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D7343 #28412773
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1056 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);(2,7)(3,6)(4,5)(9,1056)(10,1055)(11,1054)(12,1053)(13,1052)(14,1051)(15,1050)(16,1049)(17,1048)(18,1047)(19,1046)(20,1045)(21,1044)(22,1043)(23,1042)(24,1041)(25,1040)(26,1039)(27,1038)(28,1037)(29,1036)(30,1035)(31,1034)(32,1033)(33,1032)(34,1031)(35,1030)(36,1029)(37,1028)(38,1027)(39,1026)(40,1025)(41,1024)(42,1023)(43,1022)(44,1021)(45,1020)(46,1019)(47,1018)(48,1017)(49,1016)(50,1015)(51,1014)(52,1013)(53,1012)(54,1011)(55,1010)(56,1009)(57,1008)(58,1007)(59,1006)(60,1005)(61,1004)(62,1003)(63,1002)(64,1001)(65,1000)(66,999)(67,998)(68,997)(69,996)(70,995)(71,994)(72,993)(73,992)(74,991)(75,990)(76,989)(77,988)(78,987)(79,986)(80,985)(81,984)(82,983)(83,982)(84,981)(85,980)(86,979)(87,978)(88,977)(89,976)(90,975)(91,974)(92,973)(93,972)(94,971)(95,970)(96,969)(97,968)(98,967)(99,966)(100,965)(101,964)(102,963)(103,962)(104,961)(105,960)(106,959)(107,958)(108,957)(109,956)(110,955)(111,954)(112,953)(113,952)(114,951)(115,950)(116,949)(117,948)(118,947)(119,946)(120,945)(121,944)(122,943)(123,942)(124,941)(125,940)(126,939)(127,938)(128,937)(129,936)(130,935)(131,934)(132,933)(133,932)(134,931)(135,930)(136,929)(137,928)(138,927)(139,926)(140,925)(141,924)(142,923)(143,922)(144,921)(145,920)(146,919)(147,918)(148,917)(149,916)(150,915)(151,914)(152,913)(153,912)(154,911)(155,910)(156,909)(157,908)(158,907)(159,906)(160,905)(161,904)(162,903)(163,902)(164,901)(165,900)(166,899)(167,898)(168,897)(169,896)(170,895)(171,894)(172,893)(173,892)(174,891)(175,890)(176,889)(177,888)(178,887)(179,886)(180,885)(181,884)(182,883)(183,882)(184,881)(185,880)(186,879)(187,878)(188,877)(189,876)(190,875)(191,874)(192,873)(193,872)(194,871)(195,870)(196,869)(197,868)(198,867)(199,866)(200,865)(201,864)(202,863)(203,862)(204,861)(205,860)(206,859)(207,858)(208,857)(209,856)(210,855)(211,854)(212,853)(213,852)(214,851)(215,850)(216,849)(217,848)(218,847)(219,846)(220,845)(221,844)(222,843)(223,842)(224,841)(225,840)(226,839)(227,838)(228,837)(229,836)(230,835)(231,834)(232,833)(233,832)(234,831)(235,830)(236,829)(237,828)(238,827)(239,826)(240,825)(241,824)(242,823)(243,822)(244,821)(245,820)(246,819)(247,818)(248,817)(249,816)(250,815)(251,814)(252,813)(253,812)(254,811)(255,810)(256,809)(257,808)(258,807)(259,806)(260,805)(261,804)(262,803)(263,802)(264,801)(265,800)(266,799)(267,798)(268,797)(269,796)(270,795)(271,794)(272,793)(273,792)(274,791)(275,790)(276,789)(277,788)(278,787)(279,786)(280,785)(281,784)(282,783)(283,782)(284,781)(285,780)(286,779)(287,778)(288,777)(289,776)(290,775)(291,774)(292,773)(293,772)(294,771)(295,770)(296,769)(297,768)(298,767)(299,766)(300,765)(301,764)(302,763)(303,762)(304,761)(305,760)(306,759)(307,758)(308,757)(309,756)(310,755)(311,754)(312,753)(313,752)(314,751)(315,750)(316,749)(317,748)(318,747)(319,746)(320,745)(321,744)(322,743)(323,742)(324,741)(325,740)(326,739)(327,738)(328,737)(329,736)(330,735)(331,734)(332,733)(333,732)(334,731)(335,730)(336,729)(337,728)(338,727)(339,726)(340,725)(341,724)(342,723)(343,722)(344,721)(345,720)(346,719)(347,718)(348,717)(349,716)(350,715)(351,714)(352,713)(353,712)(354,711)(355,710)(356,709)(357,708)(358,707)(359,706)(360,705)(361,704)(362,703)(363,702)(364,701)(365,700)(366,699)(367,698)(368,697)(369,696)(370,695)(371,694)(372,693)(373,692)(374,691)(375,690)(376,689)(377,688)(378,687)(379,686)(380,685)(381,684)(382,683)(383,682)(384,681)(385,680)(386,679)(387,678)(388,677)(389,676)(390,675)(391,674)(392,673)(393,672)(394,671)(395,670)(396,669)(397,668)(398,667)(399,666)(400,665)(401,664)(402,663)(403,662)(404,661)(405,660)(406,659)(407,658)(408,657)(409,656)(410,655)(411,654)(412,653)(413,652)(414,651)(415,650)(416,649)(417,648)(418,647)(419,646)(420,645)(421,644)(422,643)(423,642)(424,641)(425,640)(426,639)(427,638)(428,637)(429,636)(430,635)(431,634)(432,633)(433,632)(434,631)(435,630)(436,629)(437,628)(438,627)(439,626)(440,625)(441,624)(442,623)(443,622)(444,621)(445,620)(446,619)(447,618)(448,617)(449,616)(450,615)(451,614)(452,613)(453,612)(454,611)(455,610)(456,609)(457,608)(458,607)(459,606)(460,605)(461,604)(462,603)(463,602)(464,601)(465,600)(466,599)(467,598)(468,597)(469,596)(470,595)(471,594)(472,593)(473,592)(474,591)(475,590)(476,589)(477,588)(478,587)(479,586)(480,585)(481,584)(482,583)(483,582)(484,581)(485,580)(486,579)(487,578)(488,577)(489,576)(490,575)(491,574)(492,573)(493,572)(494,571)(495,570)(496,569)(497,568)(498,567)(499,566)(500,565)(501,564)(502,563)(503,562)(504,561)(505,560)(506,559)(507,558)(508,557)(509,556)(510,555)(511,554)(512,553)(513,552)(514,551)(515,550)(516,549)(517,548)(518,547)(519,546)(520,545)(521,544)(522,543)(523,542)(524,541)(525,540)(526,539)(527,538)(528,537)(529,536)(530,535)(531,534)(532,533)
Polycyclic presentation:
2,7,1049|b^a=b^6,c^a=c^1048
Conjugacy classes & character table
3673 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14686, 3);
Finite Group Databasebeta