177,236)(178,235)(179,234)(180,233)(181,232)(182,231)(183,230)(184,229)(185,228)(186,227)(187,226)(188,225)(189,224)(190,223)(191,222)(192,221)(193,220)(194,219)(195,218)(196,217)(197,216)(198,215)(199,214)(200,213)(201,212)(202,211)(203,210)(204,209)(205,208)(206,207)
Polycyclic presentation:
2^6,283|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^282,c^b=cd,d^b=de,e^b=ef,g^b=g^282
Conjugacy classes & character table
4531 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 390);
Finite Group Databasebeta