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Dic5515 #36348126
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1112 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);(1,3,2,4)(6,9)(7,8)(11,1112)(12,1111)(13,1110)(14,1109)(15,1108)(16,1107)(17,1106)(18,1105)(19,1104)(20,1103)(21,1102)(22,1101)(23,1100)(24,1099)(25,1098)(26,1097)(27,1096)(28,1095)(29,1094)(30,1093)(31,1092)(32,1091)(33,1090)(34,1089)(35,1088)(36,1087)(37,1086)(38,1085)(39,1084)(40,1083)(41,1082)(42,1081)(43,1080)(44,1079)(45,1078)(46,1077)(47,1076)(48,1075)(49,1074)(50,1073)(51,1072)(52,1071)(53,1070)(54,1069)(55,1068)(56,1067)(57,1066)(58,1065)(59,1064)(60,1063)(61,1062)(62,1061)(63,1060)(64,1059)(65,1058)(66,1057)(67,1056)(68,1055)(69,1054)(70,1053)(71,1052)(72,1051)(73,1050)(74,1049)(75,1048)(76,1047)(77,1046)(78,1045)(79,1044)(80,1043)(81,1042)(82,1041)(83,1040)(84,1039)(85,1038)(86,1037)(87,1036)(88,1035)(89,1034)(90,1033)(91,1032)(92,1031)(93,1030)(94,1029)(95,1028)(96,1027)(97,1026)(98,1025)(99,1024)(100,1023)(101,1022)(102,1021)(103,1020)(104,1019)(105,1018)(106,1017)(107,1016)(108,1015)(109,1014)(110,1013)(111,1012)(112,1011)(113,1010)(114,1009)(115,1008)(116,1007)(117,1006)(118,1005)(119,1004)(120,1003)(121,1002)(122,1001)(123,1000)(124,999)(125,998)(126,997)(127,996)(128,995)(129,994)(130,993)(131,992)(132,991)(133,990)(134,989)(135,988)(136,987)(137,986)(138,985)(139,984)(140,983)(141,982)(142,981)(143,980)(144,979)(145,978)(146,977)(147,976)(148,975)(149,974)(150,973)(151,972)(152,971)(153,970)(154,969)(155,968)(156,967)(157,966)(158,965)(159,964)(160,963)(161,962)(162,961)(163,960)(164,959)(165,958)(166,957)(167,956)(168,955)(169,954)(170,953)(171,952)(172,951)(173,950)(174,949)(175,948)(176,947)(177,946)(178,945)(179,944)(180,943)(181,942)(182,941)(183,940)(184,939)(185,938)(186,937)(187,936)(188,935)(189,934)(190,933)(191,932)(192,931)(193,930)(194,929)(195,928)(196,927)(197,926)(198,925)(199,924)(200,923)(201,922)(202,921)(203,920)(204,919)(205,918)(206,917)(207,916)(208,915)(209,914)(210,913)(211,912)(212,911)(213,910)(214,909)(215,908)(216,907)(217,906)(218,905)(219,904)(220,903)(221,902)(222,901)(223,900)(224,899)(225,898)(226,897)(227,896)(228,895)(229,894)(230,893)(231,892)(232,891)(233,890)(234,889)(235,888)(236,887)(237,886)(238,885)(239,884)(240,883)(241,882)(242,881)(243,880)(244,879)(245,878)(246,877)(247,876)(248,875)(249,874)(250,873)(251,872)(252,871)(253,870)(254,869)(255,868)(256,867)(257,866)(258,865)(259,864)(260,863)(261,862)(262,861)(263,860)(264,859)(265,858)(266,857)(267,856)(268,855)(269,854)(270,853)(271,852)(272,851)(273,850)(274,849)(275,848)(276,847)(277,846)(278,845)(279,844)(280,843)(281,842)(282,841)(283,840)(284,839)(285,838)(286,837)(287,836)(288,835)(289,834)(290,833)(291,832)(292,831)(293,830)(294,829)(295,828)(296,827)(297,826)(298,825)(299,824)(300,823)(301,822)(302,821)(303,820)(304,819)(305,818)(306,817)(307,816)(308,815)(309,814)(310,813)(311,812)(312,811)(313,810)(314,809)(315,808)(316,807)(317,806)(318,805)(319,804)(320,803)(321,802)(322,801)(323,800)(324,799)(325,798)(326,797)(327,796)(328,795)(329,794)(330,793)(331,792)(332,791)(333,790)(334,789)(335,788)(336,787)(337,786)(338,785)(339,784)(340,783)(341,782)(342,781)(343,780)(344,779)(345,778)(346,777)(347,776)(348,775)(349,774)(350,773)(351,772)(352,771)(353,770)(354,769)(355,768)(356,767)(357,766)(358,765)(359,764)(360,763)(361,762)(362,761)(363,760)(364,759)(365,758)(366,757)(367,756)(368,755)(369,754)(370,753)(371,752)(372,751)(373,750)(374,749)(375,748)(376,747)(377,746)(378,745)(379,744)(380,743)(381,742)(382,741)(383,740)(384,739)(385,738)(386,737)(387,736)(388,735)(389,734)(390,733)(391,732)(392,731)(393,730)(394,729)(395,728)(396,727)(397,726)(398,725)(399,724)(400,723)(401,722)(402,721)(403,720)(404,719)(405,718)(406,717)(407,716)(408,715)(409,714)(410,713)(411,712)(412,711)(413,710)(414,709)(415,708)(416,707)(417,706)(418,705)(419,704)(420,703)(421,702)(422,701)(423,700)(424,699)(425,698)(426,697)(427,696)(428,695)(429,694)(430,693)(431,692)(432,691)(433,690)(434,689)(435,688)(436,687)(437,686)(438,685)(439,684)(440,683)(441,682)(442,681)(443,680)(444,679)(445,678)(446,677)(447,676)(448,675)(449,674)(450,673)(451,672)(452,671)(453,670)(454,669)(455,668)(456,667)(457,666)(458,665)(459,664)(460,663)(461,662)(462,661)(463,660)(464,659)(465,658)(466,657)(467,656)(468,655)(469,654)(470,653)(471,652)(472,651)(473,650)(474,649)(475,648)(476,647)(477,646)(478,645)(479,644)(480,643)(481,642)(482,641)(483,640)(484,639)(485,638)(486,637)(487,636)(488,635)(489,634)(490,633)(491,632)(492,631)(493,630)(494,629)(495,628)(496,627)(497,626)(498,625)(499,624)(500,623)(501,622)(502,621)(503,620)(504,619)(505,618)(506,617)(507,616)(508,615)(509,614)(510,613)(511,612)(512,611)(513,610)(514,609)(515,608)(516,607)(517,606)(518,605)(519,604)(520,603)(521,602)(522,601)(523,600)(524,599)(525,598)(526,597)(527,596)(528,595)(529,594)(530,593)(531,592)(532,591)(533,590)(534,589)(535,588)(536,587)(537,586)(538,585)(539,584)(540,583)(541,582)(542,581)(543,580)(544,579)(545,578)(546,577)(547,576)(548,575)(549,574)(550,573)(551,572)(552,571)(553,570)(554,569)(555,568)(556,567)(557,566)(558,565)(559,564)(560,563)(561,562)
Polycyclic presentation:
2,5,1103,2|a^2=d,b^a=b^4,c^a=c^1102
Conjugacy classes & character table
5518 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22060, 4);
Finite Group Databasebeta