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Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 813 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)(439,498,499,547)(443,502,503,555)(447,506,507,552)(451,510,511,548)(455,514,515,544)(459,518,519,541)(463,522,523,537)(467,526,527,533)(471,530,531,529)(475,534,535,525)(479,538,539,521)(483,500,542,517)(487,545,546,513)(491,549,550,509)(495,553,554,505)(497,556,551,501)(504,557,558,596)(508,560,561,599)(512,563,564,598)(516,566,567,597)(520,569,570,595)(524,573,574,592)(528,577,578,588)(532,581,582,584)(536,585,586,580)(540,589,590,576)(543,559,593,572)(562,600,601,635)(565,603,604,638)(568,606,607,637)(571,609,610,636)(575,612,613,634)(579,616,617,631)(583,620,621,627)(587,624,625,623)(591,628,629,619)(594,602,632,615)(605,639,640,670)(608,642,643,673)(611,645,646,672)(614,648,649,671)(618,651,652,669)(622,655,656,666)(626,659,660,662)(630,663,664,658)(633,641,667,654)(644,674,675,701)(647,677,678,704)(650,680,681,703)(653,683,684,702)(657,686,687,700)(661,690,691,697)(665,694,695,693)(668,676,698,689)(679,705,706,728)(682,708,709,731)(685,711,712,730)(688,714,715,729)(692,717,718,727)(696,721,722,724)(699,707,725,720)(710,732,733,751)(713,735,736,754)(716,738,739,753)(719,741,742,752)(723,744,745,750)(726,734,748,747)(737,755,756,770)(740,758,759,773)(743,761,762,772)(746,764,765,771)(749,757,767,769)(760,774,775,785)(763,777,778,788)(766,780,781,787)(768,776,783,786)(779,789,790,797)(782,792,793,799)(784,791,795,798)(794,800,801,805)(796,802,803,806)(804,807,808,809);(1,2,5,10,19,32,49,70,95,124,157,194,235,280,329,382,439,500,477,416,359,306,257,212,171,134,101,72,47,67,90,115,144,177,214,255,300,349,402,459,520,571,611,647,679,707,694,659,620,577,522,457,396,339,286,237,192,232,275,320,369,422,479,540,591,630,665,696,723,746,766,782,794,802,792,777,758,735,708,677,642,603,560,502,437,497,550,490,433,378,431,488,548,597,636,671,702,729,752,771,786,775,759,739,715,687,656,621,582,531,470,413,360,311,266,225,188,153,186,223,264,309,358,411,468,529,580,619,654,640,604,564,511,450,393,340,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,338,391,448,509,553,489,428,371,318,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,337,390,447,508,562,602,589,534,469,408,351,298,249,204,163,126,93,121,152,185,222,263,308,357,410,467,528,579,618,653,685,713,737,757,744,717,686,651,612,569,514,449,388,331,278,326,377,430,487,547,596,635,670,701,728,751,770,785,797,805,809,808,803,795,783,767,748,725,698,667,632,593,542,482,425,372,323,276,321,370,423,480,541,592,631,666,697,724,747,733,709,681,649,613,574,523,462,405,352,303,258,217,180,147,118,91,116,145,178,215,256,301,350,403,460,521,572,558,503,442,385,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,383,440,501,545,481,420,363,310,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,345,398,455,516,568,608,644,676,663,624,581,526,461,400,343,290,241,196,155,191,230,271,316,365,418,475,536,587,626,661,692,719,743,763,779,791,780,761,738,711,680,645,606,563,506,441,380,436,495,554,494,435,492,552,598,637,672,703,730,753,772,787,798,790,778,762,742,718,691,660,625,586,535,474,417,364,315,270,229,190,227,268,313,362,415,472,533,584,623,658,689,675,643,607,567,515,454,397,344,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,342,395,452,513,556,493,432,375,322,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,333,386,443,504,559,538,473,412,355,302,253,208,167,130,97,68,92,119,148,181,218,259,304,353,406,463,524,575,614,650,682,710,734,721,690,655,616,573,518,453,392,335,282,233,277,324,373,426,483,543,594,633,668,699,726,749,768,784,796,804,807,800,789,774,755,732,705,674,639,600,557,498,546,486,429,376,325,374,427,484,544,595,634,669,700,727,750,769,756,736,712,684,652,617,578,527,466,409,356,307,262,221,184,151,120,149,182,219,260,305,354,407,464,525,576,615,601,561,507,446,389,336,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,334,387,444,505,549,485,424,367,314,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,341,394,451,512,565,605,641,628,585,530,465,404,347,294,245,200,159,122,154,189,226,267,312,361,414,471,532,583,622,657,688,716,740,760,776,764,741,714,683,648,609,566,510,445,384,327,379,434,491,551,496,555,599,638,673,704,731,754,773,788,799,806,801,793,781,765,745,722,695,664,629,590,539,478,421,368,319,274,231,272,317,366,419,476,537,588,627,662,693,720,706,678,646,610,570,519,458,401,348,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,346,399,456,517,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)(810,811,812,813)
Conjugacy classes & character table
824 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12944, 44);
Finite Group Databasebeta