← Prev (#72272007) Next (#72272009) →
Dic7610 #72272008
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 774 points:
(1,2,3,4)(5,8,7,6)(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);(1,5,3,7)(2,6,4,8)(10,13)(11,12)(15,774)(16,773)(17,772)(18,771)(19,770)(20,769)(21,768)(22,767)(23,766)(24,765)(25,764)(26,763)(27,762)(28,761)(29,760)(30,759)(31,758)(32,757)(33,756)(34,755)(35,754)(36,753)(37,752)(38,751)(39,750)(40,749)(41,748)(42,747)(43,746)(44,745)(45,744)(46,743)(47,742)(48,741)(49,740)(50,739)(51,738)(52,737)(53,736)(54,735)(55,734)(56,733)(57,732)(58,731)(59,730)(60,729)(61,728)(62,727)(63,726)(64,725)(65,724)(66,723)(67,722)(68,721)(69,720)(70,719)(71,718)(72,717)(73,716)(74,715)(75,714)(76,713)(77,712)(78,711)(79,710)(80,709)(81,708)(82,707)(83,706)(84,705)(85,704)(86,703)(87,702)(88,701)(89,700)(90,699)(91,698)(92,697)(93,696)(94,695)(95,694)(96,693)(97,692)(98,691)(99,690)(100,689)(101,688)(102,687)(103,686)(104,685)(105,684)(106,683)(107,682)(108,681)(109,680)(110,679)(111,678)(112,677)(113,676)(114,675)(115,674)(116,673)(117,672)(118,671)(119,670)(120,669)(121,668)(122,667)(123,666)(124,665)(125,664)(126,663)(127,662)(128,661)(129,660)(130,659)(131,658)(132,657)(133,656)(134,655)(135,654)(136,653)(137,652)(138,651)(139,650)(140,649)(141,648)(142,647)(143,646)(144,645)(145,644)(146,643)(147,642)(148,641)(149,640)(150,639)(151,638)(152,637)(153,636)(154,635)(155,634)(156,633)(157,632)(158,631)(159,630)(160,629)(161,628)(162,627)(163,626)(164,625)(165,624)(166,623)(167,622)(168,621)(169,620)(170,619)(171,618)(172,617)(173,616)(174,615)(175,614)(176,613)(177,612)(178,611)(179,610)(180,609)(181,608)(182,607)(183,606)(184,605)(185,604)(186,603)(187,602)(188,601)(189,600)(190,599)(191,598)(192,597)(193,596)(194,595)(195,594)(196,593)(197,592)(198,591)(199,590)(200,589)(201,588)(202,587)(203,586)(204,585)(205,584)(206,583)(207,582)(208,581)(209,580)(210,579)(211,578)(212,577)(213,576)(214,575)(215,574)(216,573)(217,572)(218,571)(219,570)(220,569)(221,568)(222,567)(223,566)(224,565)(225,564)(226,563)(227,562)(228,561)(229,560)(230,559)(231,558)(232,557)(233,556)(234,555)(235,554)(236,553)(237,552)(238,551)(239,550)(240,549)(241,548)(242,547)(243,546)(244,545)(245,544)(246,543)(247,542)(248,541)(249,540)(250,539)(251,538)(252,537)(253,536)(254,535)(255,534)(256,533)(257,532)(258,531)(259,530)(260,529)(261,528)(262,527)(263,526)(264,525)(265,524)(266,523)(267,522)(268,521)(269,520)(270,519)(271,518)(272,517)(273,516)(274,515)(275,514)(276,513)(277,512)(278,511)(279,510)(280,509)(281,508)(282,507)(283,506)(284,505)(285,504)(286,503)(287,502)(288,501)(289,500)(290,499)(291,498)(292,497)(293,496)(294,495)(295,494)(296,493)(297,492)(298,491)(299,490)(300,489)(301,488)(302,487)(303,486)(304,485)(305,484)(306,483)(307,482)(308,481)(309,480)(310,479)(311,478)(312,477)(313,476)(314,475)(315,474)(316,473)(317,472)(318,471)(319,470)(320,469)(321,468)(322,467)(323,466)(324,465)(325,464)(326,463)(327,462)(328,461)(329,460)(330,459)(331,458)(332,457)(333,456)(334,455)(335,454)(336,453)(337,452)(338,451)(339,450)(340,449)(341,448)(342,447)(343,446)(344,445)(345,444)(346,443)(347,442)(348,441)(349,440)(350,439)(351,438)(352,437)(353,436)(354,435)(355,434)(356,433)(357,432)(358,431)(359,430)(360,429)(361,428)(362,427)(363,426)(364,425)(365,424)(366,423)(367,422)(368,421)(369,420)(370,419)(371,418)(372,417)(373,416)(374,415)(375,414)(376,413)(377,412)(378,411)(379,410)(380,409)(381,408)(382,407)(383,406)(384,405)(385,404)(386,403)(387,402)(388,401)(389,400)(390,399)(391,398)(392,397)(393,396)(394,395)
Polycyclic presentation:
2^3,5,761|a^2=c,b^2=c,b^a=bc,d^a=d^4,e^a=e^760
Conjugacy classes & character table
7613 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e");;
gap> coll := SingleCollector(F, [2, 2, 2, 5, 761]);;
gap> SetPower(coll, 1, F.3);;
gap> SetPower(coll, 2, F.3);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 4, 1, F.4^4);;
gap> SetConjugate(coll, 5, 1, F.5^760);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta