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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1077 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);(5,8)(6,7)(10,1077)(11,1076)(12,1075)(13,1074)(14,1073)(15,1072)(16,1071)(17,1070)(18,1069)(19,1068)(20,1067)(21,1066)(22,1065)(23,1064)(24,1063)(25,1062)(26,1061)(27,1060)(28,1059)(29,1058)(30,1057)(31,1056)(32,1055)(33,1054)(34,1053)(35,1052)(36,1051)(37,1050)(38,1049)(39,1048)(40,1047)(41,1046)(42,1045)(43,1044)(44,1043)(45,1042)(46,1041)(47,1040)(48,1039)(49,1038)(50,1037)(51,1036)(52,1035)(53,1034)(54,1033)(55,1032)(56,1031)(57,1030)(58,1029)(59,1028)(60,1027)(61,1026)(62,1025)(63,1024)(64,1023)(65,1022)(66,1021)(67,1020)(68,1019)(69,1018)(70,1017)(71,1016)(72,1015)(73,1014)(74,1013)(75,1012)(76,1011)(77,1010)(78,1009)(79,1008)(80,1007)(81,1006)(82,1005)(83,1004)(84,1003)(85,1002)(86,1001)(87,1000)(88,999)(89,998)(90,997)(91,996)(92,995)(93,994)(94,993)(95,992)(96,991)(97,990)(98,989)(99,988)(100,987)(101,986)(102,985)(103,984)(104,983)(105,982)(106,981)(107,980)(108,979)(109,978)(110,977)(111,976)(112,975)(113,974)(114,973)(115,972)(116,971)(117,970)(118,969)(119,968)(120,967)(121,966)(122,965)(123,964)(124,963)(125,962)(126,961)(127,960)(128,959)(129,958)(130,957)(131,956)(132,955)(133,954)(134,953)(135,952)(136,951)(137,950)(138,949)(139,948)(140,947)(141,946)(142,945)(143,944)(144,943)(145,942)(146,941)(147,940)(148,939)(149,938)(150,937)(151,936)(152,935)(153,934)(154,933)(155,932)(156,931)(157,930)(158,929)(159,928)(160,927)(161,926)(162,925)(163,924)(164,923)(165,922)(166,921)(167,920)(168,919)(169,918)(170,917)(171,916)(172,915)(173,914)(174,913)(175,912)(176,911)(177,910)(178,909)(179,908)(180,907)(181,906)(182,905)(183,904)(184,903)(185,902)(186,901)(187,900)(188,899)(189,898)(190,897)(191,896)(192,895)(193,894)(194,893)(195,892)(196,891)(197,890)(198,889)(199,888)(200,887)(201,886)(202,885)(203,884)(204,883)(205,882)(206,881)(207,880)(208,879)(209,878)(210,877)(211,876)(212,875)(213,874)(214,873)(215,872)(216,871)(217,870)(218,869)(219,868)(220,867)(221,866)(222,865)(223,864)(224,863)(225,862)(226,861)(227,860)(228,859)(229,858)(230,857)(231,856)(232,855)(233,854)(234,853)(235,852)(236,851)(237,850)(238,849)(239,848)(240,847)(241,846)(242,845)(243,844)(244,843)(245,842)(246,841)(247,840)(248,839)(249,838)(250,837)(251,836)(252,835)(253,834)(254,833)(255,832)(256,831)(257,830)(258,829)(259,828)(260,827)(261,826)(262,825)(263,824)(264,823)(265,822)(266,821)(267,820)(268,819)(269,818)(270,817)(271,816)(272,815)(273,814)(274,813)(275,812)(276,811)(277,810)(278,809)(279,808)(280,807)(281,806)(282,805)(283,804)(284,803)(285,802)(286,801)(287,800)(288,799)(289,798)(290,797)(291,796)(292,795)(293,794)(294,793)(295,792)(296,791)(297,790)(298,789)(299,788)(300,787)(301,786)(302,785)(303,784)(304,783)(305,782)(306,781)(307,780)(308,779)(309,778)(310,777)(311,776)(312,775)(313,774)(314,773)(315,772)(316,771)(317,770)(318,769)(319,768)(320,767)(321,766)(322,765)(323,764)(324,763)(325,762)(326,761)(327,760)(328,759)(329,758)(330,757)(331,756)(332,755)(333,754)(334,753)(335,752)(336,751)(337,750)(338,749)(339,748)(340,747)(341,746)(342,745)(343,744)(344,743)(345,742)(346,741)(347,740)(348,739)(349,738)(350,737)(351,736)(352,735)(353,734)(354,733)(355,732)(356,731)(357,730)(358,729)(359,728)(360,727)(361,726)(362,725)(363,724)(364,723)(365,722)(366,721)(367,720)(368,719)(369,718)(370,717)(371,716)(372,715)(373,714)(374,713)(375,712)(376,711)(377,710)(378,709)(379,708)(380,707)(381,706)(382,705)(383,704)(384,703)(385,702)(386,701)(387,700)(388,699)(389,698)(390,697)(391,696)(392,695)(393,694)(394,693)(395,692)(396,691)(397,690)(398,689)(399,688)(400,687)(401,686)(402,685)(403,684)(404,683)(405,682)(406,681)(407,680)(408,679)(409,678)(410,677)(411,676)(412,675)(413,674)(414,673)(415,672)(416,671)(417,670)(418,669)(419,668)(420,667)(421,666)(422,665)(423,664)(424,663)(425,662)(426,661)(427,660)(428,659)(429,658)(430,657)(431,656)(432,655)(433,654)(434,653)(435,652)(436,651)(437,650)(438,649)(439,648)(440,647)(441,646)(442,645)(443,644)(444,643)(445,642)(446,641)(447,640)(448,639)(449,638)(450,637)(451,636)(452,635)(453,634)(454,633)(455,632)(456,631)(457,630)(458,629)(459,628)(460,627)(461,626)(462,625)(463,624)(464,623)(465,622)(466,621)(467,620)(468,619)(469,618)(470,617)(471,616)(472,615)(473,614)(474,613)(475,612)(476,611)(477,610)(478,609)(479,608)(480,607)(481,606)(482,605)(483,604)(484,603)(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(491,596)(492,595)(493,594)(494,593)(495,592)(496,591)(497,590)(498,589)(499,588)(500,587)(501,586)(502,585)(503,584)(504,583)(505,582)(506,581)(507,580)(508,579)(509,578)(510,577)(511,576)(512,575)(513,574)(514,573)(515,572)(516,571)(517,570)(518,569)(519,568)(520,567)(521,566)(522,565)(523,564)(524,563)(525,562)(526,561)(527,560)(528,559)(529,558)(530,557)(531,556)(532,555)(533,554)(534,553)(535,552)(536,551)(537,550)(538,549)(539,548)(540,547)(541,546)(542,545)(543,544)
Conjugacy classes & character table
8022 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32070, 5);
Finite Group Databasebeta