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D15765 #44538660
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1059 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);(2,3)(5,8)(6,7)(10,1059)(11,1058)(12,1057)(13,1056)(14,1055)(15,1054)(16,1053)(17,1052)(18,1051)(19,1050)(20,1049)(21,1048)(22,1047)(23,1046)(24,1045)(25,1044)(26,1043)(27,1042)(28,1041)(29,1040)(30,1039)(31,1038)(32,1037)(33,1036)(34,1035)(35,1034)(36,1033)(37,1032)(38,1031)(39,1030)(40,1029)(41,1028)(42,1027)(43,1026)(44,1025)(45,1024)(46,1023)(47,1022)(48,1021)(49,1020)(50,1019)(51,1018)(52,1017)(53,1016)(54,1015)(55,1014)(56,1013)(57,1012)(58,1011)(59,1010)(60,1009)(61,1008)(62,1007)(63,1006)(64,1005)(65,1004)(66,1003)(67,1002)(68,1001)(69,1000)(70,999)(71,998)(72,997)(73,996)(74,995)(75,994)(76,993)(77,992)(78,991)(79,990)(80,989)(81,988)(82,987)(83,986)(84,985)(85,984)(86,983)(87,982)(88,981)(89,980)(90,979)(91,978)(92,977)(93,976)(94,975)(95,974)(96,973)(97,972)(98,971)(99,970)(100,969)(101,968)(102,967)(103,966)(104,965)(105,964)(106,963)(107,962)(108,961)(109,960)(110,959)(111,958)(112,957)(113,956)(114,955)(115,954)(116,953)(117,952)(118,951)(119,950)(120,949)(121,948)(122,947)(123,946)(124,945)(125,944)(126,943)(127,942)(128,941)(129,940)(130,939)(131,938)(132,937)(133,936)(134,935)(135,934)(136,933)(137,932)(138,931)(139,930)(140,929)(141,928)(142,927)(143,926)(144,925)(145,924)(146,923)(147,922)(148,921)(149,920)(150,919)(151,918)(152,917)(153,916)(154,915)(155,914)(156,913)(157,912)(158,911)(159,910)(160,909)(161,908)(162,907)(163,906)(164,905)(165,904)(166,903)(167,902)(168,901)(169,900)(170,899)(171,898)(172,897)(173,896)(174,895)(175,894)(176,893)(177,892)(178,891)(179,890)(180,889)(181,888)(182,887)(183,886)(184,885)(185,884)(186,883)(187,882)(188,881)(189,880)(190,879)(191,878)(192,877)(193,876)(194,875)(195,874)(196,873)(197,872)(198,871)(199,870)(200,869)(201,868)(202,867)(203,866)(204,865)(205,864)(206,863)(207,862)(208,861)(209,860)(210,859)(211,858)(212,857)(213,856)(214,855)(215,854)(216,853)(217,852)(218,851)(219,850)(220,849)(221,848)(222,847)(223,846)(224,845)(225,844)(226,843)(227,842)(228,841)(229,840)(230,839)(231,838)(232,837)(233,836)(234,835)(235,834)(236,833)(237,832)(238,831)(239,830)(240,829)(241,828)(242,827)(243,826)(244,825)(245,824)(246,823)(247,822)(248,821)(249,820)(250,819)(251,818)(252,817)(253,816)(254,815)(255,814)(256,813)(257,812)(258,811)(259,810)(260,809)(261,808)(262,807)(263,806)(264,805)(265,804)(266,803)(267,802)(268,801)(269,800)(270,799)(271,798)(272,797)(273,796)(274,795)(275,794)(276,793)(277,792)(278,791)(279,790)(280,789)(281,788)(282,787)(283,786)(284,785)(285,784)(286,783)(287,782)(288,781)(289,780)(290,779)(291,778)(292,777)(293,776)(294,775)(295,774)(296,773)(297,772)(298,771)(299,770)(300,769)(301,768)(302,767)(303,766)(304,765)(305,764)(306,763)(307,762)(308,761)(309,760)(310,759)(311,758)(312,757)(313,756)(314,755)(315,754)(316,753)(317,752)(318,751)(319,750)(320,749)(321,748)(322,747)(323,746)(324,745)(325,744)(326,743)(327,742)(328,741)(329,740)(330,739)(331,738)(332,737)(333,736)(334,735)(335,734)(336,733)(337,732)(338,731)(339,730)(340,729)(341,728)(342,727)(343,726)(344,725)(345,724)(346,723)(347,722)(348,721)(349,720)(350,719)(351,718)(352,717)(353,716)(354,715)(355,714)(356,713)(357,712)(358,711)(359,710)(360,709)(361,708)(362,707)(363,706)(364,705)(365,704)(366,703)(367,702)(368,701)(369,700)(370,699)(371,698)(372,697)(373,696)(374,695)(375,694)(376,693)(377,692)(378,691)(379,690)(380,689)(381,688)(382,687)(383,686)(384,685)(385,684)(386,683)(387,682)(388,681)(389,680)(390,679)(391,678)(392,677)(393,676)(394,675)(395,674)(396,673)(397,672)(398,671)(399,670)(400,669)(401,668)(402,667)(403,666)(404,665)(405,664)(406,663)(407,662)(408,661)(409,660)(410,659)(411,658)(412,657)(413,656)(414,655)(415,654)(416,653)(417,652)(418,651)(419,650)(420,649)(421,648)(422,647)(423,646)(424,645)(425,644)(426,643)(427,642)(428,641)(429,640)(430,639)(431,638)(432,637)(433,636)(434,635)(435,634)(436,633)(437,632)(438,631)(439,630)(440,629)(441,628)(442,627)(443,626)(444,625)(445,624)(446,623)(447,622)(448,621)(449,620)(450,619)(451,618)(452,617)(453,616)(454,615)(455,614)(456,613)(457,612)(458,611)(459,610)(460,609)(461,608)(462,607)(463,606)(464,605)(465,604)(466,603)(467,602)(468,601)(469,600)(470,599)(471,598)(472,597)(473,596)(474,595)(475,594)(476,593)(477,592)(478,591)(479,590)(480,589)(481,588)(482,587)(483,586)(484,585)(485,584)(486,583)(487,582)(488,581)(489,580)(490,579)(491,578)(492,577)(493,576)(494,575)(495,574)(496,573)(497,572)(498,571)(499,570)(500,569)(501,568)(502,567)(503,566)(504,565)(505,564)(506,563)(507,562)(508,561)(509,560)(510,559)(511,558)(512,557)(513,556)(514,555)(515,554)(516,553)(517,552)(518,551)(519,550)(520,549)(521,548)(522,547)(523,546)(524,545)(525,544)(526,543)(527,542)(528,541)(529,540)(530,539)(531,538)(532,537)(533,536)(534,535)
Polycyclic presentation:
2,3,5,1051|b^a=b^2,c^a=c^4,d^a=d^1050
Conjugacy classes & character table
7884 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31530, 11);
Finite Group Databasebeta