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Aliases
Splittings
Subgroups
22 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 779 points:
(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,153)(99,126,127,149)(103,130,131,145)(107,134,135,141)(111,138,139,137)(115,142,143,133)(119,146,147,129)(121,150,151,125)(124,155,156,190)(128,159,160,186)(132,163,164,182)(136,167,168,178)(140,171,172,174)(144,175,176,170)(148,179,180,166)(152,183,184,162)(154,187,188,158)(157,192,193,231)(161,196,197,227)(165,200,201,223)(169,204,205,219)(173,208,209,215)(177,212,213,211)(181,216,217,207)(185,220,221,203)(189,224,225,199)(191,228,229,195)(194,233,234,276)(198,237,238,272)(202,241,242,268)(206,245,246,264)(210,249,250,260)(214,253,254,256)(218,257,258,252)(222,261,262,248)(226,265,266,244)(230,269,270,240)(232,273,274,236)(235,278,279,325)(239,282,283,321)(243,286,287,317)(247,290,291,313)(251,294,295,309)(255,298,299,305)(259,302,303,301)(263,306,307,297)(267,310,311,293)(271,314,315,289)(275,318,319,285)(277,322,323,281)(280,327,328,378)(284,331,332,374)(288,335,336,370)(292,339,340,366)(296,343,344,362)(300,347,348,358)(304,351,352,354)(308,355,356,350)(312,359,360,346)(316,363,364,342)(320,367,368,338)(324,371,372,334)(326,375,376,330)(329,380,381,435)(333,384,385,431)(337,388,389,427)(341,392,393,423)(345,396,397,419)(349,400,401,415)(353,404,405,411)(357,408,409,407)(361,412,413,403)(365,416,417,399)(369,420,421,395)(373,424,425,391)(377,428,429,387)(379,432,433,383)(382,437,438,496)(386,441,442,492)(390,445,446,488)(394,449,450,484)(398,453,454,480)(402,457,458,476)(406,461,462,472)(410,465,466,468)(414,469,470,464)(418,473,474,460)(422,477,478,456)(426,481,482,452)(430,485,486,448)(434,489,490,444)(436,493,494,440)(439,498,499,561)(443,502,503,557)(447,506,507,553)(451,510,511,549)(455,514,515,545)(459,518,519,541)(463,522,523,537)(467,526,527,533)(471,530,531,529)(475,534,535,525)(479,538,539,521)(483,542,543,517)(487,546,547,513)(491,550,551,509)(495,554,555,505)(497,558,559,501)(500,563,564,630)(504,567,568,626)(508,571,572,622)(512,575,576,618)(516,579,580,614)(520,583,584,610)(524,587,588,606)(528,591,592,602)(532,595,596,598)(536,599,600,594)(540,603,604,590)(544,607,608,586)(548,611,612,582)(552,615,616,578)(556,619,620,574)(560,623,624,570)(562,627,628,566)(565,632,633,690)(569,636,637,686)(573,640,641,682)(577,644,645,678)(581,648,649,674)(585,652,653,670)(589,656,657,668)(593,659,654,666)(597,661,650,664)(601,663,646,662)(605,665,642,660)(609,667,638,658)(613,669,634,655)(617,671,672,651)(621,675,676,647)(625,679,680,643)(629,683,684,639)(631,687,688,635)(673,698,699,697)(677,701,702,696)(681,704,705,695)(685,707,708,694)(689,710,711,693)(691,700,713,692)(703,720,721,719)(706,723,724,718)(709,726,727,717)(712,729,730,716)(714,722,732,715)(725,738,739,737)(728,741,742,736)(731,744,745,735)(733,740,747,734)(743,752,753,751)(746,755,756,750)(748,754,758,749)(757,762,763,761)(759,764,765,760)(766,768,769,767)(772,773,774,776,775,777,778,779);(1,2,5,10,19,32,49,70,95,124,157,194,235,280,329,382,439,500,565,634,612,547,486,429,376,325,374,427,484,545,610,668,652,579,510,445,384,327,379,434,491,552,617,673,700,687,627,558,493,432,375,322,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,333,386,443,504,569,638,608,543,482,425,372,323,276,321,370,423,480,541,606,666,648,575,506,441,380,436,495,556,621,677,703,722,710,683,623,554,489,428,371,318,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,337,390,447,508,573,642,604,539,478,421,368,319,274,231,272,317,366,419,476,537,602,664,644,571,502,437,497,560,625,681,706,725,740,729,707,679,619,550,485,424,367,314,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,341,394,451,512,577,646,600,535,474,417,364,315,270,229,190,227,268,313,362,415,472,533,598,662,640,567,498,562,629,685,709,728,743,754,744,726,704,675,615,546,481,420,363,310,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,345,398,455,516,581,650,596,531,470,413,360,311,266,225,188,153,186,223,264,309,358,411,468,529,594,660,636,563,631,689,712,731,746,757,764,755,741,723,701,671,611,542,477,416,359,306,257,212,171,134,101,72,47,67,90,115,144,177,214,255,300,349,402,459,520,585,654,592,527,466,409,356,307,262,221,184,151,120,149,182,219,260,305,354,407,464,525,590,658,632,691,714,733,748,759,766,768,762,752,738,720,698,669,607,538,473,412,355,302,253,208,167,130,97,68,92,119,148,181,218,259,304,353,406,463,524,589,657,588,523,462,405,352,303,258,217,180,147,118,91,116,145,178,215,256,301,350,403,460,521,586,655,697,719,737,751,761,767,769,765,758,747,732,713,690,667,603,534,469,408,351,298,249,204,163,126,93,121,152,185,222,263,308,357,410,467,528,593,653,584,519,458,401,348,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,346,399,456,517,582,651,696,718,736,750,760,763,756,745,730,711,688,630,686,665,599,530,465,404,347,294,245,200,159,122,154,189,226,267,312,361,414,471,532,597,649,580,515,454,397,344,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,342,395,452,513,578,647,695,717,735,749,753,742,727,708,684,628,561,626,682,663,595,526,461,400,343,290,241,196,155,191,230,271,316,365,418,475,536,601,645,576,511,450,393,340,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,338,391,448,509,574,643,694,716,734,739,724,705,680,624,559,496,557,622,678,661,591,522,457,396,339,286,237,192,232,275,320,369,422,479,540,605,641,572,507,446,389,336,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,334,387,444,505,570,639,693,715,721,702,676,620,555,494,435,492,553,618,674,659,587,518,453,392,335,282,233,277,324,373,426,483,544,609,637,568,503,442,385,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,383,440,501,566,635,692,699,672,616,551,490,433,378,431,488,549,614,670,656,583,514,449,388,331,278,326,377,430,487,548,613,633,564,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)(770,771)
Conjugacy classes & character table
784 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12304, 47);
Finite Group Databasebeta