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D5832 #72211893
Aliases
Splittings
Subgroups
77 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 737 points:
(1,2,3,4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737);(2,8)(3,7)(4,6)(10,737)(11,736)(12,735)(13,734)(14,733)(15,732)(16,731)(17,730)(18,729)(19,728)(20,727)(21,726)(22,725)(23,724)(24,723)(25,722)(26,721)(27,720)(28,719)(29,718)(30,717)(31,716)(32,715)(33,714)(34,713)(35,712)(36,711)(37,710)(38,709)(39,708)(40,707)(41,706)(42,705)(43,704)(44,703)(45,702)(46,701)(47,700)(48,699)(49,698)(50,697)(51,696)(52,695)(53,694)(54,693)(55,692)(56,691)(57,690)(58,689)(59,688)(60,687)(61,686)(62,685)(63,684)(64,683)(65,682)(66,681)(67,680)(68,679)(69,678)(70,677)(71,676)(72,675)(73,674)(74,673)(75,672)(76,671)(77,670)(78,669)(79,668)(80,667)(81,666)(82,665)(83,664)(84,663)(85,662)(86,661)(87,660)(88,659)(89,658)(90,657)(91,656)(92,655)(93,654)(94,653)(95,652)(96,651)(97,650)(98,649)(99,648)(100,647)(101,646)(102,645)(103,644)(104,643)(105,642)(106,641)(107,640)(108,639)(109,638)(110,637)(111,636)(112,635)(113,634)(114,633)(115,632)(116,631)(117,630)(118,629)(119,628)(120,627)(121,626)(122,625)(123,624)(124,623)(125,622)(126,621)(127,620)(128,619)(129,618)(130,617)(131,616)(132,615)(133,614)(134,613)(135,612)(136,611)(137,610)(138,609)(139,608)(140,607)(141,606)(142,605)(143,604)(144,603)(145,602)(146,601)(147,600)(148,599)(149,598)(150,597)(151,596)(152,595)(153,594)(154,593)(155,592)(156,591)(157,590)(158,589)(159,588)(160,587)(161,586)(162,585)(163,584)(164,583)(165,582)(166,581)(167,580)(168,579)(169,578)(170,577)(171,576)(172,575)(173,574)(174,573)(175,572)(176,571)(177,570)(178,569)(179,568)(180,567)(181,566)(182,565)(183,564)(184,563)(185,562)(186,561)(187,560)(188,559)(189,558)(190,557)(191,556)(192,555)(193,554)(194,553)(195,552)(196,551)(197,550)(198,549)(199,548)(200,547)(201,546)(202,545)(203,544)(204,543)(205,542)(206,541)(207,540)(208,539)(209,538)(210,537)(211,536)(212,535)(213,534)(214,533)(215,532)(216,531)(217,530)(218,529)(219,528)(220,527)(221,526)(222,525)(223,524)(224,523)(225,522)(226,521)(227,520)(228,519)(229,518)(230,517)(231,516)(232,515)(233,514)(234,513)(235,512)(236,511)(237,510)(238,509)(239,508)(240,507)(241,506)(242,505)(243,504)(244,503)(245,502)(246,501)(247,500)(248,499)(249,498)(250,497)(251,496)(252,495)(253,494)(254,493)(255,492)(256,491)(257,490)(258,489)(259,488)(260,487)(261,486)(262,485)(263,484)(264,483)(265,482)(266,481)(267,480)(268,479)(269,478)(270,477)(271,476)(272,475)(273,474)(274,473)(275,472)(276,471)(277,470)(278,469)(279,468)(280,467)(281,466)(282,465)(283,464)(284,463)(285,462)(286,461)(287,460)(288,459)(289,458)(290,457)(291,456)(292,455)(293,454)(294,453)(295,452)(296,451)(297,450)(298,449)(299,448)(300,447)(301,446)(302,445)(303,444)(304,443)(305,442)(306,441)(307,440)(308,439)(309,438)(310,437)(311,436)(312,435)(313,434)(314,433)(315,432)(316,431)(317,430)(318,429)(319,428)(320,427)(321,426)(322,425)(323,424)(324,423)(325,422)(326,421)(327,420)(328,419)(329,418)(330,417)(331,416)(332,415)(333,414)(334,413)(335,412)(336,411)(337,410)(338,409)(339,408)(340,407)(341,406)(342,405)(343,404)(344,403)(345,402)(346,401)(347,400)(348,399)(349,398)(350,397)(351,396)(352,395)(353,394)(354,393)(355,392)(356,391)(357,390)(358,389)(359,388)(360,387)(361,386)(362,385)(363,384)(364,383)(365,382)(366,381)(367,380)(368,379)(369,378)(370,377)(371,376)(372,375)(373,374)
Polycyclic presentation:
2^4,3^6|b^2=cd,c^2=d,e^3=f,f^3=g,g^3=h,h^3=i,i^3=j,b^a=bc,c^a=cd,e^a=e^2f^2g^2h^2i^2j^2,f^a=f^2g^2h^2i^2j^2,g^a=g^2h^2i^2j^2,h^a=h^2i^2j^2,i^a=i^2j^2,j^a=j^2
Conjugacy classes & character table
2919 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i", "j");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 3, 3, 3, 3, 3, 3]);;
gap> SetPower(coll, 2, F.3*F.4);;
gap> SetPower(coll, 3, F.4);;
gap> SetPower(coll, 5, F.6);;
gap> SetPower(coll, 6, F.7);;
gap> SetPower(coll, 7, F.8);;
gap> SetPower(coll, 8, F.9);;
gap> SetPower(coll, 9, F.10);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 3, 1, F.3*F.4);;
gap> SetConjugate(coll, 5, 1, F.5^2*F.6^2*F.7^2*F.8^2*F.9^2*F.10^2);;
gap> SetConjugate(coll, 6, 1, F.6^2*F.7^2*F.8^2*F.9^2*F.10^2);;
gap> SetConjugate(coll, 7, 1, F.7^2*F.8^2*F.9^2*F.10^2);;
gap> SetConjugate(coll, 8, 1, F.8^2*F.9^2*F.10^2);;
gap> SetConjugate(coll, 9, 1, F.9^2*F.10^2);;
gap> SetConjugate(coll, 10, 1, F.10^2);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta