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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 710 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);(4,9)(5,8)(6,7)(11,710)(12,709)(13,708)(14,707)(15,706)(16,705)(17,704)(18,703)(19,702)(20,701)(21,700)(22,699)(23,698)(24,697)(25,696)(26,695)(27,694)(28,693)(29,692)(30,691)(31,690)(32,689)(33,688)(34,687)(35,686)(36,685)(37,684)(38,683)(39,682)(40,681)(41,680)(42,679)(43,678)(44,677)(45,676)(46,675)(47,674)(48,673)(49,672)(50,671)(51,670)(52,669)(53,668)(54,667)(55,666)(56,665)(57,664)(58,663)(59,662)(60,661)(61,660)(62,659)(63,658)(64,657)(65,656)(66,655)(67,654)(68,653)(69,652)(70,651)(71,650)(72,649)(73,648)(74,647)(75,646)(76,645)(77,644)(78,643)(79,642)(80,641)(81,640)(82,639)(83,638)(84,637)(85,636)(86,635)(87,634)(88,633)(89,632)(90,631)(91,630)(92,629)(93,628)(94,627)(95,626)(96,625)(97,624)(98,623)(99,622)(100,621)(101,620)(102,619)(103,618)(104,617)(105,616)(106,615)(107,614)(108,613)(109,612)(110,611)(111,610)(112,609)(113,608)(114,607)(115,606)(116,605)(117,604)(118,603)(119,602)(120,601)(121,600)(122,599)(123,598)(124,597)(125,596)(126,595)(127,594)(128,593)(129,592)(130,591)(131,590)(132,589)(133,588)(134,587)(135,586)(136,585)(137,584)(138,583)(139,582)(140,581)(141,580)(142,579)(143,578)(144,577)(145,576)(146,575)(147,574)(148,573)(149,572)(150,571)(151,570)(152,569)(153,568)(154,567)(155,566)(156,565)(157,564)(158,563)(159,562)(160,561)(161,560)(162,559)(163,558)(164,557)(165,556)(166,555)(167,554)(168,553)(169,552)(170,551)(171,550)(172,549)(173,548)(174,547)(175,546)(176,545)(177,544)(178,543)(179,542)(180,541)(181,540)(182,539)(183,538)(184,537)(185,536)(186,535)(187,534)(188,533)(189,532)(190,531)(191,530)(192,529)(193,528)(194,527)(195,526)(196,525)(197,524)(198,523)(199,522)(200,521)(201,520)(202,519)(203,518)(204,517)(205,516)(206,515)(207,514)(208,513)(209,512)(210,511)(211,510)(212,509)(213,508)(214,507)(215,506)(216,505)(217,504)(218,503)(219,502)(220,501)(221,500)(222,499)(223,498)(224,497)(225,496)(226,495)(227,494)(228,493)(229,492)(230,491)(231,490)(232,489)(233,488)(234,487)(235,486)(236,485)(237,484)(238,483)(239,482)(240,481)(241,480)(242,479)(243,478)(244,477)(245,476)(246,475)(247,474)(248,473)(249,472)(250,471)(251,470)(252,469)(253,468)(254,467)(255,466)(256,465)(257,464)(258,463)(259,462)(260,461)(261,460)(262,459)(263,458)(264,457)(265,456)(266,455)(267,454)(268,453)(269,452)(270,451)(271,450)(272,449)(273,448)(274,447)(275,446)(276,445)(277,444)(278,443)(279,442)(280,441)(281,440)(282,439)(283,438)(284,437)(285,436)(286,435)(287,434)(288,433)(289,432)(290,431)(291,430)(292,429)(293,428)(294,427)(295,426)(296,425)(297,424)(298,423)(299,422)(300,421)(301,420)(302,419)(303,418)(304,417)(305,416)(306,415)(307,414)(308,413)(309,412)(310,411)(311,410)(312,409)(313,408)(314,407)(315,406)(316,405)(317,404)(318,403)(319,402)(320,401)(321,400)(322,399)(323,398)(324,397)(325,396)(326,395)(327,394)(328,393)(329,392)(330,391)(331,390)(332,389)(333,388)(334,387)(335,386)(336,385)(337,384)(338,383)(339,382)(340,381)(341,380)(342,379)(343,378)(344,377)(345,376)(346,375)(347,374)(348,373)(349,372)(350,371)(351,370)(352,369)(353,368)(354,367)(355,366)(356,365)(357,364)(358,363)(359,362)(360,361)
Conjugacy classes & character table
4910 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19628, 14);
Finite Group Databasebeta