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D6503 #27188995
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 936 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);(2,7)(3,6)(4,5)(9,936)(10,935)(11,934)(12,933)(13,932)(14,931)(15,930)(16,929)(17,928)(18,927)(19,926)(20,925)(21,924)(22,923)(23,922)(24,921)(25,920)(26,919)(27,918)(28,917)(29,916)(30,915)(31,914)(32,913)(33,912)(34,911)(35,910)(36,909)(37,908)(38,907)(39,906)(40,905)(41,904)(42,903)(43,902)(44,901)(45,900)(46,899)(47,898)(48,897)(49,896)(50,895)(51,894)(52,893)(53,892)(54,891)(55,890)(56,889)(57,888)(58,887)(59,886)(60,885)(61,884)(62,883)(63,882)(64,881)(65,880)(66,879)(67,878)(68,877)(69,876)(70,875)(71,874)(72,873)(73,872)(74,871)(75,870)(76,869)(77,868)(78,867)(79,866)(80,865)(81,864)(82,863)(83,862)(84,861)(85,860)(86,859)(87,858)(88,857)(89,856)(90,855)(91,854)(92,853)(93,852)(94,851)(95,850)(96,849)(97,848)(98,847)(99,846)(100,845)(101,844)(102,843)(103,842)(104,841)(105,840)(106,839)(107,838)(108,837)(109,836)(110,835)(111,834)(112,833)(113,832)(114,831)(115,830)(116,829)(117,828)(118,827)(119,826)(120,825)(121,824)(122,823)(123,822)(124,821)(125,820)(126,819)(127,818)(128,817)(129,816)(130,815)(131,814)(132,813)(133,812)(134,811)(135,810)(136,809)(137,808)(138,807)(139,806)(140,805)(141,804)(142,803)(143,802)(144,801)(145,800)(146,799)(147,798)(148,797)(149,796)(150,795)(151,794)(152,793)(153,792)(154,791)(155,790)(156,789)(157,788)(158,787)(159,786)(160,785)(161,784)(162,783)(163,782)(164,781)(165,780)(166,779)(167,778)(168,777)(169,776)(170,775)(171,774)(172,773)(173,772)(174,771)(175,770)(176,769)(177,768)(178,767)(179,766)(180,765)(181,764)(182,763)(183,762)(184,761)(185,760)(186,759)(187,758)(188,757)(189,756)(190,755)(191,754)(192,753)(193,752)(194,751)(195,750)(196,749)(197,748)(198,747)(199,746)(200,745)(201,744)(202,743)(203,742)(204,741)(205,740)(206,739)(207,738)(208,737)(209,736)(210,735)(211,734)(212,733)(213,732)(214,731)(215,730)(216,729)(217,728)(218,727)(219,726)(220,725)(221,724)(222,723)(223,722)(224,721)(225,720)(226,719)(227,718)(228,717)(229,716)(230,715)(231,714)(232,713)(233,712)(234,711)(235,710)(236,709)(237,708)(238,707)(239,706)(240,705)(241,704)(242,703)(243,702)(244,701)(245,700)(246,699)(247,698)(248,697)(249,696)(250,695)(251,694)(252,693)(253,692)(254,691)(255,690)(256,689)(257,688)(258,687)(259,686)(260,685)(261,684)(262,683)(263,682)(264,681)(265,680)(266,679)(267,678)(268,677)(269,676)(270,675)(271,674)(272,673)(273,672)(274,671)(275,670)(276,669)(277,668)(278,667)(279,666)(280,665)(281,664)(282,663)(283,662)(284,661)(285,660)(286,659)(287,658)(288,657)(289,656)(290,655)(291,654)(292,653)(293,652)(294,651)(295,650)(296,649)(297,648)(298,647)(299,646)(300,645)(301,644)(302,643)(303,642)(304,641)(305,640)(306,639)(307,638)(308,637)(309,636)(310,635)(311,634)(312,633)(313,632)(314,631)(315,630)(316,629)(317,628)(318,627)(319,626)(320,625)(321,624)(322,623)(323,622)(324,621)(325,620)(326,619)(327,618)(328,617)(329,616)(330,615)(331,614)(332,613)(333,612)(334,611)(335,610)(336,609)(337,608)(338,607)(339,606)(340,605)(341,604)(342,603)(343,602)(344,601)(345,600)(346,599)(347,598)(348,597)(349,596)(350,595)(351,594)(352,593)(353,592)(354,591)(355,590)(356,589)(357,588)(358,587)(359,586)(360,585)(361,584)(362,583)(363,582)(364,581)(365,580)(366,579)(367,578)(368,577)(369,576)(370,575)(371,574)(372,573)(373,572)(374,571)(375,570)(376,569)(377,568)(378,567)(379,566)(380,565)(381,564)(382,563)(383,562)(384,561)(385,560)(386,559)(387,558)(388,557)(389,556)(390,555)(391,554)(392,553)(393,552)(394,551)(395,550)(396,549)(397,548)(398,547)(399,546)(400,545)(401,544)(402,543)(403,542)(404,541)(405,540)(406,539)(407,538)(408,537)(409,536)(410,535)(411,534)(412,533)(413,532)(414,531)(415,530)(416,529)(417,528)(418,527)(419,526)(420,525)(421,524)(422,523)(423,522)(424,521)(425,520)(426,519)(427,518)(428,517)(429,516)(430,515)(431,514)(432,513)(433,512)(434,511)(435,510)(436,509)(437,508)(438,507)(439,506)(440,505)(441,504)(442,503)(443,502)(444,501)(445,500)(446,499)(447,498)(448,497)(449,496)(450,495)(451,494)(452,493)(453,492)(454,491)(455,490)(456,489)(457,488)(458,487)(459,486)(460,485)(461,484)(462,483)(463,482)(464,481)(465,480)(466,479)(467,478)(468,477)(469,476)(470,475)(471,474)(472,473)
Polycyclic presentation:
2,7,929|b^a=b^6,c^a=c^928
Conjugacy classes & character table
3253 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13006, 3);
Finite Group Databasebeta