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Dic6727 #41002048
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 972 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);(1,3,2,4)(6,11)(7,10)(8,9)(13,972)(14,971)(15,970)(16,969)(17,968)(18,967)(19,966)(20,965)(21,964)(22,963)(23,962)(24,961)(25,960)(26,959)(27,958)(28,957)(29,956)(30,955)(31,954)(32,953)(33,952)(34,951)(35,950)(36,949)(37,948)(38,947)(39,946)(40,945)(41,944)(42,943)(43,942)(44,941)(45,940)(46,939)(47,938)(48,937)(49,936)(50,935)(51,934)(52,933)(53,932)(54,931)(55,930)(56,929)(57,928)(58,927)(59,926)(60,925)(61,924)(62,923)(63,922)(64,921)(65,920)(66,919)(67,918)(68,917)(69,916)(70,915)(71,914)(72,913)(73,912)(74,911)(75,910)(76,909)(77,908)(78,907)(79,906)(80,905)(81,904)(82,903)(83,902)(84,901)(85,900)(86,899)(87,898)(88,897)(89,896)(90,895)(91,894)(92,893)(93,892)(94,891)(95,890)(96,889)(97,888)(98,887)(99,886)(100,885)(101,884)(102,883)(103,882)(104,881)(105,880)(106,879)(107,878)(108,877)(109,876)(110,875)(111,874)(112,873)(113,872)(114,871)(115,870)(116,869)(117,868)(118,867)(119,866)(120,865)(121,864)(122,863)(123,862)(124,861)(125,860)(126,859)(127,858)(128,857)(129,856)(130,855)(131,854)(132,853)(133,852)(134,851)(135,850)(136,849)(137,848)(138,847)(139,846)(140,845)(141,844)(142,843)(143,842)(144,841)(145,840)(146,839)(147,838)(148,837)(149,836)(150,835)(151,834)(152,833)(153,832)(154,831)(155,830)(156,829)(157,828)(158,827)(159,826)(160,825)(161,824)(162,823)(163,822)(164,821)(165,820)(166,819)(167,818)(168,817)(169,816)(170,815)(171,814)(172,813)(173,812)(174,811)(175,810)(176,809)(177,808)(178,807)(179,806)(180,805)(181,804)(182,803)(183,802)(184,801)(185,800)(186,799)(187,798)(188,797)(189,796)(190,795)(191,794)(192,793)(193,792)(194,791)(195,790)(196,789)(197,788)(198,787)(199,786)(200,785)(201,784)(202,783)(203,782)(204,781)(205,780)(206,779)(207,778)(208,777)(209,776)(210,775)(211,774)(212,773)(213,772)(214,771)(215,770)(216,769)(217,768)(218,767)(219,766)(220,765)(221,764)(222,763)(223,762)(224,761)(225,760)(226,759)(227,758)(228,757)(229,756)(230,755)(231,754)(232,753)(233,752)(234,751)(235,750)(236,749)(237,748)(238,747)(239,746)(240,745)(241,744)(242,743)(243,742)(244,741)(245,740)(246,739)(247,738)(248,737)(249,736)(250,735)(251,734)(252,733)(253,732)(254,731)(255,730)(256,729)(257,728)(258,727)(259,726)(260,725)(261,724)(262,723)(263,722)(264,721)(265,720)(266,719)(267,718)(268,717)(269,716)(270,715)(271,714)(272,713)(273,712)(274,711)(275,710)(276,709)(277,708)(278,707)(279,706)(280,705)(281,704)(282,703)(283,702)(284,701)(285,700)(286,699)(287,698)(288,697)(289,696)(290,695)(291,694)(292,693)(293,692)(294,691)(295,690)(296,689)(297,688)(298,687)(299,686)(300,685)(301,684)(302,683)(303,682)(304,681)(305,680)(306,679)(307,678)(308,677)(309,676)(310,675)(311,674)(312,673)(313,672)(314,671)(315,670)(316,669)(317,668)(318,667)(319,666)(320,665)(321,664)(322,663)(323,662)(324,661)(325,660)(326,659)(327,658)(328,657)(329,656)(330,655)(331,654)(332,653)(333,652)(334,651)(335,650)(336,649)(337,648)(338,647)(339,646)(340,645)(341,644)(342,643)(343,642)(344,641)(345,640)(346,639)(347,638)(348,637)(349,636)(350,635)(351,634)(352,633)(353,632)(354,631)(355,630)(356,629)(357,628)(358,627)(359,626)(360,625)(361,624)(362,623)(363,622)(364,621)(365,620)(366,619)(367,618)(368,617)(369,616)(370,615)(371,614)(372,613)(373,612)(374,611)(375,610)(376,609)(377,608)(378,607)(379,606)(380,605)(381,604)(382,603)(383,602)(384,601)(385,600)(386,599)(387,598)(388,597)(389,596)(390,595)(391,594)(392,593)(393,592)(394,591)(395,590)(396,589)(397,588)(398,587)(399,586)(400,585)(401,584)(402,583)(403,582)(404,581)(405,580)(406,579)(407,578)(408,577)(409,576)(410,575)(411,574)(412,573)(413,572)(414,571)(415,570)(416,569)(417,568)(418,567)(419,566)(420,565)(421,564)(422,563)(423,562)(424,561)(425,560)(426,559)(427,558)(428,557)(429,556)(430,555)(431,554)(432,553)(433,552)(434,551)(435,550)(436,549)(437,548)(438,547)(439,546)(440,545)(441,544)(442,543)(443,542)(444,541)(445,540)(446,539)(447,538)(448,537)(449,536)(450,535)(451,534)(452,533)(453,532)(454,531)(455,530)(456,529)(457,528)(458,527)(459,526)(460,525)(461,524)(462,523)(463,522)(464,521)(465,520)(466,519)(467,518)(468,517)(469,516)(470,515)(471,514)(472,513)(473,512)(474,511)(475,510)(476,509)(477,508)(478,507)(479,506)(480,505)(481,504)(482,503)(483,502)(484,501)(485,500)(486,499)(487,498)(488,497)(489,496)(490,495)(491,494)(492,493)
Polycyclic presentation:
2,7,31,2,31|a^2=d,c^31=e^30,b^a=b^6,c^a=c^30e,e^a=e^30
Conjugacy classes & character table
6730 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26908, 4);
Finite Group Databasebeta