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Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 730 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);(4,11)(5,10)(6,9)(7,8)(13,730)(14,729)(15,728)(16,727)(17,726)(18,725)(19,724)(20,723)(21,722)(22,721)(23,720)(24,719)(25,718)(26,717)(27,716)(28,715)(29,714)(30,713)(31,712)(32,711)(33,710)(34,709)(35,708)(36,707)(37,706)(38,705)(39,704)(40,703)(41,702)(42,701)(43,700)(44,699)(45,698)(46,697)(47,696)(48,695)(49,694)(50,693)(51,692)(52,691)(53,690)(54,689)(55,688)(56,687)(57,686)(58,685)(59,684)(60,683)(61,682)(62,681)(63,680)(64,679)(65,678)(66,677)(67,676)(68,675)(69,674)(70,673)(71,672)(72,671)(73,670)(74,669)(75,668)(76,667)(77,666)(78,665)(79,664)(80,663)(81,662)(82,661)(83,660)(84,659)(85,658)(86,657)(87,656)(88,655)(89,654)(90,653)(91,652)(92,651)(93,650)(94,649)(95,648)(96,647)(97,646)(98,645)(99,644)(100,643)(101,642)(102,641)(103,640)(104,639)(105,638)(106,637)(107,636)(108,635)(109,634)(110,633)(111,632)(112,631)(113,630)(114,629)(115,628)(116,627)(117,626)(118,625)(119,624)(120,623)(121,622)(122,621)(123,620)(124,619)(125,618)(126,617)(127,616)(128,615)(129,614)(130,613)(131,612)(132,611)(133,610)(134,609)(135,608)(136,607)(137,606)(138,605)(139,604)(140,603)(141,602)(142,601)(143,600)(144,599)(145,598)(146,597)(147,596)(148,595)(149,594)(150,593)(151,592)(152,591)(153,590)(154,589)(155,588)(156,587)(157,586)(158,585)(159,584)(160,583)(161,582)(162,581)(163,580)(164,579)(165,578)(166,577)(167,576)(168,575)(169,574)(170,573)(171,572)(172,571)(173,570)(174,569)(175,568)(176,567)(177,566)(178,565)(179,564)(180,563)(181,562)(182,561)(183,560)(184,559)(185,558)(186,557)(187,556)(188,555)(189,554)(190,553)(191,552)(192,551)(193,550)(194,549)(195,548)(196,547)(197,546)(198,545)(199,544)(200,543)(201,542)(202,541)(203,540)(204,539)(205,538)(206,537)(207,536)(208,535)(209,534)(210,533)(211,532)(212,531)(213,530)(214,529)(215,528)(216,527)(217,526)(218,525)(219,524)(220,523)(221,522)(222,521)(223,520)(224,519)(225,518)(226,517)(227,516)(228,515)(229,514)(230,513)(231,512)(232,511)(233,510)(234,509)(235,508)(236,507)(237,506)(238,505)(239,504)(240,503)(241,502)(242,501)(243,500)(244,499)(245,498)(246,497)(247,496)(248,495)(249,494)(250,493)(251,492)(252,491)(253,490)(254,489)(255,488)(256,487)(257,486)(258,485)(259,484)(260,483)(261,482)(262,481)(263,480)(264,479)(265,478)(266,477)(267,476)(268,475)(269,474)(270,473)(271,472)(272,471)(273,470)(274,469)(275,468)(276,467)(277,466)(278,465)(279,464)(280,463)(281,462)(282,461)(283,460)(284,459)(285,458)(286,457)(287,456)(288,455)(289,454)(290,453)(291,452)(292,451)(293,450)(294,449)(295,448)(296,447)(297,446)(298,445)(299,444)(300,443)(301,442)(302,441)(303,440)(304,439)(305,438)(306,437)(307,436)(308,435)(309,434)(310,433)(311,432)(312,431)(313,430)(314,429)(315,428)(316,427)(317,426)(318,425)(319,424)(320,423)(321,422)(322,421)(323,420)(324,419)(325,418)(326,417)(327,416)(328,415)(329,414)(330,413)(331,412)(332,411)(333,410)(334,409)(335,408)(336,407)(337,406)(338,405)(339,404)(340,403)(341,402)(342,401)(343,400)(344,399)(345,398)(346,397)(347,396)(348,395)(349,394)(350,393)(351,392)(352,391)(353,390)(354,389)(355,388)(356,387)(357,386)(358,385)(359,384)(360,383)(361,382)(362,381)(363,380)(364,379)(365,378)(366,377)(367,376)(368,375)(369,374)(370,373)(371,372)
Conjugacy classes & character table
6474 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25884, 8);
Finite Group Databasebeta