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D5455 #24926321
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1096 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);(2,5)(3,4)(7,1096)(8,1095)(9,1094)(10,1093)(11,1092)(12,1091)(13,1090)(14,1089)(15,1088)(16,1087)(17,1086)(18,1085)(19,1084)(20,1083)(21,1082)(22,1081)(23,1080)(24,1079)(25,1078)(26,1077)(27,1076)(28,1075)(29,1074)(30,1073)(31,1072)(32,1071)(33,1070)(34,1069)(35,1068)(36,1067)(37,1066)(38,1065)(39,1064)(40,1063)(41,1062)(42,1061)(43,1060)(44,1059)(45,1058)(46,1057)(47,1056)(48,1055)(49,1054)(50,1053)(51,1052)(52,1051)(53,1050)(54,1049)(55,1048)(56,1047)(57,1046)(58,1045)(59,1044)(60,1043)(61,1042)(62,1041)(63,1040)(64,1039)(65,1038)(66,1037)(67,1036)(68,1035)(69,1034)(70,1033)(71,1032)(72,1031)(73,1030)(74,1029)(75,1028)(76,1027)(77,1026)(78,1025)(79,1024)(80,1023)(81,1022)(82,1021)(83,1020)(84,1019)(85,1018)(86,1017)(87,1016)(88,1015)(89,1014)(90,1013)(91,1012)(92,1011)(93,1010)(94,1009)(95,1008)(96,1007)(97,1006)(98,1005)(99,1004)(100,1003)(101,1002)(102,1001)(103,1000)(104,999)(105,998)(106,997)(107,996)(108,995)(109,994)(110,993)(111,992)(112,991)(113,990)(114,989)(115,988)(116,987)(117,986)(118,985)(119,984)(120,983)(121,982)(122,981)(123,980)(124,979)(125,978)(126,977)(127,976)(128,975)(129,974)(130,973)(131,972)(132,971)(133,970)(134,969)(135,968)(136,967)(137,966)(138,965)(139,964)(140,963)(141,962)(142,961)(143,960)(144,959)(145,958)(146,957)(147,956)(148,955)(149,954)(150,953)(151,952)(152,951)(153,950)(154,949)(155,948)(156,947)(157,946)(158,945)(159,944)(160,943)(161,942)(162,941)(163,940)(164,939)(165,938)(166,937)(167,936)(168,935)(169,934)(170,933)(171,932)(172,931)(173,930)(174,929)(175,928)(176,927)(177,926)(178,925)(179,924)(180,923)(181,922)(182,921)(183,920)(184,919)(185,918)(186,917)(187,916)(188,915)(189,914)(190,913)(191,912)(192,911)(193,910)(194,909)(195,908)(196,907)(197,906)(198,905)(199,904)(200,903)(201,902)(202,901)(203,900)(204,899)(205,898)(206,897)(207,896)(208,895)(209,894)(210,893)(211,892)(212,891)(213,890)(214,889)(215,888)(216,887)(217,886)(218,885)(219,884)(220,883)(221,882)(222,881)(223,880)(224,879)(225,878)(226,877)(227,876)(228,875)(229,874)(230,873)(231,872)(232,871)(233,870)(234,869)(235,868)(236,867)(237,866)(238,865)(239,864)(240,863)(241,862)(242,861)(243,860)(244,859)(245,858)(246,857)(247,856)(248,855)(249,854)(250,853)(251,852)(252,851)(253,850)(254,849)(255,848)(256,847)(257,846)(258,845)(259,844)(260,843)(261,842)(262,841)(263,840)(264,839)(265,838)(266,837)(267,836)(268,835)(269,834)(270,833)(271,832)(272,831)(273,830)(274,829)(275,828)(276,827)(277,826)(278,825)(279,824)(280,823)(281,822)(282,821)(283,820)(284,819)(285,818)(286,817)(287,816)(288,815)(289,814)(290,813)(291,812)(292,811)(293,810)(294,809)(295,808)(296,807)(297,806)(298,805)(299,804)(300,803)(301,802)(302,801)(303,800)(304,799)(305,798)(306,797)(307,796)(308,795)(309,794)(310,793)(311,792)(312,791)(313,790)(314,789)(315,788)(316,787)(317,786)(318,785)(319,784)(320,783)(321,782)(322,781)(323,780)(324,779)(325,778)(326,777)(327,776)(328,775)(329,774)(330,773)(331,772)(332,771)(333,770)(334,769)(335,768)(336,767)(337,766)(338,765)(339,764)(340,763)(341,762)(342,761)(343,760)(344,759)(345,758)(346,757)(347,756)(348,755)(349,754)(350,753)(351,752)(352,751)(353,750)(354,749)(355,748)(356,747)(357,746)(358,745)(359,744)(360,743)(361,742)(362,741)(363,740)(364,739)(365,738)(366,737)(367,736)(368,735)(369,734)(370,733)(371,732)(372,731)(373,730)(374,729)(375,728)(376,727)(377,726)(378,725)(379,724)(380,723)(381,722)(382,721)(383,720)(384,719)(385,718)(386,717)(387,716)(388,715)(389,714)(390,713)(391,712)(392,711)(393,710)(394,709)(395,708)(396,707)(397,706)(398,705)(399,704)(400,703)(401,702)(402,701)(403,700)(404,699)(405,698)(406,697)(407,696)(408,695)(409,694)(410,693)(411,692)(412,691)(413,690)(414,689)(415,688)(416,687)(417,686)(418,685)(419,684)(420,683)(421,682)(422,681)(423,680)(424,679)(425,678)(426,677)(427,676)(428,675)(429,674)(430,673)(431,672)(432,671)(433,670)(434,669)(435,668)(436,667)(437,666)(438,665)(439,664)(440,663)(441,662)(442,661)(443,660)(444,659)(445,658)(446,657)(447,656)(448,655)(449,654)(450,653)(451,652)(452,651)(453,650)(454,649)(455,648)(456,647)(457,646)(458,645)(459,644)(460,643)(461,642)(462,641)(463,640)(464,639)(465,638)(466,637)(467,636)(468,635)(469,634)(470,633)(471,632)(472,631)(473,630)(474,629)(475,628)(476,627)(477,626)(478,625)(479,624)(480,623)(481,622)(482,621)(483,620)(484,619)(485,618)(486,617)(487,616)(488,615)(489,614)(490,613)(491,612)(492,611)(493,610)(494,609)(495,608)(496,607)(497,606)(498,605)(499,604)(500,603)(501,602)(502,601)(503,600)(504,599)(505,598)(506,597)(507,596)(508,595)(509,594)(510,593)(511,592)(512,591)(513,590)(514,589)(515,588)(516,587)(517,586)(518,585)(519,584)(520,583)(521,582)(522,581)(523,580)(524,579)(525,578)(526,577)(527,576)(528,575)(529,574)(530,573)(531,572)(532,571)(533,570)(534,569)(535,568)(536,567)(537,566)(538,565)(539,564)(540,563)(541,562)(542,561)(543,560)(544,559)(545,558)(546,557)(547,556)(548,555)(549,554)(550,553)(551,552)
Polycyclic presentation:
2,5,1091|b^a=b^4,c^a=c^1090
Conjugacy classes & character table
2729 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10910, 5);
Finite Group Databasebeta