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D12828 #72235283
Aliases
Splittings
Subgroups
32 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1076 points:
(1,2,3,4)(5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076);(2,4)(6,7)(9,1076)(10,1075)(11,1074)(12,1073)(13,1072)(14,1071)(15,1070)(16,1069)(17,1068)(18,1067)(19,1066)(20,1065)(21,1064)(22,1063)(23,1062)(24,1061)(25,1060)(26,1059)(27,1058)(28,1057)(29,1056)(30,1055)(31,1054)(32,1053)(33,1052)(34,1051)(35,1050)(36,1049)(37,1048)(38,1047)(39,1046)(40,1045)(41,1044)(42,1043)(43,1042)(44,1041)(45,1040)(46,1039)(47,1038)(48,1037)(49,1036)(50,1035)(51,1034)(52,1033)(53,1032)(54,1031)(55,1030)(56,1029)(57,1028)(58,1027)(59,1026)(60,1025)(61,1024)(62,1023)(63,1022)(64,1021)(65,1020)(66,1019)(67,1018)(68,1017)(69,1016)(70,1015)(71,1014)(72,1013)(73,1012)(74,1011)(75,1010)(76,1009)(77,1008)(78,1007)(79,1006)(80,1005)(81,1004)(82,1003)(83,1002)(84,1001)(85,1000)(86,999)(87,998)(88,997)(89,996)(90,995)(91,994)(92,993)(93,992)(94,991)(95,990)(96,989)(97,988)(98,987)(99,986)(100,985)(101,984)(102,983)(103,982)(104,981)(105,980)(106,979)(107,978)(108,977)(109,976)(110,975)(111,974)(112,973)(113,972)(114,971)(115,970)(116,969)(117,968)(118,967)(119,966)(120,965)(121,964)(122,963)(123,962)(124,961)(125,960)(126,959)(127,958)(128,957)(129,956)(130,955)(131,954)(132,953)(133,952)(134,951)(135,950)(136,949)(137,948)(138,947)(139,946)(140,945)(141,944)(142,943)(143,942)(144,941)(145,940)(146,939)(147,938)(148,937)(149,936)(150,935)(151,934)(152,933)(153,932)(154,931)(155,930)(156,929)(157,928)(158,927)(159,926)(160,925)(161,924)(162,923)(163,922)(164,921)(165,920)(166,919)(167,918)(168,917)(169,916)(170,915)(171,914)(172,913)(173,912)(174,911)(175,910)(176,909)(177,908)(178,907)(179,906)(180,905)(181,904)(182,903)(183,902)(184,901)(185,900)(186,899)(187,898)(188,897)(189,896)(190,895)(191,894)(192,893)(193,892)(194,891)(195,890)(196,889)(197,888)(198,887)(199,886)(200,885)(201,884)(202,883)(203,882)(204,881)(205,880)(206,879)(207,878)(208,877)(209,876)(210,875)(211,874)(212,873)(213,872)(214,871)(215,870)(216,869)(217,868)(218,867)(219,866)(220,865)(221,864)(222,863)(223,862)(224,861)(225,860)(226,859)(227,858)(228,857)(229,856)(230,855)(231,854)(232,853)(233,852)(234,851)(235,850)(236,849)(237,848)(238,847)(239,846)(240,845)(241,844)(242,843)(243,842)(244,841)(245,840)(246,839)(247,838)(248,837)(249,836)(250,835)(251,834)(252,833)(253,832)(254,831)(255,830)(256,829)(257,828)(258,827)(259,826)(260,825)(261,824)(262,823)(263,822)(264,821)(265,820)(266,819)(267,818)(268,817)(269,816)(270,815)(271,814)(272,813)(273,812)(274,811)(275,810)(276,809)(277,808)(278,807)(279,806)(280,805)(281,804)(282,803)(283,802)(284,801)(285,800)(286,799)(287,798)(288,797)(289,796)(290,795)(291,794)(292,793)(293,792)(294,791)(295,790)(296,789)(297,788)(298,787)(299,786)(300,785)(301,784)(302,783)(303,782)(304,781)(305,780)(306,779)(307,778)(308,777)(309,776)(310,775)(311,774)(312,773)(313,772)(314,771)(315,770)(316,769)(317,768)(318,767)(319,766)(320,765)(321,764)(322,763)(323,762)(324,761)(325,760)(326,759)(327,758)(328,757)(329,756)(330,755)(331,754)(332,753)(333,752)(334,751)(335,750)(336,749)(337,748)(338,747)(339,746)(340,745)(341,744)(342,743)(343,742)(344,741)(345,740)(346,739)(347,738)(348,737)(349,736)(350,735)(351,734)(352,733)(353,732)(354,731)(355,730)(356,729)(357,728)(358,727)(359,726)(360,725)(361,724)(362,723)(363,722)(364,721)(365,720)(366,719)(367,718)(368,717)(369,716)(370,715)(371,714)(372,713)(373,712)(374,711)(375,710)(376,709)(377,708)(378,707)(379,706)(380,705)(381,704)(382,703)(383,702)(384,701)(385,700)(386,699)(387,698)(388,697)(389,696)(390,695)(391,694)(392,693)(393,692)(394,691)(395,690)(396,689)(397,688)(398,687)(399,686)(400,685)(401,684)(402,683)(403,682)(404,681)(405,680)(406,679)(407,678)(408,677)(409,676)(410,675)(411,674)(412,673)(413,672)(414,671)(415,670)(416,669)(417,668)(418,667)(419,666)(420,665)(421,664)(422,663)(423,662)(424,661)(425,660)(426,659)(427,658)(428,657)(429,656)(430,655)(431,654)(432,653)(433,652)(434,651)(435,650)(436,649)(437,648)(438,647)(439,646)(440,645)(441,644)(442,643)(443,642)(444,641)(445,640)(446,639)(447,638)(448,637)(449,636)(450,635)(451,634)(452,633)(453,632)(454,631)(455,630)(456,629)(457,628)(458,627)(459,626)(460,625)(461,624)(462,623)(463,622)(464,621)(465,620)(466,619)(467,618)(468,617)(469,616)(470,615)(471,614)(472,613)(473,612)(474,611)(475,610)(476,609)(477,608)(478,607)(479,606)(480,605)(481,604)(482,603)(483,602)(484,601)(485,600)(486,599)(487,598)(488,597)(489,596)(490,595)(491,594)(492,593)(493,592)(494,591)(495,590)(496,589)(497,588)(498,587)(499,586)(500,585)(501,584)(502,583)(503,582)(504,581)(505,580)(506,579)(507,578)(508,577)(509,576)(510,575)(511,574)(512,573)(513,572)(514,571)(515,570)(516,569)(517,568)(518,567)(519,566)(520,565)(521,564)(522,563)(523,562)(524,561)(525,560)(526,559)(527,558)(528,557)(529,556)(530,555)(531,554)(532,553)(533,552)(534,551)(535,550)(536,549)(537,548)(538,547)(539,546)(540,545)(541,544)(542,543)
Polycyclic presentation:
2^3,3,1069|b^2=c,b^a=bc,d^a=d^2,e^a=e^1068
Conjugacy classes & character table
6417 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");;
gap> coll := SingleCollector(F, [2, 2, 2, 3, 1069]);;
gap> SetPower(coll, 2, F.3);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 4, 1, F.4^2);;
gap> SetConjugate(coll, 5, 1, F.5^1068);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta