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Dic7407 #44444197
Aliases
Splittings
Subgroups
18 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,836)(16,835)(17,834)(18,833)(19,832)(20,831)(21,830)(22,829)(23,828)(24,827)(25,826)(26,825)(27,824)(28,823)(29,822)(30,821)(31,820)(32,819)(33,818)(34,817)(35,816)(36,815)(37,814)(38,813)(39,812)(40,811)(41,810)(42,809)(43,808)(44,807)(45,806)(46,805)(47,804)(48,803)(49,802)(50,801)(51,800)(52,799)(53,798)(54,797)(55,796)(56,795)(57,794)(58,793)(59,792)(60,791)(61,790)(62,789)(63,788)(64,787)(65,786)(66,785)(67,784)(68,783)(69,782)(70,781)(71,780)(72,779)(73,778)(74,777)(75,776)(76,775)(77,774)(78,773)(79,772)(80,771)(81,770)(82,769)(83,768)(84,767)(85,766)(86,765)(87,764)(88,763)(89,762)(90,761)(91,760)(92,759)(93,758)(94,757)(95,756)(96,755)(97,754)(98,753)(99,752)(100,751)(101,750)(102,749)(103,748)(104,747)(105,746)(106,745)(107,744)(108,743)(109,742)(110,741)(111,740)(112,739)(113,738)(114,737)(115,736)(116,735)(117,734)(118,733)(119,732)(120,731)(121,730)(122,729)(123,728)(124,727)(125,726)(126,725)(127,724)(128,723)(129,722)(130,721)(131,720)(132,719)(133,718)(134,717)(135,716)(136,715)(137,714)(138,713)(139,712)(140,711)(141,710)(142,709)(143,708)(144,707)(145,706)(146,705)(147,704)(148,703)(149,702)(150,701)(151,700)(152,699)(153,698)(154,697)(155,696)(156,695)(157,694)(158,693)(159,692)(160,691)(161,690)(162,689)(163,688)(164,687)(165,686)(166,685)(167,684)(168,683)(169,682)(170,681)(171,680)(172,679)(173,678)(174,677)(175,676)(176,675)(177,674)(178,673)(179,672)(180,671)(181,670)(182,669)(183,668)(184,667)(185,666)(186,665)(187,664)(188,663)(189,662)(190,661)(191,660)(192,659)(193,658)(194,657)(195,656)(196,655)(197,654)(198,653)(199,652)(200,651)(201,650)(202,649)(203,648)(204,647)(205,646)(206,645)(207,644)(208,643)(209,642)(210,641)(211,640)(212,639)(213,638)(214,637)(215,636)(216,635)(217,634)(218,633)(219,632)(220,631)(221,630)(222,629)(223,628)(224,627)(225,626)(226,625)(227,624)(228,623)(229,622)(230,621)(231,620)(232,619)(233,618)(234,617)(235,616)(236,615)(237,614)(238,613)(239,612)(240,611)(241,610)(242,609)(243,608)(244,607)(245,606)(246,605)(247,604)(248,603)(249,602)(250,601)(251,600)(252,599)(253,598)(254,597)(255,596)(256,595)(257,594)(258,593)(259,592)(260,591)(261,590)(262,589)(263,588)(264,587)(265,586)(266,585)(267,584)(268,583)(269,582)(270,581)(271,580)(272,579)(273,578)(274,577)(275,576)(276,575)(277,574)(278,573)(279,572)(280,571)(281,570)(282,569)(283,568)(284,567)(285,566)(286,565)(287,564)(288,563)(289,562)(290,561)(291,560)(292,559)(293,558)(294,557)(295,556)(296,555)(297,554)(298,553)(299,552)(300,551)(301,550)(302,549)(303,548)(304,547)(305,546)(306,545)(307,544)(308,543)(309,542)(310,541)(311,540)(312,539)(313,538)(314,537)(315,536)(316,535)(317,534)(318,533)(319,532)(320,531)(321,530)(322,529)(323,528)(324,527)(325,526)(326,525)(327,524)(328,523)(329,522)(330,521)(331,520)(332,519)(333,518)(334,517)(335,516)(336,515)(337,514)(338,513)(339,512)(340,511)(341,510)(342,509)(343,508)(344,507)(345,506)(346,505)(347,504)(348,503)(349,502)(350,501)(351,500)(352,499)(353,498)(354,497)(355,496)(356,495)(357,494)(358,493)(359,492)(360,491)(361,490)(362,489)(363,488)(364,487)(365,486)(366,485)(367,484)(368,483)(369,482)(370,481)(371,480)(372,479)(373,478)(374,477)(375,476)(376,475)(377,474)(378,473)(379,472)(380,471)(381,470)(382,469)(383,468)(384,467)(385,466)(386,465)(387,464)(388,463)(389,462)(390,461)(391,460)(392,459)(393,458)(394,457)(395,456)(396,455)(397,454)(398,453)(399,452)(400,451)(401,450)(402,449)(403,448)(404,447)(405,446)(406,445)(407,444)(408,443)(409,442)(410,441)(411,440)(412,439)(413,438)(414,437)(415,436)(416,435)(417,434)(418,433)(419,432)(420,431)(421,430)(422,429)(423,428)(424,427)(425,426)
Polycyclic presentation:
2,3,823,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^822,e^a=e^2
Conjugacy classes & character table
7410 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29628, 6);
Finite Group Databasebeta