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D7352 #28413627
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 927 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);(2,8)(3,7)(4,6)(10,927)(11,926)(12,925)(13,924)(14,923)(15,922)(16,921)(17,920)(18,919)(19,918)(20,917)(21,916)(22,915)(23,914)(24,913)(25,912)(26,911)(27,910)(28,909)(29,908)(30,907)(31,906)(32,905)(33,904)(34,903)(35,902)(36,901)(37,900)(38,899)(39,898)(40,897)(41,896)(42,895)(43,894)(44,893)(45,892)(46,891)(47,890)(48,889)(49,888)(50,887)(51,886)(52,885)(53,884)(54,883)(55,882)(56,881)(57,880)(58,879)(59,878)(60,877)(61,876)(62,875)(63,874)(64,873)(65,872)(66,871)(67,870)(68,869)(69,868)(70,867)(71,866)(72,865)(73,864)(74,863)(75,862)(76,861)(77,860)(78,859)(79,858)(80,857)(81,856)(82,855)(83,854)(84,853)(85,852)(86,851)(87,850)(88,849)(89,848)(90,847)(91,846)(92,845)(93,844)(94,843)(95,842)(96,841)(97,840)(98,839)(99,838)(100,837)(101,836)(102,835)(103,834)(104,833)(105,832)(106,831)(107,830)(108,829)(109,828)(110,827)(111,826)(112,825)(113,824)(114,823)(115,822)(116,821)(117,820)(118,819)(119,818)(120,817)(121,816)(122,815)(123,814)(124,813)(125,812)(126,811)(127,810)(128,809)(129,808)(130,807)(131,806)(132,805)(133,804)(134,803)(135,802)(136,801)(137,800)(138,799)(139,798)(140,797)(141,796)(142,795)(143,794)(144,793)(145,792)(146,791)(147,790)(148,789)(149,788)(150,787)(151,786)(152,785)(153,784)(154,783)(155,782)(156,781)(157,780)(158,779)(159,778)(160,777)(161,776)(162,775)(163,774)(164,773)(165,772)(166,771)(167,770)(168,769)(169,768)(170,767)(171,766)(172,765)(173,764)(174,763)(175,762)(176,761)(177,760)(178,759)(179,758)(180,757)(181,756)(182,755)(183,754)(184,753)(185,752)(186,751)(187,750)(188,749)(189,748)(190,747)(191,746)(192,745)(193,744)(194,743)(195,742)(196,741)(197,740)(198,739)(199,738)(200,737)(201,736)(202,735)(203,734)(204,733)(205,732)(206,731)(207,730)(208,729)(209,728)(210,727)(211,726)(212,725)(213,724)(214,723)(215,722)(216,721)(217,720)(218,719)(219,718)(220,717)(221,716)(222,715)(223,714)(224,713)(225,712)(226,711)(227,710)(228,709)(229,708)(230,707)(231,706)(232,705)(233,704)(234,703)(235,702)(236,701)(237,700)(238,699)(239,698)(240,697)(241,696)(242,695)(243,694)(244,693)(245,692)(246,691)(247,690)(248,689)(249,688)(250,687)(251,686)(252,685)(253,684)(254,683)(255,682)(256,681)(257,680)(258,679)(259,678)(260,677)(261,676)(262,675)(263,674)(264,673)(265,672)(266,671)(267,670)(268,669)(269,668)(270,667)(271,666)(272,665)(273,664)(274,663)(275,662)(276,661)(277,660)(278,659)(279,658)(280,657)(281,656)(282,655)(283,654)(284,653)(285,652)(286,651)(287,650)(288,649)(289,648)(290,647)(291,646)(292,645)(293,644)(294,643)(295,642)(296,641)(297,640)(298,639)(299,638)(300,637)(301,636)(302,635)(303,634)(304,633)(305,632)(306,631)(307,630)(308,629)(309,628)(310,627)(311,626)(312,625)(313,624)(314,623)(315,622)(316,621)(317,620)(318,619)(319,618)(320,617)(321,616)(322,615)(323,614)(324,613)(325,612)(326,611)(327,610)(328,609)(329,608)(330,607)(331,606)(332,605)(333,604)(334,603)(335,602)(336,601)(337,600)(338,599)(339,598)(340,597)(341,596)(342,595)(343,594)(344,593)(345,592)(346,591)(347,590)(348,589)(349,588)(350,587)(351,586)(352,585)(353,584)(354,583)(355,582)(356,581)(357,580)(358,579)(359,578)(360,577)(361,576)(362,575)(363,574)(364,573)(365,572)(366,571)(367,570)(368,569)(369,568)(370,567)(371,566)(372,565)(373,564)(374,563)(375,562)(376,561)(377,560)(378,559)(379,558)(380,557)(381,556)(382,555)(383,554)(384,553)(385,552)(386,551)(387,550)(388,549)(389,548)(390,547)(391,546)(392,545)(393,544)(394,543)(395,542)(396,541)(397,540)(398,539)(399,538)(400,537)(401,536)(402,535)(403,534)(404,533)(405,532)(406,531)(407,530)(408,529)(409,528)(410,527)(411,526)(412,525)(413,524)(414,523)(415,522)(416,521)(417,520)(418,519)(419,518)(420,517)(421,516)(422,515)(423,514)(424,513)(425,512)(426,511)(427,510)(428,509)(429,508)(430,507)(431,506)(432,505)(433,504)(434,503)(435,502)(436,501)(437,500)(438,499)(439,498)(440,497)(441,496)(442,495)(443,494)(444,493)(445,492)(446,491)(447,490)(448,489)(449,488)(450,487)(451,486)(452,485)(453,484)(454,483)(455,482)(456,481)(457,480)(458,479)(459,478)(460,477)(461,476)(462,475)(463,474)(464,473)(465,472)(466,471)(467,470)(468,469)
Polycyclic presentation:
2^4,919|c^2=d,b^a=bc,c^a=cd,e^a=e^918,c^b=cd,e^b=e^918
Conjugacy classes & character table
3679 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14704, 26);
Finite Group Databasebeta