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D6008 #26046628
Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 759 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);(2,8)(3,7)(4,6)(10,759)(11,758)(12,757)(13,756)(14,755)(15,754)(16,753)(17,752)(18,751)(19,750)(20,749)(21,748)(22,747)(23,746)(24,745)(25,744)(26,743)(27,742)(28,741)(29,740)(30,739)(31,738)(32,737)(33,736)(34,735)(35,734)(36,733)(37,732)(38,731)(39,730)(40,729)(41,728)(42,727)(43,726)(44,725)(45,724)(46,723)(47,722)(48,721)(49,720)(50,719)(51,718)(52,717)(53,716)(54,715)(55,714)(56,713)(57,712)(58,711)(59,710)(60,709)(61,708)(62,707)(63,706)(64,705)(65,704)(66,703)(67,702)(68,701)(69,700)(70,699)(71,698)(72,697)(73,696)(74,695)(75,694)(76,693)(77,692)(78,691)(79,690)(80,689)(81,688)(82,687)(83,686)(84,685)(85,684)(86,683)(87,682)(88,681)(89,680)(90,679)(91,678)(92,677)(93,676)(94,675)(95,674)(96,673)(97,672)(98,671)(99,670)(100,669)(101,668)(102,667)(103,666)(104,665)(105,664)(106,663)(107,662)(108,661)(109,660)(110,659)(111,658)(112,657)(113,656)(114,655)(115,654)(116,653)(117,652)(118,651)(119,650)(120,649)(121,648)(122,647)(123,646)(124,645)(125,644)(126,643)(127,642)(128,641)(129,640)(130,639)(131,638)(132,637)(133,636)(134,635)(135,634)(136,633)(137,632)(138,631)(139,630)(140,629)(141,628)(142,627)(143,626)(144,625)(145,624)(146,623)(147,622)(148,621)(149,620)(150,619)(151,618)(152,617)(153,616)(154,615)(155,614)(156,613)(157,612)(158,611)(159,610)(160,609)(161,608)(162,607)(163,606)(164,605)(165,604)(166,603)(167,602)(168,601)(169,600)(170,599)(171,598)(172,597)(173,596)(174,595)(175,594)(176,593)(177,592)(178,591)(179,590)(180,589)(181,588)(182,587)(183,586)(184,585)(185,584)(186,583)(187,582)(188,581)(189,580)(190,579)(191,578)(192,577)(193,576)(194,575)(195,574)(196,573)(197,572)(198,571)(199,570)(200,569)(201,568)(202,567)(203,566)(204,565)(205,564)(206,563)(207,562)(208,561)(209,560)(210,559)(211,558)(212,557)(213,556)(214,555)(215,554)(216,553)(217,552)(218,551)(219,550)(220,549)(221,548)(222,547)(223,546)(224,545)(225,544)(226,543)(227,542)(228,541)(229,540)(230,539)(231,538)(232,537)(233,536)(234,535)(235,534)(236,533)(237,532)(238,531)(239,530)(240,529)(241,528)(242,527)(243,526)(244,525)(245,524)(246,523)(247,522)(248,521)(249,520)(250,519)(251,518)(252,517)(253,516)(254,515)(255,514)(256,513)(257,512)(258,511)(259,510)(260,509)(261,508)(262,507)(263,506)(264,505)(265,504)(266,503)(267,502)(268,501)(269,500)(270,499)(271,498)(272,497)(273,496)(274,495)(275,494)(276,493)(277,492)(278,491)(279,490)(280,489)(281,488)(282,487)(283,486)(284,485)(285,484)(286,483)(287,482)(288,481)(289,480)(290,479)(291,478)(292,477)(293,476)(294,475)(295,474)(296,473)(297,472)(298,471)(299,470)(300,469)(301,468)(302,467)(303,466)(304,465)(305,464)(306,463)(307,462)(308,461)(309,460)(310,459)(311,458)(312,457)(313,456)(314,455)(315,454)(316,453)(317,452)(318,451)(319,450)(320,449)(321,448)(322,447)(323,446)(324,445)(325,444)(326,443)(327,442)(328,441)(329,440)(330,439)(331,438)(332,437)(333,436)(334,435)(335,434)(336,433)(337,432)(338,431)(339,430)(340,429)(341,428)(342,427)(343,426)(344,425)(345,424)(346,423)(347,422)(348,421)(349,420)(350,419)(351,418)(352,417)(353,416)(354,415)(355,414)(356,413)(357,412)(358,411)(359,410)(360,409)(361,408)(362,407)(363,406)(364,405)(365,404)(366,403)(367,402)(368,401)(369,400)(370,399)(371,398)(372,397)(373,396)(374,395)(375,394)(376,393)(377,392)(378,391)(379,390)(380,389)(381,388)(382,387)(383,386)(384,385)
Polycyclic presentation:
2^4,751|c^2=d,b^a=bc,c^a=cd,e^a=e^750,c^b=cd,e^b=e^750
Conjugacy classes & character table
3007 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12016, 26);
Finite Group Databasebeta