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D7427 #28415367
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1068 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);(2,7)(3,6)(4,5)(9,1068)(10,1067)(11,1066)(12,1065)(13,1064)(14,1063)(15,1062)(16,1061)(17,1060)(18,1059)(19,1058)(20,1057)(21,1056)(22,1055)(23,1054)(24,1053)(25,1052)(26,1051)(27,1050)(28,1049)(29,1048)(30,1047)(31,1046)(32,1045)(33,1044)(34,1043)(35,1042)(36,1041)(37,1040)(38,1039)(39,1038)(40,1037)(41,1036)(42,1035)(43,1034)(44,1033)(45,1032)(46,1031)(47,1030)(48,1029)(49,1028)(50,1027)(51,1026)(52,1025)(53,1024)(54,1023)(55,1022)(56,1021)(57,1020)(58,1019)(59,1018)(60,1017)(61,1016)(62,1015)(63,1014)(64,1013)(65,1012)(66,1011)(67,1010)(68,1009)(69,1008)(70,1007)(71,1006)(72,1005)(73,1004)(74,1003)(75,1002)(76,1001)(77,1000)(78,999)(79,998)(80,997)(81,996)(82,995)(83,994)(84,993)(85,992)(86,991)(87,990)(88,989)(89,988)(90,987)(91,986)(92,985)(93,984)(94,983)(95,982)(96,981)(97,980)(98,979)(99,978)(100,977)(101,976)(102,975)(103,974)(104,973)(105,972)(106,971)(107,970)(108,969)(109,968)(110,967)(111,966)(112,965)(113,964)(114,963)(115,962)(116,961)(117,960)(118,959)(119,958)(120,957)(121,956)(122,955)(123,954)(124,953)(125,952)(126,951)(127,950)(128,949)(129,948)(130,947)(131,946)(132,945)(133,944)(134,943)(135,942)(136,941)(137,940)(138,939)(139,938)(140,937)(141,936)(142,935)(143,934)(144,933)(145,932)(146,931)(147,930)(148,929)(149,928)(150,927)(151,926)(152,925)(153,924)(154,923)(155,922)(156,921)(157,920)(158,919)(159,918)(160,917)(161,916)(162,915)(163,914)(164,913)(165,912)(166,911)(167,910)(168,909)(169,908)(170,907)(171,906)(172,905)(173,904)(174,903)(175,902)(176,901)(177,900)(178,899)(179,898)(180,897)(181,896)(182,895)(183,894)(184,893)(185,892)(186,891)(187,890)(188,889)(189,888)(190,887)(191,886)(192,885)(193,884)(194,883)(195,882)(196,881)(197,880)(198,879)(199,878)(200,877)(201,876)(202,875)(203,874)(204,873)(205,872)(206,871)(207,870)(208,869)(209,868)(210,867)(211,866)(212,865)(213,864)(214,863)(215,862)(216,861)(217,860)(218,859)(219,858)(220,857)(221,856)(222,855)(223,854)(224,853)(225,852)(226,851)(227,850)(228,849)(229,848)(230,847)(231,846)(232,845)(233,844)(234,843)(235,842)(236,841)(237,840)(238,839)(239,838)(240,837)(241,836)(242,835)(243,834)(244,833)(245,832)(246,831)(247,830)(248,829)(249,828)(250,827)(251,826)(252,825)(253,824)(254,823)(255,822)(256,821)(257,820)(258,819)(259,818)(260,817)(261,816)(262,815)(263,814)(264,813)(265,812)(266,811)(267,810)(268,809)(269,808)(270,807)(271,806)(272,805)(273,804)(274,803)(275,802)(276,801)(277,800)(278,799)(279,798)(280,797)(281,796)(282,795)(283,794)(284,793)(285,792)(286,791)(287,790)(288,789)(289,788)(290,787)(291,786)(292,785)(293,784)(294,783)(295,782)(296,781)(297,780)(298,779)(299,778)(300,777)(301,776)(302,775)(303,774)(304,773)(305,772)(306,771)(307,770)(308,769)(309,768)(310,767)(311,766)(312,765)(313,764)(314,763)(315,762)(316,761)(317,760)(318,759)(319,758)(320,757)(321,756)(322,755)(323,754)(324,753)(325,752)(326,751)(327,750)(328,749)(329,748)(330,747)(331,746)(332,745)(333,744)(334,743)(335,742)(336,741)(337,740)(338,739)(339,738)(340,737)(341,736)(342,735)(343,734)(344,733)(345,732)(346,731)(347,730)(348,729)(349,728)(350,727)(351,726)(352,725)(353,724)(354,723)(355,722)(356,721)(357,720)(358,719)(359,718)(360,717)(361,716)(362,715)(363,714)(364,713)(365,712)(366,711)(367,710)(368,709)(369,708)(370,707)(371,706)(372,705)(373,704)(374,703)(375,702)(376,701)(377,700)(378,699)(379,698)(380,697)(381,696)(382,695)(383,694)(384,693)(385,692)(386,691)(387,690)(388,689)(389,688)(390,687)(391,686)(392,685)(393,684)(394,683)(395,682)(396,681)(397,680)(398,679)(399,678)(400,677)(401,676)(402,675)(403,674)(404,673)(405,672)(406,671)(407,670)(408,669)(409,668)(410,667)(411,666)(412,665)(413,664)(414,663)(415,662)(416,661)(417,660)(418,659)(419,658)(420,657)(421,656)(422,655)(423,654)(424,653)(425,652)(426,651)(427,650)(428,649)(429,648)(430,647)(431,646)(432,645)(433,644)(434,643)(435,642)(436,641)(437,640)(438,639)(439,638)(440,637)(441,636)(442,635)(443,634)(444,633)(445,632)(446,631)(447,630)(448,629)(449,628)(450,627)(451,626)(452,625)(453,624)(454,623)(455,622)(456,621)(457,620)(458,619)(459,618)(460,617)(461,616)(462,615)(463,614)(464,613)(465,612)(466,611)(467,610)(468,609)(469,608)(470,607)(471,606)(472,605)(473,604)(474,603)(475,602)(476,601)(477,600)(478,599)(479,598)(480,597)(481,596)(482,595)(483,594)(484,593)(485,592)(486,591)(487,590)(488,589)(489,588)(490,587)(491,586)(492,585)(493,584)(494,583)(495,582)(496,581)(497,580)(498,579)(499,578)(500,577)(501,576)(502,575)(503,574)(504,573)(505,572)(506,571)(507,570)(508,569)(509,568)(510,567)(511,566)(512,565)(513,564)(514,563)(515,562)(516,561)(517,560)(518,559)(519,558)(520,557)(521,556)(522,555)(523,554)(524,553)(525,552)(526,551)(527,550)(528,549)(529,548)(530,547)(531,546)(532,545)(533,544)(534,543)(535,542)(536,541)(537,540)(538,539)
Polycyclic presentation:
2,7,1061|b^a=b^6,c^a=c^1060
Conjugacy classes & character table
3715 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14854, 3);
Finite Group Databasebeta