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D14183 #43248674
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1104 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,1104)(16,1103)(17,1102)(18,1101)(19,1100)(20,1099)(21,1098)(22,1097)(23,1096)(24,1095)(25,1094)(26,1093)(27,1092)(28,1091)(29,1090)(30,1089)(31,1088)(32,1087)(33,1086)(34,1085)(35,1084)(36,1083)(37,1082)(38,1081)(39,1080)(40,1079)(41,1078)(42,1077)(43,1076)(44,1075)(45,1074)(46,1073)(47,1072)(48,1071)(49,1070)(50,1069)(51,1068)(52,1067)(53,1066)(54,1065)(55,1064)(56,1063)(57,1062)(58,1061)(59,1060)(60,1059)(61,1058)(62,1057)(63,1056)(64,1055)(65,1054)(66,1053)(67,1052)(68,1051)(69,1050)(70,1049)(71,1048)(72,1047)(73,1046)(74,1045)(75,1044)(76,1043)(77,1042)(78,1041)(79,1040)(80,1039)(81,1038)(82,1037)(83,1036)(84,1035)(85,1034)(86,1033)(87,1032)(88,1031)(89,1030)(90,1029)(91,1028)(92,1027)(93,1026)(94,1025)(95,1024)(96,1023)(97,1022)(98,1021)(99,1020)(100,1019)(101,1018)(102,1017)(103,1016)(104,1015)(105,1014)(106,1013)(107,1012)(108,1011)(109,1010)(110,1009)(111,1008)(112,1007)(113,1006)(114,1005)(115,1004)(116,1003)(117,1002)(118,1001)(119,1000)(120,999)(121,998)(122,997)(123,996)(124,995)(125,994)(126,993)(127,992)(128,991)(129,990)(130,989)(131,988)(132,987)(133,986)(134,985)(135,984)(136,983)(137,982)(138,981)(139,980)(140,979)(141,978)(142,977)(143,976)(144,975)(145,974)(146,973)(147,972)(148,971)(149,970)(150,969)(151,968)(152,967)(153,966)(154,965)(155,964)(156,963)(157,962)(158,961)(159,960)(160,959)(161,958)(162,957)(163,956)(164,955)(165,954)(166,953)(167,952)(168,951)(169,950)(170,949)(171,948)(172,947)(173,946)(174,945)(175,944)(176,943)(177,942)(178,941)(179,940)(180,939)(181,938)(182,937)(183,936)(184,935)(185,934)(186,933)(187,932)(188,931)(189,930)(190,929)(191,928)(192,927)(193,926)(194,925)(195,924)(196,923)(197,922)(198,921)(199,920)(200,919)(201,918)(202,917)(203,916)(204,915)(205,914)(206,913)(207,912)(208,911)(209,910)(210,909)(211,908)(212,907)(213,906)(214,905)(215,904)(216,903)(217,902)(218,901)(219,900)(220,899)(221,898)(222,897)(223,896)(224,895)(225,894)(226,893)(227,892)(228,891)(229,890)(230,889)(231,888)(232,887)(233,886)(234,885)(235,884)(236,883)(237,882)(238,881)(239,880)(240,879)(241,878)(242,877)(243,876)(244,875)(245,874)(246,873)(247,872)(248,871)(249,870)(250,869)(251,868)(252,867)(253,866)(254,865)(255,864)(256,863)(257,862)(258,861)(259,860)(260,859)(261,858)(262,857)(263,856)(264,855)(265,854)(266,853)(267,852)(268,851)(269,850)(270,849)(271,848)(272,847)(273,846)(274,845)(275,844)(276,843)(277,842)(278,841)(279,840)(280,839)(281,838)(282,837)(283,836)(284,835)(285,834)(286,833)(287,832)(288,831)(289,830)(290,829)(291,828)(292,827)(293,826)(294,825)(295,824)(296,823)(297,822)(298,821)(299,820)(300,819)(301,818)(302,817)(303,816)(304,815)(305,814)(306,813)(307,812)(308,811)(309,810)(310,809)(311,808)(312,807)(313,806)(314,805)(315,804)(316,803)(317,802)(318,801)(319,800)(320,799)(321,798)(322,797)(323,796)(324,795)(325,794)(326,793)(327,792)(328,791)(329,790)(330,789)(331,788)(332,787)(333,786)(334,785)(335,784)(336,783)(337,782)(338,781)(339,780)(340,779)(341,778)(342,777)(343,776)(344,775)(345,774)(346,773)(347,772)(348,771)(349,770)(350,769)(351,768)(352,767)(353,766)(354,765)(355,764)(356,763)(357,762)(358,761)(359,760)(360,759)(361,758)(362,757)(363,756)(364,755)(365,754)(366,753)(367,752)(368,751)(369,750)(370,749)(371,748)(372,747)(373,746)(374,745)(375,744)(376,743)(377,742)(378,741)(379,740)(380,739)(381,738)(382,737)(383,736)(384,735)(385,734)(386,733)(387,732)(388,731)(389,730)(390,729)(391,728)(392,727)(393,726)(394,725)(395,724)(396,723)(397,722)(398,721)(399,720)(400,719)(401,718)(402,717)(403,716)(404,715)(405,714)(406,713)(407,712)(408,711)(409,710)(410,709)(411,708)(412,707)(413,706)(414,705)(415,704)(416,703)(417,702)(418,701)(419,700)(420,699)(421,698)(422,697)(423,696)(424,695)(425,694)(426,693)(427,692)(428,691)(429,690)(430,689)(431,688)(432,687)(433,686)(434,685)(435,684)(436,683)(437,682)(438,681)(439,680)(440,679)(441,678)(442,677)(443,676)(444,675)(445,674)(446,673)(447,672)(448,671)(449,670)(450,669)(451,668)(452,667)(453,666)(454,665)(455,664)(456,663)(457,662)(458,661)(459,660)(460,659)(461,658)(462,657)(463,656)(464,655)(465,654)(466,653)(467,652)(468,651)(469,650)(470,649)(471,648)(472,647)(473,646)(474,645)(475,644)(476,643)(477,642)(478,641)(479,640)(480,639)(481,638)(482,637)(483,636)(484,635)(485,634)(486,633)(487,632)(488,631)(489,630)(490,629)(491,628)(492,627)(493,626)(494,625)(495,624)(496,623)(497,622)(498,621)(499,620)(500,619)(501,618)(502,617)(503,616)(504,615)(505,614)(506,613)(507,612)(508,611)(509,610)(510,609)(511,608)(512,607)(513,606)(514,605)(515,604)(516,603)(517,602)(518,601)(519,600)(520,599)(521,598)(522,597)(523,596)(524,595)(525,594)(526,593)(527,592)(528,591)(529,590)(530,589)(531,588)(532,587)(533,586)(534,585)(535,584)(536,583)(537,582)(538,581)(539,580)(540,579)(541,578)(542,577)(543,576)(544,575)(545,574)(546,573)(547,572)(548,571)(549,570)(550,569)(551,568)(552,567)(553,566)(554,565)(555,564)(556,563)(557,562)(558,561)(559,560)
Polycyclic presentation:
2,13,1091|b^a=b^12,c^a=c^1090
Conjugacy classes & character table
7093 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28366, 3);
Finite Group Databasebeta