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D14599 #44416002
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1136 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,1136)(16,1135)(17,1134)(18,1133)(19,1132)(20,1131)(21,1130)(22,1129)(23,1128)(24,1127)(25,1126)(26,1125)(27,1124)(28,1123)(29,1122)(30,1121)(31,1120)(32,1119)(33,1118)(34,1117)(35,1116)(36,1115)(37,1114)(38,1113)(39,1112)(40,1111)(41,1110)(42,1109)(43,1108)(44,1107)(45,1106)(46,1105)(47,1104)(48,1103)(49,1102)(50,1101)(51,1100)(52,1099)(53,1098)(54,1097)(55,1096)(56,1095)(57,1094)(58,1093)(59,1092)(60,1091)(61,1090)(62,1089)(63,1088)(64,1087)(65,1086)(66,1085)(67,1084)(68,1083)(69,1082)(70,1081)(71,1080)(72,1079)(73,1078)(74,1077)(75,1076)(76,1075)(77,1074)(78,1073)(79,1072)(80,1071)(81,1070)(82,1069)(83,1068)(84,1067)(85,1066)(86,1065)(87,1064)(88,1063)(89,1062)(90,1061)(91,1060)(92,1059)(93,1058)(94,1057)(95,1056)(96,1055)(97,1054)(98,1053)(99,1052)(100,1051)(101,1050)(102,1049)(103,1048)(104,1047)(105,1046)(106,1045)(107,1044)(108,1043)(109,1042)(110,1041)(111,1040)(112,1039)(113,1038)(114,1037)(115,1036)(116,1035)(117,1034)(118,1033)(119,1032)(120,1031)(121,1030)(122,1029)(123,1028)(124,1027)(125,1026)(126,1025)(127,1024)(128,1023)(129,1022)(130,1021)(131,1020)(132,1019)(133,1018)(134,1017)(135,1016)(136,1015)(137,1014)(138,1013)(139,1012)(140,1011)(141,1010)(142,1009)(143,1008)(144,1007)(145,1006)(146,1005)(147,1004)(148,1003)(149,1002)(150,1001)(151,1000)(152,999)(153,998)(154,997)(155,996)(156,995)(157,994)(158,993)(159,992)(160,991)(161,990)(162,989)(163,988)(164,987)(165,986)(166,985)(167,984)(168,983)(169,982)(170,981)(171,980)(172,979)(173,978)(174,977)(175,976)(176,975)(177,974)(178,973)(179,972)(180,971)(181,970)(182,969)(183,968)(184,967)(185,966)(186,965)(187,964)(188,963)(189,962)(190,961)(191,960)(192,959)(193,958)(194,957)(195,956)(196,955)(197,954)(198,953)(199,952)(200,951)(201,950)(202,949)(203,948)(204,947)(205,946)(206,945)(207,944)(208,943)(209,942)(210,941)(211,940)(212,939)(213,938)(214,937)(215,936)(216,935)(217,934)(218,933)(219,932)(220,931)(221,930)(222,929)(223,928)(224,927)(225,926)(226,925)(227,924)(228,923)(229,922)(230,921)(231,920)(232,919)(233,918)(234,917)(235,916)(236,915)(237,914)(238,913)(239,912)(240,911)(241,910)(242,909)(243,908)(244,907)(245,906)(246,905)(247,904)(248,903)(249,902)(250,901)(251,900)(252,899)(253,898)(254,897)(255,896)(256,895)(257,894)(258,893)(259,892)(260,891)(261,890)(262,889)(263,888)(264,887)(265,886)(266,885)(267,884)(268,883)(269,882)(270,881)(271,880)(272,879)(273,878)(274,877)(275,876)(276,875)(277,874)(278,873)(279,872)(280,871)(281,870)(282,869)(283,868)(284,867)(285,866)(286,865)(287,864)(288,863)(289,862)(290,861)(291,860)(292,859)(293,858)(294,857)(295,856)(296,855)(297,854)(298,853)(299,852)(300,851)(301,850)(302,849)(303,848)(304,847)(305,846)(306,845)(307,844)(308,843)(309,842)(310,841)(311,840)(312,839)(313,838)(314,837)(315,836)(316,835)(317,834)(318,833)(319,832)(320,831)(321,830)(322,829)(323,828)(324,827)(325,826)(326,825)(327,824)(328,823)(329,822)(330,821)(331,820)(332,819)(333,818)(334,817)(335,816)(336,815)(337,814)(338,813)(339,812)(340,811)(341,810)(342,809)(343,808)(344,807)(345,806)(346,805)(347,804)(348,803)(349,802)(350,801)(351,800)(352,799)(353,798)(354,797)(355,796)(356,795)(357,794)(358,793)(359,792)(360,791)(361,790)(362,789)(363,788)(364,787)(365,786)(366,785)(367,784)(368,783)(369,782)(370,781)(371,780)(372,779)(373,778)(374,777)(375,776)(376,775)(377,774)(378,773)(379,772)(380,771)(381,770)(382,769)(383,768)(384,767)(385,766)(386,765)(387,764)(388,763)(389,762)(390,761)(391,760)(392,759)(393,758)(394,757)(395,756)(396,755)(397,754)(398,753)(399,752)(400,751)(401,750)(402,749)(403,748)(404,747)(405,746)(406,745)(407,744)(408,743)(409,742)(410,741)(411,740)(412,739)(413,738)(414,737)(415,736)(416,735)(417,734)(418,733)(419,732)(420,731)(421,730)(422,729)(423,728)(424,727)(425,726)(426,725)(427,724)(428,723)(429,722)(430,721)(431,720)(432,719)(433,718)(434,717)(435,716)(436,715)(437,714)(438,713)(439,712)(440,711)(441,710)(442,709)(443,708)(444,707)(445,706)(446,705)(447,704)(448,703)(449,702)(450,701)(451,700)(452,699)(453,698)(454,697)(455,696)(456,695)(457,694)(458,693)(459,692)(460,691)(461,690)(462,689)(463,688)(464,687)(465,686)(466,685)(467,684)(468,683)(469,682)(470,681)(471,680)(472,679)(473,678)(474,677)(475,676)(476,675)(477,674)(478,673)(479,672)(480,671)(481,670)(482,669)(483,668)(484,667)(485,666)(486,665)(487,664)(488,663)(489,662)(490,661)(491,660)(492,659)(493,658)(494,657)(495,656)(496,655)(497,654)(498,653)(499,652)(500,651)(501,650)(502,649)(503,648)(504,647)(505,646)(506,645)(507,644)(508,643)(509,642)(510,641)(511,640)(512,639)(513,638)(514,637)(515,636)(516,635)(517,634)(518,633)(519,632)(520,631)(521,630)(522,629)(523,628)(524,627)(525,626)(526,625)(527,624)(528,623)(529,622)(530,621)(531,620)(532,619)(533,618)(534,617)(535,616)(536,615)(537,614)(538,613)(539,612)(540,611)(541,610)(542,609)(543,608)(544,607)(545,606)(546,605)(547,604)(548,603)(549,602)(550,601)(551,600)(552,599)(553,598)(554,597)(555,596)(556,595)(557,594)(558,593)(559,592)(560,591)(561,590)(562,589)(563,588)(564,587)(565,586)(566,585)(567,584)(568,583)(569,582)(570,581)(571,580)(572,579)(573,578)(574,577)(575,576)
Polycyclic presentation:
2,13,1123|b^a=b^12,c^a=c^1122
Conjugacy classes & character table
7301 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29198, 3);
Finite Group Databasebeta