← Prev (#44446013) Next (#44446015) →
Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1070 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);(4,9)(5,8)(6,7)(11,1070)(12,1069)(13,1068)(14,1067)(15,1066)(16,1065)(17,1064)(18,1063)(19,1062)(20,1061)(21,1060)(22,1059)(23,1058)(24,1057)(25,1056)(26,1055)(27,1054)(28,1053)(29,1052)(30,1051)(31,1050)(32,1049)(33,1048)(34,1047)(35,1046)(36,1045)(37,1044)(38,1043)(39,1042)(40,1041)(41,1040)(42,1039)(43,1038)(44,1037)(45,1036)(46,1035)(47,1034)(48,1033)(49,1032)(50,1031)(51,1030)(52,1029)(53,1028)(54,1027)(55,1026)(56,1025)(57,1024)(58,1023)(59,1022)(60,1021)(61,1020)(62,1019)(63,1018)(64,1017)(65,1016)(66,1015)(67,1014)(68,1013)(69,1012)(70,1011)(71,1010)(72,1009)(73,1008)(74,1007)(75,1006)(76,1005)(77,1004)(78,1003)(79,1002)(80,1001)(81,1000)(82,999)(83,998)(84,997)(85,996)(86,995)(87,994)(88,993)(89,992)(90,991)(91,990)(92,989)(93,988)(94,987)(95,986)(96,985)(97,984)(98,983)(99,982)(100,981)(101,980)(102,979)(103,978)(104,977)(105,976)(106,975)(107,974)(108,973)(109,972)(110,971)(111,970)(112,969)(113,968)(114,967)(115,966)(116,965)(117,964)(118,963)(119,962)(120,961)(121,960)(122,959)(123,958)(124,957)(125,956)(126,955)(127,954)(128,953)(129,952)(130,951)(131,950)(132,949)(133,948)(134,947)(135,946)(136,945)(137,944)(138,943)(139,942)(140,941)(141,940)(142,939)(143,938)(144,937)(145,936)(146,935)(147,934)(148,933)(149,932)(150,931)(151,930)(152,929)(153,928)(154,927)(155,926)(156,925)(157,924)(158,923)(159,922)(160,921)(161,920)(162,919)(163,918)(164,917)(165,916)(166,915)(167,914)(168,913)(169,912)(170,911)(171,910)(172,909)(173,908)(174,907)(175,906)(176,905)(177,904)(178,903)(179,902)(180,901)(181,900)(182,899)(183,898)(184,897)(185,896)(186,895)(187,894)(188,893)(189,892)(190,891)(191,890)(192,889)(193,888)(194,887)(195,886)(196,885)(197,884)(198,883)(199,882)(200,881)(201,880)(202,879)(203,878)(204,877)(205,876)(206,875)(207,874)(208,873)(209,872)(210,871)(211,870)(212,869)(213,868)(214,867)(215,866)(216,865)(217,864)(218,863)(219,862)(220,861)(221,860)(222,859)(223,858)(224,857)(225,856)(226,855)(227,854)(228,853)(229,852)(230,851)(231,850)(232,849)(233,848)(234,847)(235,846)(236,845)(237,844)(238,843)(239,842)(240,841)(241,840)(242,839)(243,838)(244,837)(245,836)(246,835)(247,834)(248,833)(249,832)(250,831)(251,830)(252,829)(253,828)(254,827)(255,826)(256,825)(257,824)(258,823)(259,822)(260,821)(261,820)(262,819)(263,818)(264,817)(265,816)(266,815)(267,814)(268,813)(269,812)(270,811)(271,810)(272,809)(273,808)(274,807)(275,806)(276,805)(277,804)(278,803)(279,802)(280,801)(281,800)(282,799)(283,798)(284,797)(285,796)(286,795)(287,794)(288,793)(289,792)(290,791)(291,790)(292,789)(293,788)(294,787)(295,786)(296,785)(297,784)(298,783)(299,782)(300,781)(301,780)(302,779)(303,778)(304,777)(305,776)(306,775)(307,774)(308,773)(309,772)(310,771)(311,770)(312,769)(313,768)(314,767)(315,766)(316,765)(317,764)(318,763)(319,762)(320,761)(321,760)(322,759)(323,758)(324,757)(325,756)(326,755)(327,754)(328,753)(329,752)(330,751)(331,750)(332,749)(333,748)(334,747)(335,746)(336,745)(337,744)(338,743)(339,742)(340,741)(341,740)(342,739)(343,738)(344,737)(345,736)(346,735)(347,734)(348,733)(349,732)(350,731)(351,730)(352,729)(353,728)(354,727)(355,726)(356,725)(357,724)(358,723)(359,722)(360,721)(361,720)(362,719)(363,718)(364,717)(365,716)(366,715)(367,714)(368,713)(369,712)(370,711)(371,710)(372,709)(373,708)(374,707)(375,706)(376,705)(377,704)(378,703)(379,702)(380,701)(381,700)(382,699)(383,698)(384,697)(385,696)(386,695)(387,694)(388,693)(389,692)(390,691)(391,690)(392,689)(393,688)(394,687)(395,686)(396,685)(397,684)(398,683)(399,682)(400,681)(401,680)(402,679)(403,678)(404,677)(405,676)(406,675)(407,674)(408,673)(409,672)(410,671)(411,670)(412,669)(413,668)(414,667)(415,666)(416,665)(417,664)(418,663)(419,662)(420,661)(421,660)(422,659)(423,658)(424,657)(425,656)(426,655)(427,654)(428,653)(429,652)(430,651)(431,650)(432,649)(433,648)(434,647)(435,646)(436,645)(437,644)(438,643)(439,642)(440,641)(441,640)(442,639)(443,638)(444,637)(445,636)(446,635)(447,634)(448,633)(449,632)(450,631)(451,630)(452,629)(453,628)(454,627)(455,626)(456,625)(457,624)(458,623)(459,622)(460,621)(461,620)(462,619)(463,618)(464,617)(465,616)(466,615)(467,614)(468,613)(469,612)(470,611)(471,610)(472,609)(473,608)(474,607)(475,606)(476,605)(477,604)(478,603)(479,602)(480,601)(481,600)(482,599)(483,598)(484,597)(485,596)(486,595)(487,594)(488,593)(489,592)(490,591)(491,590)(492,589)(493,588)(494,587)(495,586)(496,585)(497,584)(498,583)(499,582)(500,581)(501,580)(502,579)(503,578)(504,577)(505,576)(506,575)(507,574)(508,573)(509,572)(510,571)(511,570)(512,569)(513,568)(514,567)(515,566)(516,565)(517,564)(518,563)(519,562)(520,561)(521,560)(522,559)(523,558)(524,557)(525,556)(526,555)(527,554)(528,553)(529,552)(530,551)(531,550)(532,549)(533,548)(534,547)(535,546)(536,545)(537,544)(538,543)(539,542)(540,541)
Conjugacy classes & character table
7430 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29708, 11);
Finite Group Databasebeta