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Dic5435 #36344100
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1096 points:
(1,2)(3,4)(5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096);(1,3,2,4)(6,9)(7,8)(11,1096)(12,1095)(13,1094)(14,1093)(15,1092)(16,1091)(17,1090)(18,1089)(19,1088)(20,1087)(21,1086)(22,1085)(23,1084)(24,1083)(25,1082)(26,1081)(27,1080)(28,1079)(29,1078)(30,1077)(31,1076)(32,1075)(33,1074)(34,1073)(35,1072)(36,1071)(37,1070)(38,1069)(39,1068)(40,1067)(41,1066)(42,1065)(43,1064)(44,1063)(45,1062)(46,1061)(47,1060)(48,1059)(49,1058)(50,1057)(51,1056)(52,1055)(53,1054)(54,1053)(55,1052)(56,1051)(57,1050)(58,1049)(59,1048)(60,1047)(61,1046)(62,1045)(63,1044)(64,1043)(65,1042)(66,1041)(67,1040)(68,1039)(69,1038)(70,1037)(71,1036)(72,1035)(73,1034)(74,1033)(75,1032)(76,1031)(77,1030)(78,1029)(79,1028)(80,1027)(81,1026)(82,1025)(83,1024)(84,1023)(85,1022)(86,1021)(87,1020)(88,1019)(89,1018)(90,1017)(91,1016)(92,1015)(93,1014)(94,1013)(95,1012)(96,1011)(97,1010)(98,1009)(99,1008)(100,1007)(101,1006)(102,1005)(103,1004)(104,1003)(105,1002)(106,1001)(107,1000)(108,999)(109,998)(110,997)(111,996)(112,995)(113,994)(114,993)(115,992)(116,991)(117,990)(118,989)(119,988)(120,987)(121,986)(122,985)(123,984)(124,983)(125,982)(126,981)(127,980)(128,979)(129,978)(130,977)(131,976)(132,975)(133,974)(134,973)(135,972)(136,971)(137,970)(138,969)(139,968)(140,967)(141,966)(142,965)(143,964)(144,963)(145,962)(146,961)(147,960)(148,959)(149,958)(150,957)(151,956)(152,955)(153,954)(154,953)(155,952)(156,951)(157,950)(158,949)(159,948)(160,947)(161,946)(162,945)(163,944)(164,943)(165,942)(166,941)(167,940)(168,939)(169,938)(170,937)(171,936)(172,935)(173,934)(174,933)(175,932)(176,931)(177,930)(178,929)(179,928)(180,927)(181,926)(182,925)(183,924)(184,923)(185,922)(186,921)(187,920)(188,919)(189,918)(190,917)(191,916)(192,915)(193,914)(194,913)(195,912)(196,911)(197,910)(198,909)(199,908)(200,907)(201,906)(202,905)(203,904)(204,903)(205,902)(206,901)(207,900)(208,899)(209,898)(210,897)(211,896)(212,895)(213,894)(214,893)(215,892)(216,891)(217,890)(218,889)(219,888)(220,887)(221,886)(222,885)(223,884)(224,883)(225,882)(226,881)(227,880)(228,879)(229,878)(230,877)(231,876)(232,875)(233,874)(234,873)(235,872)(236,871)(237,870)(238,869)(239,868)(240,867)(241,866)(242,865)(243,864)(244,863)(245,862)(246,861)(247,860)(248,859)(249,858)(250,857)(251,856)(252,855)(253,854)(254,853)(255,852)(256,851)(257,850)(258,849)(259,848)(260,847)(261,846)(262,845)(263,844)(264,843)(265,842)(266,841)(267,840)(268,839)(269,838)(270,837)(271,836)(272,835)(273,834)(274,833)(275,832)(276,831)(277,830)(278,829)(279,828)(280,827)(281,826)(282,825)(283,824)(284,823)(285,822)(286,821)(287,820)(288,819)(289,818)(290,817)(291,816)(292,815)(293,814)(294,813)(295,812)(296,811)(297,810)(298,809)(299,808)(300,807)(301,806)(302,805)(303,804)(304,803)(305,802)(306,801)(307,800)(308,799)(309,798)(310,797)(311,796)(312,795)(313,794)(314,793)(315,792)(316,791)(317,790)(318,789)(319,788)(320,787)(321,786)(322,785)(323,784)(324,783)(325,782)(326,781)(327,780)(328,779)(329,778)(330,777)(331,776)(332,775)(333,774)(334,773)(335,772)(336,771)(337,770)(338,769)(339,768)(340,767)(341,766)(342,765)(343,764)(344,763)(345,762)(346,761)(347,760)(348,759)(349,758)(350,757)(351,756)(352,755)(353,754)(354,753)(355,752)(356,751)(357,750)(358,749)(359,748)(360,747)(361,746)(362,745)(363,744)(364,743)(365,742)(366,741)(367,740)(368,739)(369,738)(370,737)(371,736)(372,735)(373,734)(374,733)(375,732)(376,731)(377,730)(378,729)(379,728)(380,727)(381,726)(382,725)(383,724)(384,723)(385,722)(386,721)(387,720)(388,719)(389,718)(390,717)(391,716)(392,715)(393,714)(394,713)(395,712)(396,711)(397,710)(398,709)(399,708)(400,707)(401,706)(402,705)(403,704)(404,703)(405,702)(406,701)(407,700)(408,699)(409,698)(410,697)(411,696)(412,695)(413,694)(414,693)(415,692)(416,691)(417,690)(418,689)(419,688)(420,687)(421,686)(422,685)(423,684)(424,683)(425,682)(426,681)(427,680)(428,679)(429,678)(430,677)(431,676)(432,675)(433,674)(434,673)(435,672)(436,671)(437,670)(438,669)(439,668)(440,667)(441,666)(442,665)(443,664)(444,663)(445,662)(446,661)(447,660)(448,659)(449,658)(450,657)(451,656)(452,655)(453,654)(454,653)(455,652)(456,651)(457,650)(458,649)(459,648)(460,647)(461,646)(462,645)(463,644)(464,643)(465,642)(466,641)(467,640)(468,639)(469,638)(470,637)(471,636)(472,635)(473,634)(474,633)(475,632)(476,631)(477,630)(478,629)(479,628)(480,627)(481,626)(482,625)(483,624)(484,623)(485,622)(486,621)(487,620)(488,619)(489,618)(490,617)(491,616)(492,615)(493,614)(494,613)(495,612)(496,611)(497,610)(498,609)(499,608)(500,607)(501,606)(502,605)(503,604)(504,603)(505,602)(506,601)(507,600)(508,599)(509,598)(510,597)(511,596)(512,595)(513,594)(514,593)(515,592)(516,591)(517,590)(518,589)(519,588)(520,587)(521,586)(522,585)(523,584)(524,583)(525,582)(526,581)(527,580)(528,579)(529,578)(530,577)(531,576)(532,575)(533,574)(534,573)(535,572)(536,571)(537,570)(538,569)(539,568)(540,567)(541,566)(542,565)(543,564)(544,563)(545,562)(546,561)(547,560)(548,559)(549,558)(550,557)(551,556)(552,555)(553,554)
Polycyclic presentation:
2,5,1087,2|a^2=d,b^a=b^4,c^a=c^1086
Conjugacy classes & character table
5438 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21740, 4);
Finite Group Databasebeta