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D13793 #42119905
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1074 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,1074)(16,1073)(17,1072)(18,1071)(19,1070)(20,1069)(21,1068)(22,1067)(23,1066)(24,1065)(25,1064)(26,1063)(27,1062)(28,1061)(29,1060)(30,1059)(31,1058)(32,1057)(33,1056)(34,1055)(35,1054)(36,1053)(37,1052)(38,1051)(39,1050)(40,1049)(41,1048)(42,1047)(43,1046)(44,1045)(45,1044)(46,1043)(47,1042)(48,1041)(49,1040)(50,1039)(51,1038)(52,1037)(53,1036)(54,1035)(55,1034)(56,1033)(57,1032)(58,1031)(59,1030)(60,1029)(61,1028)(62,1027)(63,1026)(64,1025)(65,1024)(66,1023)(67,1022)(68,1021)(69,1020)(70,1019)(71,1018)(72,1017)(73,1016)(74,1015)(75,1014)(76,1013)(77,1012)(78,1011)(79,1010)(80,1009)(81,1008)(82,1007)(83,1006)(84,1005)(85,1004)(86,1003)(87,1002)(88,1001)(89,1000)(90,999)(91,998)(92,997)(93,996)(94,995)(95,994)(96,993)(97,992)(98,991)(99,990)(100,989)(101,988)(102,987)(103,986)(104,985)(105,984)(106,983)(107,982)(108,981)(109,980)(110,979)(111,978)(112,977)(113,976)(114,975)(115,974)(116,973)(117,972)(118,971)(119,970)(120,969)(121,968)(122,967)(123,966)(124,965)(125,964)(126,963)(127,962)(128,961)(129,960)(130,959)(131,958)(132,957)(133,956)(134,955)(135,954)(136,953)(137,952)(138,951)(139,950)(140,949)(141,948)(142,947)(143,946)(144,945)(145,944)(146,943)(147,942)(148,941)(149,940)(150,939)(151,938)(152,937)(153,936)(154,935)(155,934)(156,933)(157,932)(158,931)(159,930)(160,929)(161,928)(162,927)(163,926)(164,925)(165,924)(166,923)(167,922)(168,921)(169,920)(170,919)(171,918)(172,917)(173,916)(174,915)(175,914)(176,913)(177,912)(178,911)(179,910)(180,909)(181,908)(182,907)(183,906)(184,905)(185,904)(186,903)(187,902)(188,901)(189,900)(190,899)(191,898)(192,897)(193,896)(194,895)(195,894)(196,893)(197,892)(198,891)(199,890)(200,889)(201,888)(202,887)(203,886)(204,885)(205,884)(206,883)(207,882)(208,881)(209,880)(210,879)(211,878)(212,877)(213,876)(214,875)(215,874)(216,873)(217,872)(218,871)(219,870)(220,869)(221,868)(222,867)(223,866)(224,865)(225,864)(226,863)(227,862)(228,861)(229,860)(230,859)(231,858)(232,857)(233,856)(234,855)(235,854)(236,853)(237,852)(238,851)(239,850)(240,849)(241,848)(242,847)(243,846)(244,845)(245,844)(246,843)(247,842)(248,841)(249,840)(250,839)(251,838)(252,837)(253,836)(254,835)(255,834)(256,833)(257,832)(258,831)(259,830)(260,829)(261,828)(262,827)(263,826)(264,825)(265,824)(266,823)(267,822)(268,821)(269,820)(270,819)(271,818)(272,817)(273,816)(274,815)(275,814)(276,813)(277,812)(278,811)(279,810)(280,809)(281,808)(282,807)(283,806)(284,805)(285,804)(286,803)(287,802)(288,801)(289,800)(290,799)(291,798)(292,797)(293,796)(294,795)(295,794)(296,793)(297,792)(298,791)(299,790)(300,789)(301,788)(302,787)(303,786)(304,785)(305,784)(306,783)(307,782)(308,781)(309,780)(310,779)(311,778)(312,777)(313,776)(314,775)(315,774)(316,773)(317,772)(318,771)(319,770)(320,769)(321,768)(322,767)(323,766)(324,765)(325,764)(326,763)(327,762)(328,761)(329,760)(330,759)(331,758)(332,757)(333,756)(334,755)(335,754)(336,753)(337,752)(338,751)(339,750)(340,749)(341,748)(342,747)(343,746)(344,745)(345,744)(346,743)(347,742)(348,741)(349,740)(350,739)(351,738)(352,737)(353,736)(354,735)(355,734)(356,733)(357,732)(358,731)(359,730)(360,729)(361,728)(362,727)(363,726)(364,725)(365,724)(366,723)(367,722)(368,721)(369,720)(370,719)(371,718)(372,717)(373,716)(374,715)(375,714)(376,713)(377,712)(378,711)(379,710)(380,709)(381,708)(382,707)(383,706)(384,705)(385,704)(386,703)(387,702)(388,701)(389,700)(390,699)(391,698)(392,697)(393,696)(394,695)(395,694)(396,693)(397,692)(398,691)(399,690)(400,689)(401,688)(402,687)(403,686)(404,685)(405,684)(406,683)(407,682)(408,681)(409,680)(410,679)(411,678)(412,677)(413,676)(414,675)(415,674)(416,673)(417,672)(418,671)(419,670)(420,669)(421,668)(422,667)(423,666)(424,665)(425,664)(426,663)(427,662)(428,661)(429,660)(430,659)(431,658)(432,657)(433,656)(434,655)(435,654)(436,653)(437,652)(438,651)(439,650)(440,649)(441,648)(442,647)(443,646)(444,645)(445,644)(446,643)(447,642)(448,641)(449,640)(450,639)(451,638)(452,637)(453,636)(454,635)(455,634)(456,633)(457,632)(458,631)(459,630)(460,629)(461,628)(462,627)(463,626)(464,625)(465,624)(466,623)(467,622)(468,621)(469,620)(470,619)(471,618)(472,617)(473,616)(474,615)(475,614)(476,613)(477,612)(478,611)(479,610)(480,609)(481,608)(482,607)(483,606)(484,605)(485,604)(486,603)(487,602)(488,601)(489,600)(490,599)(491,598)(492,597)(493,596)(494,595)(495,594)(496,593)(497,592)(498,591)(499,590)(500,589)(501,588)(502,587)(503,586)(504,585)(505,584)(506,583)(507,582)(508,581)(509,580)(510,579)(511,578)(512,577)(513,576)(514,575)(515,574)(516,573)(517,572)(518,571)(519,570)(520,569)(521,568)(522,567)(523,566)(524,565)(525,564)(526,563)(527,562)(528,561)(529,560)(530,559)(531,558)(532,557)(533,556)(534,555)(535,554)(536,553)(537,552)(538,551)(539,550)(540,549)(541,548)(542,547)(543,546)(544,545)
Polycyclic presentation:
2,13,1061|b^a=b^12,c^a=c^1060
Conjugacy classes & character table
6898 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27586, 3);
Finite Group Databasebeta