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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 888 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,425)(336,381,422)(339,384,419)(342,387,416)(345,390,413)(348,393,410)(351,396,407)(354,399,404)(357,402,401)(360,405,398)(363,408,395)(366,411,392)(369,414,389)(372,417,386)(375,420,383)(377,423,380)(379,427,477)(382,430,474)(385,433,471)(388,436,468)(391,439,465)(394,442,462)(397,445,459)(400,448,456)(403,451,453)(406,454,450)(409,457,447)(412,460,444)(415,463,441)(418,466,438)(421,469,435)(424,472,432)(426,475,429)(428,479,488)(431,481,528)(434,484,525)(437,487,522)(440,490,519)(443,493,516)(446,496,513)(449,499,510)(452,502,507)(455,505,504)(458,508,501)(461,511,498)(464,514,495)(467,517,492)(470,520,489)(473,523,486)(476,526,483)(478,529,480)(482,533,538)(485,535,577)(491,540,572)(494,543,569)(497,546,566)(500,549,563)(503,552,560)(506,555,557)(509,558,554)(512,561,551)(515,564,548)(518,567,545)(521,570,542)(524,573,539)(527,575,537)(530,578,534)(531,541,532)(536,582,584)(544,587,616)(547,590,613)(550,593,610)(553,596,607)(556,599,604)(559,602,601)(562,605,598)(565,608,595)(568,611,592)(571,614,589)(574,617,586)(576,619,585)(579,621,583)(580,588,581)(591,628,654)(594,631,651)(597,634,648)(600,637,645)(603,640,642)(606,643,639)(609,646,636)(612,649,633)(615,652,630)(618,655,627)(620,657,626)(622,659,625)(623,629,624)(632,666,689)(635,669,686)(638,672,683)(641,675,680)(644,678,677)(647,681,674)(650,684,671)(653,687,668)(656,690,665)(658,692,664)(660,694,663)(661,667,662)(670,701,721)(673,704,718)(676,707,715)(679,710,712)(682,713,709)(685,716,706)(688,719,703)(691,722,700)(693,724,699)(695,726,698)(696,702,697)(705,733,750)(708,736,747)(711,739,744)(714,742,741)(717,745,738)(720,748,735)(723,751,732)(725,753,731)(727,755,730)(728,734,729)(737,762,776)(740,765,773)(743,768,770)(746,771,767)(749,774,764)(752,777,761)(754,779,760)(756,781,759)(757,763,758)(766,788,799)(769,791,796)(772,794,793)(775,797,790)(778,800,787)(780,802,786)(782,804,785)(783,789,784)(792,811,819)(795,814,816)(798,817,813)(801,820,810)(803,822,809)(805,824,808)(806,812,807)(815,831,836)(818,834,833)(821,837,830)(823,839,829)(825,841,828)(826,832,827)(835,848,850)(838,851,847)(840,853,846)(842,855,845)(843,849,844)(852,862,861)(854,864,860)(856,866,859)(857,863,858)(865,872,871)(867,874,870)(868,873,869)(875,879,878)(876,880,877)(881,883,882)(884,885,886,887,888);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,433,335,249,288,329,372,418,467,518,568,612,650,685,717,746,772,795,815,832,804,753,690,614,517,414,322,242,174,117,142,170,201,235,272,312,355,401,450,501,551,595,633,668,700,731,759,784,762,704,634,549,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,494,544,588,529,425,474,525,479,531,580,623,661,696,728,757,783,806,826,843,857,868,876,881,883,874,853,820,774,716,646,561,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,486,537,583,624,587,490,387,295,215,147,177,209,243,280,320,363,409,458,509,559,603,641,676,708,737,763,726,657,573,469,371,285,210,244,281,321,364,410,459,510,560,604,642,677,709,738,764,787,809,828,844,831,791,739,675,599,502,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,485,536,535,430,332,377,424,473,524,574,618,656,691,723,752,778,801,821,838,852,863,841,802,751,687,611,514,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,495,545,589,627,664,698,729,701,631,546,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,500,550,594,632,667,621,526,423,330,373,419,468,519,569,613,651,686,718,747,773,796,816,833,847,860,870,877,872,851,817,771,713,643,558,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,480,532,487,384,292,212,248,286,326,369,415,464,515,565,609,647,682,714,743,769,792,812,781,724,655,570,466,368,282,208,145,173,204,238,275,315,358,404,453,504,554,598,636,671,703,732,760,785,807,788,736,672,596,499,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,491,541,477,528,577,533,427,478,530,579,622,660,695,727,756,782,805,825,842,856,867,875,880,866,839,800,748,684,608,511,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,489,539,585,625,662,628,543,439,341,255,181,119,146,175,206,240,277,317,360,406,455,506,556,600,638,673,705,734,694,619,523,420,328,247,284,324,367,413,462,513,563,607,645,680,712,741,767,790,810,829,845,858,848,814,768,710,640,555,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,482,484,381,289,331,375,421,470,521,571,615,653,688,720,749,775,798,818,835,849,824,779,722,652,567,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,498,548,592,630,665,699,730,758,733,669,593,496,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,497,547,591,629,578,475,376,422,471,522,572,616,654,689,721,750,776,799,819,836,850,861,871,878,882,879,864,837,797,745,681,605,508,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,483,534,581,540,436,338,252,178,211,246,283,323,366,412,461,512,562,606,644,679,711,740,766,789,755,692,617,520,417,325,245,176,207,241,278,318,361,407,456,507,557,601,639,674,706,735,761,786,808,827,811,765,707,637,552,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,488,538,584,582,481,378,426,476,527,576,620,658,693,725,754,780,803,823,840,854,865,873,855,822,777,719,649,564,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,492,542,586,626,663,697,666,590,493,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,503,553,597,635,670,702,659,575,472,374,287,327,370,416,465,516,566,610,648,683,715,744,770,793,813,830,846,859,869,862,834,794,742,678,602,505,402,310,230,162,106,62,30,10)
Conjugacy classes & character table
1485 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13245, 1);
Finite Group Databasebeta