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D1123 #14555877
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1123 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);(2,1123)(3,1122)(4,1121)(5,1120)(6,1119)(7,1118)(8,1117)(9,1116)(10,1115)(11,1114)(12,1113)(13,1112)(14,1111)(15,1110)(16,1109)(17,1108)(18,1107)(19,1106)(20,1105)(21,1104)(22,1103)(23,1102)(24,1101)(25,1100)(26,1099)(27,1098)(28,1097)(29,1096)(30,1095)(31,1094)(32,1093)(33,1092)(34,1091)(35,1090)(36,1089)(37,1088)(38,1087)(39,1086)(40,1085)(41,1084)(42,1083)(43,1082)(44,1081)(45,1080)(46,1079)(47,1078)(48,1077)(49,1076)(50,1075)(51,1074)(52,1073)(53,1072)(54,1071)(55,1070)(56,1069)(57,1068)(58,1067)(59,1066)(60,1065)(61,1064)(62,1063)(63,1062)(64,1061)(65,1060)(66,1059)(67,1058)(68,1057)(69,1056)(70,1055)(71,1054)(72,1053)(73,1052)(74,1051)(75,1050)(76,1049)(77,1048)(78,1047)(79,1046)(80,1045)(81,1044)(82,1043)(83,1042)(84,1041)(85,1040)(86,1039)(87,1038)(88,1037)(89,1036)(90,1035)(91,1034)(92,1033)(93,1032)(94,1031)(95,1030)(96,1029)(97,1028)(98,1027)(99,1026)(100,1025)(101,1024)(102,1023)(103,1022)(104,1021)(105,1020)(106,1019)(107,1018)(108,1017)(109,1016)(110,1015)(111,1014)(112,1013)(113,1012)(114,1011)(115,1010)(116,1009)(117,1008)(118,1007)(119,1006)(120,1005)(121,1004)(122,1003)(123,1002)(124,1001)(125,1000)(126,999)(127,998)(128,997)(129,996)(130,995)(131,994)(132,993)(133,992)(134,991)(135,990)(136,989)(137,988)(138,987)(139,986)(140,985)(141,984)(142,983)(143,982)(144,981)(145,980)(146,979)(147,978)(148,977)(149,976)(150,975)(151,974)(152,973)(153,972)(154,971)(155,970)(156,969)(157,968)(158,967)(159,966)(160,965)(161,964)(162,963)(163,962)(164,961)(165,960)(166,959)(167,958)(168,957)(169,956)(170,955)(171,954)(172,953)(173,952)(174,951)(175,950)(176,949)(177,948)(178,947)(179,946)(180,945)(181,944)(182,943)(183,942)(184,941)(185,940)(186,939)(187,938)(188,937)(189,936)(190,935)(191,934)(192,933)(193,932)(194,931)(195,930)(196,929)(197,928)(198,927)(199,926)(200,925)(201,924)(202,923)(203,922)(204,921)(205,920)(206,919)(207,918)(208,917)(209,916)(210,915)(211,914)(212,913)(213,912)(214,911)(215,910)(216,909)(217,908)(218,907)(219,906)(220,905)(221,904)(222,903)(223,902)(224,901)(225,900)(226,899)(227,898)(228,897)(229,896)(230,895)(231,894)(232,893)(233,892)(234,891)(235,890)(236,889)(237,888)(238,887)(239,886)(240,885)(241,884)(242,883)(243,882)(244,881)(245,880)(246,879)(247,878)(248,877)(249,876)(250,875)(251,874)(252,873)(253,872)(254,871)(255,870)(256,869)(257,868)(258,867)(259,866)(260,865)(261,864)(262,863)(263,862)(264,861)(265,860)(266,859)(267,858)(268,857)(269,856)(270,855)(271,854)(272,853)(273,852)(274,851)(275,850)(276,849)(277,848)(278,847)(279,846)(280,845)(281,844)(282,843)(283,842)(284,841)(285,840)(286,839)(287,838)(288,837)(289,836)(290,835)(291,834)(292,833)(293,832)(294,831)(295,830)(296,829)(297,828)(298,827)(299,826)(300,825)(301,824)(302,823)(303,822)(304,821)(305,820)(306,819)(307,818)(308,817)(309,816)(310,815)(311,814)(312,813)(313,812)(314,811)(315,810)(316,809)(317,808)(318,807)(319,806)(320,805)(321,804)(322,803)(323,802)(324,801)(325,800)(326,799)(327,798)(328,797)(329,796)(330,795)(331,794)(332,793)(333,792)(334,791)(335,790)(336,789)(337,788)(338,787)(339,786)(340,785)(341,784)(342,783)(343,782)(344,781)(345,780)(346,779)(347,778)(348,777)(349,776)(350,775)(351,774)(352,773)(353,772)(354,771)(355,770)(356,769)(357,768)(358,767)(359,766)(360,765)(361,764)(362,763)(363,762)(364,761)(365,760)(366,759)(367,758)(368,757)(369,756)(370,755)(371,754)(372,753)(373,752)(374,751)(375,750)(376,749)(377,748)(378,747)(379,746)(380,745)(381,744)(382,743)(383,742)(384,741)(385,740)(386,739)(387,738)(388,737)(389,736)(390,735)(391,734)(392,733)(393,732)(394,731)(395,730)(396,729)(397,728)(398,727)(399,726)(400,725)(401,724)(402,723)(403,722)(404,721)(405,720)(406,719)(407,718)(408,717)(409,716)(410,715)(411,714)(412,713)(413,712)(414,711)(415,710)(416,709)(417,708)(418,707)(419,706)(420,705)(421,704)(422,703)(423,702)(424,701)(425,700)(426,699)(427,698)(428,697)(429,696)(430,695)(431,694)(432,693)(433,692)(434,691)(435,690)(436,689)(437,688)(438,687)(439,686)(440,685)(441,684)(442,683)(443,682)(444,681)(445,680)(446,679)(447,678)(448,677)(449,676)(450,675)(451,674)(452,673)(453,672)(454,671)(455,670)(456,669)(457,668)(458,667)(459,666)(460,665)(461,664)(462,663)(463,662)(464,661)(465,660)(466,659)(467,658)(468,657)(469,656)(470,655)(471,654)(472,653)(473,652)(474,651)(475,650)(476,649)(477,648)(478,647)(479,646)(480,645)(481,644)(482,643)(483,642)(484,641)(485,640)(486,639)(487,638)(488,637)(489,636)(490,635)(491,634)(492,633)(493,632)(494,631)(495,630)(496,629)(497,628)(498,627)(499,626)(500,625)(501,624)(502,623)(503,622)(504,621)(505,620)(506,619)(507,618)(508,617)(509,616)(510,615)(511,614)(512,613)(513,612)(514,611)(515,610)(516,609)(517,608)(518,607)(519,606)(520,605)(521,604)(522,603)(523,602)(524,601)(525,600)(526,599)(527,598)(528,597)(529,596)(530,595)(531,594)(532,593)(533,592)(534,591)(535,590)(536,589)(537,588)(538,587)(539,586)(540,585)(541,584)(542,583)(543,582)(544,581)(545,580)(546,579)(547,578)(548,577)(549,576)(550,575)(551,574)(552,573)(553,572)(554,571)(555,570)(556,569)(557,568)(558,567)(559,566)(560,565)(561,564)(562,563)
Polycyclic presentation:
2,1123|b^a=b^1122
Conjugacy classes & character table
563 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2246, 1);
Finite Group Databasebeta