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Dic919 #16814730
Aliases
Splittings
Subgroups
6 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 923 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);(1,3,2,4)(6,923)(7,922)(8,921)(9,920)(10,919)(11,918)(12,917)(13,916)(14,915)(15,914)(16,913)(17,912)(18,911)(19,910)(20,909)(21,908)(22,907)(23,906)(24,905)(25,904)(26,903)(27,902)(28,901)(29,900)(30,899)(31,898)(32,897)(33,896)(34,895)(35,894)(36,893)(37,892)(38,891)(39,890)(40,889)(41,888)(42,887)(43,886)(44,885)(45,884)(46,883)(47,882)(48,881)(49,880)(50,879)(51,878)(52,877)(53,876)(54,875)(55,874)(56,873)(57,872)(58,871)(59,870)(60,869)(61,868)(62,867)(63,866)(64,865)(65,864)(66,863)(67,862)(68,861)(69,860)(70,859)(71,858)(72,857)(73,856)(74,855)(75,854)(76,853)(77,852)(78,851)(79,850)(80,849)(81,848)(82,847)(83,846)(84,845)(85,844)(86,843)(87,842)(88,841)(89,840)(90,839)(91,838)(92,837)(93,836)(94,835)(95,834)(96,833)(97,832)(98,831)(99,830)(100,829)(101,828)(102,827)(103,826)(104,825)(105,824)(106,823)(107,822)(108,821)(109,820)(110,819)(111,818)(112,817)(113,816)(114,815)(115,814)(116,813)(117,812)(118,811)(119,810)(120,809)(121,808)(122,807)(123,806)(124,805)(125,804)(126,803)(127,802)(128,801)(129,800)(130,799)(131,798)(132,797)(133,796)(134,795)(135,794)(136,793)(137,792)(138,791)(139,790)(140,789)(141,788)(142,787)(143,786)(144,785)(145,784)(146,783)(147,782)(148,781)(149,780)(150,779)(151,778)(152,777)(153,776)(154,775)(155,774)(156,773)(157,772)(158,771)(159,770)(160,769)(161,768)(162,767)(163,766)(164,765)(165,764)(166,763)(167,762)(168,761)(169,760)(170,759)(171,758)(172,757)(173,756)(174,755)(175,754)(176,753)(177,752)(178,751)(179,750)(180,749)(181,748)(182,747)(183,746)(184,745)(185,744)(186,743)(187,742)(188,741)(189,740)(190,739)(191,738)(192,737)(193,736)(194,735)(195,734)(196,733)(197,732)(198,731)(199,730)(200,729)(201,728)(202,727)(203,726)(204,725)(205,724)(206,723)(207,722)(208,721)(209,720)(210,719)(211,718)(212,717)(213,716)(214,715)(215,714)(216,713)(217,712)(218,711)(219,710)(220,709)(221,708)(222,707)(223,706)(224,705)(225,704)(226,703)(227,702)(228,701)(229,700)(230,699)(231,698)(232,697)(233,696)(234,695)(235,694)(236,693)(237,692)(238,691)(239,690)(240,689)(241,688)(242,687)(243,686)(244,685)(245,684)(246,683)(247,682)(248,681)(249,680)(250,679)(251,678)(252,677)(253,676)(254,675)(255,674)(256,673)(257,672)(258,671)(259,670)(260,669)(261,668)(262,667)(263,666)(264,665)(265,664)(266,663)(267,662)(268,661)(269,660)(270,659)(271,658)(272,657)(273,656)(274,655)(275,654)(276,653)(277,652)(278,651)(279,650)(280,649)(281,648)(282,647)(283,646)(284,645)(285,644)(286,643)(287,642)(288,641)(289,640)(290,639)(291,638)(292,637)(293,636)(294,635)(295,634)(296,633)(297,632)(298,631)(299,630)(300,629)(301,628)(302,627)(303,626)(304,625)(305,624)(306,623)(307,622)(308,621)(309,620)(310,619)(311,618)(312,617)(313,616)(314,615)(315,614)(316,613)(317,612)(318,611)(319,610)(320,609)(321,608)(322,607)(323,606)(324,605)(325,604)(326,603)(327,602)(328,601)(329,600)(330,599)(331,598)(332,597)(333,596)(334,595)(335,594)(336,593)(337,592)(338,591)(339,590)(340,589)(341,588)(342,587)(343,586)(344,585)(345,584)(346,583)(347,582)(348,581)(349,580)(350,579)(351,578)(352,577)(353,576)(354,575)(355,574)(356,573)(357,572)(358,571)(359,570)(360,569)(361,568)(362,567)(363,566)(364,565)(365,564)(366,563)(367,562)(368,561)(369,560)(370,559)(371,558)(372,557)(373,556)(374,555)(375,554)(376,553)(377,552)(378,551)(379,550)(380,549)(381,548)(382,547)(383,546)(384,545)(385,544)(386,543)(387,542)(388,541)(389,540)(390,539)(391,538)(392,537)(393,536)(394,535)(395,534)(396,533)(397,532)(398,531)(399,530)(400,529)(401,528)(402,527)(403,526)(404,525)(405,524)(406,523)(407,522)(408,521)(409,520)(410,519)(411,518)(412,517)(413,516)(414,515)(415,514)(416,513)(417,512)(418,511)(419,510)(420,509)(421,508)(422,507)(423,506)(424,505)(425,504)(426,503)(427,502)(428,501)(429,500)(430,499)(431,498)(432,497)(433,496)(434,495)(435,494)(436,493)(437,492)(438,491)(439,490)(440,489)(441,488)(442,487)(443,486)(444,485)(445,484)(446,483)(447,482)(448,481)(449,480)(450,479)(451,478)(452,477)(453,476)(454,475)(455,474)(456,473)(457,472)(458,471)(459,470)(460,469)(461,468)(462,467)(463,466)(464,465)
Polycyclic presentation:
2^2,919|a^2=b,c^a=c^918
Conjugacy classes & character table
922 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3676, 1);
Finite Group Databasebeta