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Dic6559 #39910896
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 948 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);(1,3,2,4)(6,11)(7,10)(8,9)(13,948)(14,947)(15,946)(16,945)(17,944)(18,943)(19,942)(20,941)(21,940)(22,939)(23,938)(24,937)(25,936)(26,935)(27,934)(28,933)(29,932)(30,931)(31,930)(32,929)(33,928)(34,927)(35,926)(36,925)(37,924)(38,923)(39,922)(40,921)(41,920)(42,919)(43,918)(44,917)(45,916)(46,915)(47,914)(48,913)(49,912)(50,911)(51,910)(52,909)(53,908)(54,907)(55,906)(56,905)(57,904)(58,903)(59,902)(60,901)(61,900)(62,899)(63,898)(64,897)(65,896)(66,895)(67,894)(68,893)(69,892)(70,891)(71,890)(72,889)(73,888)(74,887)(75,886)(76,885)(77,884)(78,883)(79,882)(80,881)(81,880)(82,879)(83,878)(84,877)(85,876)(86,875)(87,874)(88,873)(89,872)(90,871)(91,870)(92,869)(93,868)(94,867)(95,866)(96,865)(97,864)(98,863)(99,862)(100,861)(101,860)(102,859)(103,858)(104,857)(105,856)(106,855)(107,854)(108,853)(109,852)(110,851)(111,850)(112,849)(113,848)(114,847)(115,846)(116,845)(117,844)(118,843)(119,842)(120,841)(121,840)(122,839)(123,838)(124,837)(125,836)(126,835)(127,834)(128,833)(129,832)(130,831)(131,830)(132,829)(133,828)(134,827)(135,826)(136,825)(137,824)(138,823)(139,822)(140,821)(141,820)(142,819)(143,818)(144,817)(145,816)(146,815)(147,814)(148,813)(149,812)(150,811)(151,810)(152,809)(153,808)(154,807)(155,806)(156,805)(157,804)(158,803)(159,802)(160,801)(161,800)(162,799)(163,798)(164,797)(165,796)(166,795)(167,794)(168,793)(169,792)(170,791)(171,790)(172,789)(173,788)(174,787)(175,786)(176,785)(177,784)(178,783)(179,782)(180,781)(181,780)(182,779)(183,778)(184,777)(185,776)(186,775)(187,774)(188,773)(189,772)(190,771)(191,770)(192,769)(193,768)(194,767)(195,766)(196,765)(197,764)(198,763)(199,762)(200,761)(201,760)(202,759)(203,758)(204,757)(205,756)(206,755)(207,754)(208,753)(209,752)(210,751)(211,750)(212,749)(213,748)(214,747)(215,746)(216,745)(217,744)(218,743)(219,742)(220,741)(221,740)(222,739)(223,738)(224,737)(225,736)(226,735)(227,734)(228,733)(229,732)(230,731)(231,730)(232,729)(233,728)(234,727)(235,726)(236,725)(237,724)(238,723)(239,722)(240,721)(241,720)(242,719)(243,718)(244,717)(245,716)(246,715)(247,714)(248,713)(249,712)(250,711)(251,710)(252,709)(253,708)(254,707)(255,706)(256,705)(257,704)(258,703)(259,702)(260,701)(261,700)(262,699)(263,698)(264,697)(265,696)(266,695)(267,694)(268,693)(269,692)(270,691)(271,690)(272,689)(273,688)(274,687)(275,686)(276,685)(277,684)(278,683)(279,682)(280,681)(281,680)(282,679)(283,678)(284,677)(285,676)(286,675)(287,674)(288,673)(289,672)(290,671)(291,670)(292,669)(293,668)(294,667)(295,666)(296,665)(297,664)(298,663)(299,662)(300,661)(301,660)(302,659)(303,658)(304,657)(305,656)(306,655)(307,654)(308,653)(309,652)(310,651)(311,650)(312,649)(313,648)(314,647)(315,646)(316,645)(317,644)(318,643)(319,642)(320,641)(321,640)(322,639)(323,638)(324,637)(325,636)(326,635)(327,634)(328,633)(329,632)(330,631)(331,630)(332,629)(333,628)(334,627)(335,626)(336,625)(337,624)(338,623)(339,622)(340,621)(341,620)(342,619)(343,618)(344,617)(345,616)(346,615)(347,614)(348,613)(349,612)(350,611)(351,610)(352,609)(353,608)(354,607)(355,606)(356,605)(357,604)(358,603)(359,602)(360,601)(361,600)(362,599)(363,598)(364,597)(365,596)(366,595)(367,594)(368,593)(369,592)(370,591)(371,590)(372,589)(373,588)(374,587)(375,586)(376,585)(377,584)(378,583)(379,582)(380,581)(381,580)(382,579)(383,578)(384,577)(385,576)(386,575)(387,574)(388,573)(389,572)(390,571)(391,570)(392,569)(393,568)(394,567)(395,566)(396,565)(397,564)(398,563)(399,562)(400,561)(401,560)(402,559)(403,558)(404,557)(405,556)(406,555)(407,554)(408,553)(409,552)(410,551)(411,550)(412,549)(413,548)(414,547)(415,546)(416,545)(417,544)(418,543)(419,542)(420,541)(421,540)(422,539)(423,538)(424,537)(425,536)(426,535)(427,534)(428,533)(429,532)(430,531)(431,530)(432,529)(433,528)(434,527)(435,526)(436,525)(437,524)(438,523)(439,522)(440,521)(441,520)(442,519)(443,518)(444,517)(445,516)(446,515)(447,514)(448,513)(449,512)(450,511)(451,510)(452,509)(453,508)(454,507)(455,506)(456,505)(457,504)(458,503)(459,502)(460,501)(461,500)(462,499)(463,498)(464,497)(465,496)(466,495)(467,494)(468,493)(469,492)(470,491)(471,490)(472,489)(473,488)(474,487)(475,486)(476,485)(477,484)(478,483)(479,482)(480,481)
Polycyclic presentation:
2,7,937,2|a^2=d,b^a=b^6,c^a=c^936
Conjugacy classes & character table
6562 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26236, 4);
Finite Group Databasebeta