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D1091 #14546136
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1091 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091);(2,1091)(3,1090)(4,1089)(5,1088)(6,1087)(7,1086)(8,1085)(9,1084)(10,1083)(11,1082)(12,1081)(13,1080)(14,1079)(15,1078)(16,1077)(17,1076)(18,1075)(19,1074)(20,1073)(21,1072)(22,1071)(23,1070)(24,1069)(25,1068)(26,1067)(27,1066)(28,1065)(29,1064)(30,1063)(31,1062)(32,1061)(33,1060)(34,1059)(35,1058)(36,1057)(37,1056)(38,1055)(39,1054)(40,1053)(41,1052)(42,1051)(43,1050)(44,1049)(45,1048)(46,1047)(47,1046)(48,1045)(49,1044)(50,1043)(51,1042)(52,1041)(53,1040)(54,1039)(55,1038)(56,1037)(57,1036)(58,1035)(59,1034)(60,1033)(61,1032)(62,1031)(63,1030)(64,1029)(65,1028)(66,1027)(67,1026)(68,1025)(69,1024)(70,1023)(71,1022)(72,1021)(73,1020)(74,1019)(75,1018)(76,1017)(77,1016)(78,1015)(79,1014)(80,1013)(81,1012)(82,1011)(83,1010)(84,1009)(85,1008)(86,1007)(87,1006)(88,1005)(89,1004)(90,1003)(91,1002)(92,1001)(93,1000)(94,999)(95,998)(96,997)(97,996)(98,995)(99,994)(100,993)(101,992)(102,991)(103,990)(104,989)(105,988)(106,987)(107,986)(108,985)(109,984)(110,983)(111,982)(112,981)(113,980)(114,979)(115,978)(116,977)(117,976)(118,975)(119,974)(120,973)(121,972)(122,971)(123,970)(124,969)(125,968)(126,967)(127,966)(128,965)(129,964)(130,963)(131,962)(132,961)(133,960)(134,959)(135,958)(136,957)(137,956)(138,955)(139,954)(140,953)(141,952)(142,951)(143,950)(144,949)(145,948)(146,947)(147,946)(148,945)(149,944)(150,943)(151,942)(152,941)(153,940)(154,939)(155,938)(156,937)(157,936)(158,935)(159,934)(160,933)(161,932)(162,931)(163,930)(164,929)(165,928)(166,927)(167,926)(168,925)(169,924)(170,923)(171,922)(172,921)(173,920)(174,919)(175,918)(176,917)(177,916)(178,915)(179,914)(180,913)(181,912)(182,911)(183,910)(184,909)(185,908)(186,907)(187,906)(188,905)(189,904)(190,903)(191,902)(192,901)(193,900)(194,899)(195,898)(196,897)(197,896)(198,895)(199,894)(200,893)(201,892)(202,891)(203,890)(204,889)(205,888)(206,887)(207,886)(208,885)(209,884)(210,883)(211,882)(212,881)(213,880)(214,879)(215,878)(216,877)(217,876)(218,875)(219,874)(220,873)(221,872)(222,871)(223,870)(224,869)(225,868)(226,867)(227,866)(228,865)(229,864)(230,863)(231,862)(232,861)(233,860)(234,859)(235,858)(236,857)(237,856)(238,855)(239,854)(240,853)(241,852)(242,851)(243,850)(244,849)(245,848)(246,847)(247,846)(248,845)(249,844)(250,843)(251,842)(252,841)(253,840)(254,839)(255,838)(256,837)(257,836)(258,835)(259,834)(260,833)(261,832)(262,831)(263,830)(264,829)(265,828)(266,827)(267,826)(268,825)(269,824)(270,823)(271,822)(272,821)(273,820)(274,819)(275,818)(276,817)(277,816)(278,815)(279,814)(280,813)(281,812)(282,811)(283,810)(284,809)(285,808)(286,807)(287,806)(288,805)(289,804)(290,803)(291,802)(292,801)(293,800)(294,799)(295,798)(296,797)(297,796)(298,795)(299,794)(300,793)(301,792)(302,791)(303,790)(304,789)(305,788)(306,787)(307,786)(308,785)(309,784)(310,783)(311,782)(312,781)(313,780)(314,779)(315,778)(316,777)(317,776)(318,775)(319,774)(320,773)(321,772)(322,771)(323,770)(324,769)(325,768)(326,767)(327,766)(328,765)(329,764)(330,763)(331,762)(332,761)(333,760)(334,759)(335,758)(336,757)(337,756)(338,755)(339,754)(340,753)(341,752)(342,751)(343,750)(344,749)(345,748)(346,747)(347,746)(348,745)(349,744)(350,743)(351,742)(352,741)(353,740)(354,739)(355,738)(356,737)(357,736)(358,735)(359,734)(360,733)(361,732)(362,731)(363,730)(364,729)(365,728)(366,727)(367,726)(368,725)(369,724)(370,723)(371,722)(372,721)(373,720)(374,719)(375,718)(376,717)(377,716)(378,715)(379,714)(380,713)(381,712)(382,711)(383,710)(384,709)(385,708)(386,707)(387,706)(388,705)(389,704)(390,703)(391,702)(392,701)(393,700)(394,699)(395,698)(396,697)(397,696)(398,695)(399,694)(400,693)(401,692)(402,691)(403,690)(404,689)(405,688)(406,687)(407,686)(408,685)(409,684)(410,683)(411,682)(412,681)(413,680)(414,679)(415,678)(416,677)(417,676)(418,675)(419,674)(420,673)(421,672)(422,671)(423,670)(424,669)(425,668)(426,667)(427,666)(428,665)(429,664)(430,663)(431,662)(432,661)(433,660)(434,659)(435,658)(436,657)(437,656)(438,655)(439,654)(440,653)(441,652)(442,651)(443,650)(444,649)(445,648)(446,647)(447,646)(448,645)(449,644)(450,643)(451,642)(452,641)(453,640)(454,639)(455,638)(456,637)(457,636)(458,635)(459,634)(460,633)(461,632)(462,631)(463,630)(464,629)(465,628)(466,627)(467,626)(468,625)(469,624)(470,623)(471,622)(472,621)(473,620)(474,619)(475,618)(476,617)(477,616)(478,615)(479,614)(480,613)(481,612)(482,611)(483,610)(484,609)(485,608)(486,607)(487,606)(488,605)(489,604)(490,603)(491,602)(492,601)(493,600)(494,599)(495,598)(496,597)(497,596)(498,595)(499,594)(500,593)(501,592)(502,591)(503,590)(504,589)(505,588)(506,587)(507,586)(508,585)(509,584)(510,583)(511,582)(512,581)(513,580)(514,579)(515,578)(516,577)(517,576)(518,575)(519,574)(520,573)(521,572)(522,571)(523,570)(524,569)(525,568)(526,567)(527,566)(528,565)(529,564)(530,563)(531,562)(532,561)(533,560)(534,559)(535,558)(536,557)(537,556)(538,555)(539,554)(540,553)(541,552)(542,551)(543,550)(544,549)(545,548)(546,547)
Polycyclic presentation:
2,1091|b^a=b^1090
Conjugacy classes & character table
547 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2182, 1);
Finite Group Databasebeta