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D5803 #26042445
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 836 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);(2,7)(3,6)(4,5)(9,836)(10,835)(11,834)(12,833)(13,832)(14,831)(15,830)(16,829)(17,828)(18,827)(19,826)(20,825)(21,824)(22,823)(23,822)(24,821)(25,820)(26,819)(27,818)(28,817)(29,816)(30,815)(31,814)(32,813)(33,812)(34,811)(35,810)(36,809)(37,808)(38,807)(39,806)(40,805)(41,804)(42,803)(43,802)(44,801)(45,800)(46,799)(47,798)(48,797)(49,796)(50,795)(51,794)(52,793)(53,792)(54,791)(55,790)(56,789)(57,788)(58,787)(59,786)(60,785)(61,784)(62,783)(63,782)(64,781)(65,780)(66,779)(67,778)(68,777)(69,776)(70,775)(71,774)(72,773)(73,772)(74,771)(75,770)(76,769)(77,768)(78,767)(79,766)(80,765)(81,764)(82,763)(83,762)(84,761)(85,760)(86,759)(87,758)(88,757)(89,756)(90,755)(91,754)(92,753)(93,752)(94,751)(95,750)(96,749)(97,748)(98,747)(99,746)(100,745)(101,744)(102,743)(103,742)(104,741)(105,740)(106,739)(107,738)(108,737)(109,736)(110,735)(111,734)(112,733)(113,732)(114,731)(115,730)(116,729)(117,728)(118,727)(119,726)(120,725)(121,724)(122,723)(123,722)(124,721)(125,720)(126,719)(127,718)(128,717)(129,716)(130,715)(131,714)(132,713)(133,712)(134,711)(135,710)(136,709)(137,708)(138,707)(139,706)(140,705)(141,704)(142,703)(143,702)(144,701)(145,700)(146,699)(147,698)(148,697)(149,696)(150,695)(151,694)(152,693)(153,692)(154,691)(155,690)(156,689)(157,688)(158,687)(159,686)(160,685)(161,684)(162,683)(163,682)(164,681)(165,680)(166,679)(167,678)(168,677)(169,676)(170,675)(171,674)(172,673)(173,672)(174,671)(175,670)(176,669)(177,668)(178,667)(179,666)(180,665)(181,664)(182,663)(183,662)(184,661)(185,660)(186,659)(187,658)(188,657)(189,656)(190,655)(191,654)(192,653)(193,652)(194,651)(195,650)(196,649)(197,648)(198,647)(199,646)(200,645)(201,644)(202,643)(203,642)(204,641)(205,640)(206,639)(207,638)(208,637)(209,636)(210,635)(211,634)(212,633)(213,632)(214,631)(215,630)(216,629)(217,628)(218,627)(219,626)(220,625)(221,624)(222,623)(223,622)(224,621)(225,620)(226,619)(227,618)(228,617)(229,616)(230,615)(231,614)(232,613)(233,612)(234,611)(235,610)(236,609)(237,608)(238,607)(239,606)(240,605)(241,604)(242,603)(243,602)(244,601)(245,600)(246,599)(247,598)(248,597)(249,596)(250,595)(251,594)(252,593)(253,592)(254,591)(255,590)(256,589)(257,588)(258,587)(259,586)(260,585)(261,584)(262,583)(263,582)(264,581)(265,580)(266,579)(267,578)(268,577)(269,576)(270,575)(271,574)(272,573)(273,572)(274,571)(275,570)(276,569)(277,568)(278,567)(279,566)(280,565)(281,564)(282,563)(283,562)(284,561)(285,560)(286,559)(287,558)(288,557)(289,556)(290,555)(291,554)(292,553)(293,552)(294,551)(295,550)(296,549)(297,548)(298,547)(299,546)(300,545)(301,544)(302,543)(303,542)(304,541)(305,540)(306,539)(307,538)(308,537)(309,536)(310,535)(311,534)(312,533)(313,532)(314,531)(315,530)(316,529)(317,528)(318,527)(319,526)(320,525)(321,524)(322,523)(323,522)(324,521)(325,520)(326,519)(327,518)(328,517)(329,516)(330,515)(331,514)(332,513)(333,512)(334,511)(335,510)(336,509)(337,508)(338,507)(339,506)(340,505)(341,504)(342,503)(343,502)(344,501)(345,500)(346,499)(347,498)(348,497)(349,496)(350,495)(351,494)(352,493)(353,492)(354,491)(355,490)(356,489)(357,488)(358,487)(359,486)(360,485)(361,484)(362,483)(363,482)(364,481)(365,480)(366,479)(367,478)(368,477)(369,476)(370,475)(371,474)(372,473)(373,472)(374,471)(375,470)(376,469)(377,468)(378,467)(379,466)(380,465)(381,464)(382,463)(383,462)(384,461)(385,460)(386,459)(387,458)(388,457)(389,456)(390,455)(391,454)(392,453)(393,452)(394,451)(395,450)(396,449)(397,448)(398,447)(399,446)(400,445)(401,444)(402,443)(403,442)(404,441)(405,440)(406,439)(407,438)(408,437)(409,436)(410,435)(411,434)(412,433)(413,432)(414,431)(415,430)(416,429)(417,428)(418,427)(419,426)(420,425)(421,424)(422,423)
Polycyclic presentation:
2,7,829|b^a=b^6,c^a=c^828
Conjugacy classes & character table
2903 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11606, 3);
Finite Group Databasebeta