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