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D13429 #41001684
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1046 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,1046)(16,1045)(17,1044)(18,1043)(19,1042)(20,1041)(21,1040)(22,1039)(23,1038)(24,1037)(25,1036)(26,1035)(27,1034)(28,1033)(29,1032)(30,1031)(31,1030)(32,1029)(33,1028)(34,1027)(35,1026)(36,1025)(37,1024)(38,1023)(39,1022)(40,1021)(41,1020)(42,1019)(43,1018)(44,1017)(45,1016)(46,1015)(47,1014)(48,1013)(49,1012)(50,1011)(51,1010)(52,1009)(53,1008)(54,1007)(55,1006)(56,1005)(57,1004)(58,1003)(59,1002)(60,1001)(61,1000)(62,999)(63,998)(64,997)(65,996)(66,995)(67,994)(68,993)(69,992)(70,991)(71,990)(72,989)(73,988)(74,987)(75,986)(76,985)(77,984)(78,983)(79,982)(80,981)(81,980)(82,979)(83,978)(84,977)(85,976)(86,975)(87,974)(88,973)(89,972)(90,971)(91,970)(92,969)(93,968)(94,967)(95,966)(96,965)(97,964)(98,963)(99,962)(100,961)(101,960)(102,959)(103,958)(104,957)(105,956)(106,955)(107,954)(108,953)(109,952)(110,951)(111,950)(112,949)(113,948)(114,947)(115,946)(116,945)(117,944)(118,943)(119,942)(120,941)(121,940)(122,939)(123,938)(124,937)(125,936)(126,935)(127,934)(128,933)(129,932)(130,931)(131,930)(132,929)(133,928)(134,927)(135,926)(136,925)(137,924)(138,923)(139,922)(140,921)(141,920)(142,919)(143,918)(144,917)(145,916)(146,915)(147,914)(148,913)(149,912)(150,911)(151,910)(152,909)(153,908)(154,907)(155,906)(156,905)(157,904)(158,903)(159,902)(160,901)(161,900)(162,899)(163,898)(164,897)(165,896)(166,895)(167,894)(168,893)(169,892)(170,891)(171,890)(172,889)(173,888)(174,887)(175,886)(176,885)(177,884)(178,883)(179,882)(180,881)(181,880)(182,879)(183,878)(184,877)(185,876)(186,875)(187,874)(188,873)(189,872)(190,871)(191,870)(192,869)(193,868)(194,867)(195,866)(196,865)(197,864)(198,863)(199,862)(200,861)(201,860)(202,859)(203,858)(204,857)(205,856)(206,855)(207,854)(208,853)(209,852)(210,851)(211,850)(212,849)(213,848)(214,847)(215,846)(216,845)(217,844)(218,843)(219,842)(220,841)(221,840)(222,839)(223,838)(224,837)(225,836)(226,835)(227,834)(228,833)(229,832)(230,831)(231,830)(232,829)(233,828)(234,827)(235,826)(236,825)(237,824)(238,823)(239,822)(240,821)(241,820)(242,819)(243,818)(244,817)(245,816)(246,815)(247,814)(248,813)(249,812)(250,811)(251,810)(252,809)(253,808)(254,807)(255,806)(256,805)(257,804)(258,803)(259,802)(260,801)(261,800)(262,799)(263,798)(264,797)(265,796)(266,795)(267,794)(268,793)(269,792)(270,791)(271,790)(272,789)(273,788)(274,787)(275,786)(276,785)(277,784)(278,783)(279,782)(280,781)(281,780)(282,779)(283,778)(284,777)(285,776)(286,775)(287,774)(288,773)(289,772)(290,771)(291,770)(292,769)(293,768)(294,767)(295,766)(296,765)(297,764)(298,763)(299,762)(300,761)(301,760)(302,759)(303,758)(304,757)(305,756)(306,755)(307,754)(308,753)(309,752)(310,751)(311,750)(312,749)(313,748)(314,747)(315,746)(316,745)(317,744)(318,743)(319,742)(320,741)(321,740)(322,739)(323,738)(324,737)(325,736)(326,735)(327,734)(328,733)(329,732)(330,731)(331,730)(332,729)(333,728)(334,727)(335,726)(336,725)(337,724)(338,723)(339,722)(340,721)(341,720)(342,719)(343,718)(344,717)(345,716)(346,715)(347,714)(348,713)(349,712)(350,711)(351,710)(352,709)(353,708)(354,707)(355,706)(356,705)(357,704)(358,703)(359,702)(360,701)(361,700)(362,699)(363,698)(364,697)(365,696)(366,695)(367,694)(368,693)(369,692)(370,691)(371,690)(372,689)(373,688)(374,687)(375,686)(376,685)(377,684)(378,683)(379,682)(380,681)(381,680)(382,679)(383,678)(384,677)(385,676)(386,675)(387,674)(388,673)(389,672)(390,671)(391,670)(392,669)(393,668)(394,667)(395,666)(396,665)(397,664)(398,663)(399,662)(400,661)(401,660)(402,659)(403,658)(404,657)(405,656)(406,655)(407,654)(408,653)(409,652)(410,651)(411,650)(412,649)(413,648)(414,647)(415,646)(416,645)(417,644)(418,643)(419,642)(420,641)(421,640)(422,639)(423,638)(424,637)(425,636)(426,635)(427,634)(428,633)(429,632)(430,631)(431,630)(432,629)(433,628)(434,627)(435,626)(436,625)(437,624)(438,623)(439,622)(440,621)(441,620)(442,619)(443,618)(444,617)(445,616)(446,615)(447,614)(448,613)(449,612)(450,611)(451,610)(452,609)(453,608)(454,607)(455,606)(456,605)(457,604)(458,603)(459,602)(460,601)(461,600)(462,599)(463,598)(464,597)(465,596)(466,595)(467,594)(468,593)(469,592)(470,591)(471,590)(472,589)(473,588)(474,587)(475,586)(476,585)(477,584)(478,583)(479,582)(480,581)(481,580)(482,579)(483,578)(484,577)(485,576)(486,575)(487,574)(488,573)(489,572)(490,571)(491,570)(492,569)(493,568)(494,567)(495,566)(496,565)(497,564)(498,563)(499,562)(500,561)(501,560)(502,559)(503,558)(504,557)(505,556)(506,555)(507,554)(508,553)(509,552)(510,551)(511,550)(512,549)(513,548)(514,547)(515,546)(516,545)(517,544)(518,543)(519,542)(520,541)(521,540)(522,539)(523,538)(524,537)(525,536)(526,535)(527,534)(528,533)(529,532)(530,531)
Polycyclic presentation:
2,13,1033|b^a=b^12,c^a=c^1032
Conjugacy classes & character table
6716 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26858, 3);
Finite Group Databasebeta