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Dic5887 #37555369
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 852 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);(1,3,2,4)(6,11)(7,10)(8,9)(13,852)(14,851)(15,850)(16,849)(17,848)(18,847)(19,846)(20,845)(21,844)(22,843)(23,842)(24,841)(25,840)(26,839)(27,838)(28,837)(29,836)(30,835)(31,834)(32,833)(33,832)(34,831)(35,830)(36,829)(37,828)(38,827)(39,826)(40,825)(41,824)(42,823)(43,822)(44,821)(45,820)(46,819)(47,818)(48,817)(49,816)(50,815)(51,814)(52,813)(53,812)(54,811)(55,810)(56,809)(57,808)(58,807)(59,806)(60,805)(61,804)(62,803)(63,802)(64,801)(65,800)(66,799)(67,798)(68,797)(69,796)(70,795)(71,794)(72,793)(73,792)(74,791)(75,790)(76,789)(77,788)(78,787)(79,786)(80,785)(81,784)(82,783)(83,782)(84,781)(85,780)(86,779)(87,778)(88,777)(89,776)(90,775)(91,774)(92,773)(93,772)(94,771)(95,770)(96,769)(97,768)(98,767)(99,766)(100,765)(101,764)(102,763)(103,762)(104,761)(105,760)(106,759)(107,758)(108,757)(109,756)(110,755)(111,754)(112,753)(113,752)(114,751)(115,750)(116,749)(117,748)(118,747)(119,746)(120,745)(121,744)(122,743)(123,742)(124,741)(125,740)(126,739)(127,738)(128,737)(129,736)(130,735)(131,734)(132,733)(133,732)(134,731)(135,730)(136,729)(137,728)(138,727)(139,726)(140,725)(141,724)(142,723)(143,722)(144,721)(145,720)(146,719)(147,718)(148,717)(149,716)(150,715)(151,714)(152,713)(153,712)(154,711)(155,710)(156,709)(157,708)(158,707)(159,706)(160,705)(161,704)(162,703)(163,702)(164,701)(165,700)(166,699)(167,698)(168,697)(169,696)(170,695)(171,694)(172,693)(173,692)(174,691)(175,690)(176,689)(177,688)(178,687)(179,686)(180,685)(181,684)(182,683)(183,682)(184,681)(185,680)(186,679)(187,678)(188,677)(189,676)(190,675)(191,674)(192,673)(193,672)(194,671)(195,670)(196,669)(197,668)(198,667)(199,666)(200,665)(201,664)(202,663)(203,662)(204,661)(205,660)(206,659)(207,658)(208,657)(209,656)(210,655)(211,654)(212,653)(213,652)(214,651)(215,650)(216,649)(217,648)(218,647)(219,646)(220,645)(221,644)(222,643)(223,642)(224,641)(225,640)(226,639)(227,638)(228,637)(229,636)(230,635)(231,634)(232,633)(233,632)(234,631)(235,630)(236,629)(237,628)(238,627)(239,626)(240,625)(241,624)(242,623)(243,622)(244,621)(245,620)(246,619)(247,618)(248,617)(249,616)(250,615)(251,614)(252,613)(253,612)(254,611)(255,610)(256,609)(257,608)(258,607)(259,606)(260,605)(261,604)(262,603)(263,602)(264,601)(265,600)(266,599)(267,598)(268,597)(269,596)(270,595)(271,594)(272,593)(273,592)(274,591)(275,590)(276,589)(277,588)(278,587)(279,586)(280,585)(281,584)(282,583)(283,582)(284,581)(285,580)(286,579)(287,578)(288,577)(289,576)(290,575)(291,574)(292,573)(293,572)(294,571)(295,570)(296,569)(297,568)(298,567)(299,566)(300,565)(301,564)(302,563)(303,562)(304,561)(305,560)(306,559)(307,558)(308,557)(309,556)(310,555)(311,554)(312,553)(313,552)(314,551)(315,550)(316,549)(317,548)(318,547)(319,546)(320,545)(321,544)(322,543)(323,542)(324,541)(325,540)(326,539)(327,538)(328,537)(329,536)(330,535)(331,534)(332,533)(333,532)(334,531)(335,530)(336,529)(337,528)(338,527)(339,526)(340,525)(341,524)(342,523)(343,522)(344,521)(345,520)(346,519)(347,518)(348,517)(349,516)(350,515)(351,514)(352,513)(353,512)(354,511)(355,510)(356,509)(357,508)(358,507)(359,506)(360,505)(361,504)(362,503)(363,502)(364,501)(365,500)(366,499)(367,498)(368,497)(369,496)(370,495)(371,494)(372,493)(373,492)(374,491)(375,490)(376,489)(377,488)(378,487)(379,486)(380,485)(381,484)(382,483)(383,482)(384,481)(385,480)(386,479)(387,478)(388,477)(389,476)(390,475)(391,474)(392,473)(393,472)(394,471)(395,470)(396,469)(397,468)(398,467)(399,466)(400,465)(401,464)(402,463)(403,462)(404,461)(405,460)(406,459)(407,458)(408,457)(409,456)(410,455)(411,454)(412,453)(413,452)(414,451)(415,450)(416,449)(417,448)(418,447)(419,446)(420,445)(421,444)(422,443)(423,442)(424,441)(425,440)(426,439)(427,438)(428,437)(429,436)(430,435)(431,434)(432,433)
Polycyclic presentation:
2,7,29,2,29|a^2=d,c^29=e^28,b^a=b^6,c^a=c^28e,e^a=e^28
Conjugacy classes & character table
5890 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23548, 6);
Finite Group Databasebeta