← Prev (#30628692) Next (#30628694) →
Dic3935 #30628693
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 796 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);(1,3,2,4)(6,9)(7,8)(11,796)(12,795)(13,794)(14,793)(15,792)(16,791)(17,790)(18,789)(19,788)(20,787)(21,786)(22,785)(23,784)(24,783)(25,782)(26,781)(27,780)(28,779)(29,778)(30,777)(31,776)(32,775)(33,774)(34,773)(35,772)(36,771)(37,770)(38,769)(39,768)(40,767)(41,766)(42,765)(43,764)(44,763)(45,762)(46,761)(47,760)(48,759)(49,758)(50,757)(51,756)(52,755)(53,754)(54,753)(55,752)(56,751)(57,750)(58,749)(59,748)(60,747)(61,746)(62,745)(63,744)(64,743)(65,742)(66,741)(67,740)(68,739)(69,738)(70,737)(71,736)(72,735)(73,734)(74,733)(75,732)(76,731)(77,730)(78,729)(79,728)(80,727)(81,726)(82,725)(83,724)(84,723)(85,722)(86,721)(87,720)(88,719)(89,718)(90,717)(91,716)(92,715)(93,714)(94,713)(95,712)(96,711)(97,710)(98,709)(99,708)(100,707)(101,706)(102,705)(103,704)(104,703)(105,702)(106,701)(107,700)(108,699)(109,698)(110,697)(111,696)(112,695)(113,694)(114,693)(115,692)(116,691)(117,690)(118,689)(119,688)(120,687)(121,686)(122,685)(123,684)(124,683)(125,682)(126,681)(127,680)(128,679)(129,678)(130,677)(131,676)(132,675)(133,674)(134,673)(135,672)(136,671)(137,670)(138,669)(139,668)(140,667)(141,666)(142,665)(143,664)(144,663)(145,662)(146,661)(147,660)(148,659)(149,658)(150,657)(151,656)(152,655)(153,654)(154,653)(155,652)(156,651)(157,650)(158,649)(159,648)(160,647)(161,646)(162,645)(163,644)(164,643)(165,642)(166,641)(167,640)(168,639)(169,638)(170,637)(171,636)(172,635)(173,634)(174,633)(175,632)(176,631)(177,630)(178,629)(179,628)(180,627)(181,626)(182,625)(183,624)(184,623)(185,622)(186,621)(187,620)(188,619)(189,618)(190,617)(191,616)(192,615)(193,614)(194,613)(195,612)(196,611)(197,610)(198,609)(199,608)(200,607)(201,606)(202,605)(203,604)(204,603)(205,602)(206,601)(207,600)(208,599)(209,598)(210,597)(211,596)(212,595)(213,594)(214,593)(215,592)(216,591)(217,590)(218,589)(219,588)(220,587)(221,586)(222,585)(223,584)(224,583)(225,582)(226,581)(227,580)(228,579)(229,578)(230,577)(231,576)(232,575)(233,574)(234,573)(235,572)(236,571)(237,570)(238,569)(239,568)(240,567)(241,566)(242,565)(243,564)(244,563)(245,562)(246,561)(247,560)(248,559)(249,558)(250,557)(251,556)(252,555)(253,554)(254,553)(255,552)(256,551)(257,550)(258,549)(259,548)(260,547)(261,546)(262,545)(263,544)(264,543)(265,542)(266,541)(267,540)(268,539)(269,538)(270,537)(271,536)(272,535)(273,534)(274,533)(275,532)(276,531)(277,530)(278,529)(279,528)(280,527)(281,526)(282,525)(283,524)(284,523)(285,522)(286,521)(287,520)(288,519)(289,518)(290,517)(291,516)(292,515)(293,514)(294,513)(295,512)(296,511)(297,510)(298,509)(299,508)(300,507)(301,506)(302,505)(303,504)(304,503)(305,502)(306,501)(307,500)(308,499)(309,498)(310,497)(311,496)(312,495)(313,494)(314,493)(315,492)(316,491)(317,490)(318,489)(319,488)(320,487)(321,486)(322,485)(323,484)(324,483)(325,482)(326,481)(327,480)(328,479)(329,478)(330,477)(331,476)(332,475)(333,474)(334,473)(335,472)(336,471)(337,470)(338,469)(339,468)(340,467)(341,466)(342,465)(343,464)(344,463)(345,462)(346,461)(347,460)(348,459)(349,458)(350,457)(351,456)(352,455)(353,454)(354,453)(355,452)(356,451)(357,450)(358,449)(359,448)(360,447)(361,446)(362,445)(363,444)(364,443)(365,442)(366,441)(367,440)(368,439)(369,438)(370,437)(371,436)(372,435)(373,434)(374,433)(375,432)(376,431)(377,430)(378,429)(379,428)(380,427)(381,426)(382,425)(383,424)(384,423)(385,422)(386,421)(387,420)(388,419)(389,418)(390,417)(391,416)(392,415)(393,414)(394,413)(395,412)(396,411)(397,410)(398,409)(399,408)(400,407)(401,406)(402,405)(403,404)
Polycyclic presentation:
2,5,787,2|a^2=d,b^a=b^4,c^a=c^786
Conjugacy classes & character table
3938 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15740, 4);
Finite Group Databasebeta