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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1072 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)(428,479,532)(431,482,529)(434,485,526)(437,488,523)(440,491,520)(443,494,517)(446,497,514)(449,500,511)(452,503,508)(455,506,505)(458,509,502)(461,512,499)(464,515,496)(467,518,493)(470,521,490)(473,524,487)(476,527,484)(478,530,481)(480,534,590)(483,537,587)(486,540,584)(489,543,581)(492,546,578)(495,549,575)(498,552,572)(501,555,569)(504,558,566)(507,561,563)(510,564,560)(513,567,557)(516,570,554)(519,573,551)(522,576,548)(525,579,545)(528,582,542)(531,585,539)(533,588,536)(535,592,650)(538,595,647)(541,598,644)(544,601,641)(547,604,639)(550,607,636)(553,610,633)(556,613,630)(559,616,627)(562,619,624)(565,622,621)(568,625,618)(571,628,615)(574,631,612)(577,634,609)(580,637,606)(583,593,603)(586,642,600)(589,645,597)(591,648,594)(596,653,707)(599,656,704)(602,659,701)(605,662,699)(608,665,697)(611,668,694)(614,671,691)(617,674,688)(620,677,685)(623,680,682)(626,683,679)(629,686,676)(632,689,673)(635,692,670)(638,695,667)(640,654,664)(643,700,661)(646,702,658)(649,705,655)(651,708,652)(657,711,759)(660,714,756)(663,717,754)(666,719,753)(669,722,751)(672,725,748)(675,728,745)(678,731,742)(681,734,739)(684,737,736)(687,740,733)(690,743,730)(693,746,727)(696,749,724)(698,712,721)(703,755,716)(706,757,713)(709,760,710)(715,763,805)(718,766,803)(720,768,802)(723,770,801)(726,773,799)(729,776,796)(732,779,793)(735,782,790)(738,785,787)(741,788,784)(744,791,781)(747,794,778)(750,797,775)(752,764,772)(758,804,765)(761,806,762)(767,809,846)(769,811,845)(771,813,844)(774,815,843)(777,818,841)(780,821,838)(783,824,835)(786,827,832)(789,830,829)(792,833,826)(795,836,823)(798,839,820)(800,810,817)(807,847,808)(812,848,882)(814,850,881)(816,852,880)(819,854,879)(822,857,877)(825,860,874)(828,863,871)(831,866,868)(834,869,865)(837,872,862)(840,875,859)(842,849,856)(851,883,914)(853,885,913)(855,887,912)(858,889,911)(861,892,909)(864,895,906)(867,898,903)(870,901,900)(873,904,897)(876,907,894)(878,884,891)(886,915,943)(888,917,942)(890,919,941)(893,921,940)(896,924,938)(899,927,935)(902,930,932)(905,933,929)(908,936,926)(910,916,923)(918,944,969)(920,946,968)(922,948,967)(925,950,966)(928,953,964)(931,956,961)(934,959,958)(937,962,955)(939,945,952)(947,970,992)(949,972,991)(951,974,990)(954,976,989)(957,979,987)(960,982,984)(963,985,981)(965,971,978)(973,993,1012)(975,995,1011)(977,997,1010)(980,999,1009)(983,1002,1007)(986,1005,1004)(988,994,1001)(996,1013,1029)(998,1015,1028)(1000,1017,1027)(1003,1019,1026)(1006,1022,1024)(1008,1014,1021)(1016,1030,1043)(1018,1032,1042)(1020,1034,1041)(1023,1036,1040)(1025,1031,1038)(1033,1044,1054)(1035,1046,1053)(1037,1048,1052)(1039,1045,1051)(1047,1055,1062)(1049,1057,1061)(1050,1056,1060)(1058,1063,1067)(1059,1064,1066)(1065,1068,1069)(1071,1072);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,593,524,420,328,247,284,324,367,413,462,514,569,627,685,739,787,829,865,897,926,952,915,850,768,662,543,433,335,249,288,329,372,418,467,519,574,632,690,744,792,834,870,902,931,957,980,1000,1018,1033,1045,1022,982,930,866,785,680,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,654,579,469,371,285,210,244,281,321,364,410,459,511,566,624,682,736,784,826,862,894,923,883,811,717,601,485,381,289,331,375,421,470,522,577,635,693,747,795,837,873,905,934,960,983,1003,1020,1035,1047,1056,1036,1002,956,898,827,734,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,657,712,637,521,417,325,245,176,207,241,278,318,361,407,456,508,563,621,679,733,781,823,859,891,848,766,659,540,430,332,377,424,473,525,580,638,696,750,798,840,876,908,937,963,986,1006,1023,1037,1049,1058,1064,1048,1019,979,927,863,782,677,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,660,715,764,695,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,676,730,778,820,856,809,714,598,482,378,426,476,528,583,640,698,752,800,842,878,910,939,965,988,1008,1025,1039,1050,1059,1065,1068,1057,1034,999,953,895,824,731,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,663,718,767,810,749,634,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,615,673,727,775,817,763,656,537,427,478,531,586,643,650,707,759,805,846,882,914,943,969,992,1012,1029,1043,1054,1062,1067,1069,1063,1046,1017,976,924,860,779,674,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,666,720,769,812,849,797,692,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,612,670,724,772,711,595,479,533,589,646,703,708,590,647,704,756,803,845,881,913,942,968,991,1011,1028,1042,1053,1061,1066,1055,1032,997,950,892,821,728,613,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,611,669,723,771,814,851,884,839,746,631,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,667,721,653,534,591,649,706,758,760,648,532,587,644,701,754,802,844,880,912,941,967,990,1010,1027,1041,1052,1060,1044,1015,974,921,857,776,671,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,614,672,726,774,816,853,886,916,875,794,689,570,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,664,592,651,709,761,807,806,705,588,477,529,584,641,699,753,801,843,879,911,940,966,989,1009,1026,1040,1051,1030,995,948,889,818,725,610,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,617,675,729,777,819,855,888,918,945,907,836,743,628,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,661,716,765,808,847,757,645,530,425,474,526,581,639,697,751,799,841,877,909,938,964,987,1007,1024,1038,1013,972,919,854,773,668,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,620,678,732,780,822,858,890,920,947,971,936,872,791,686,567,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,658,713,762,804,702,585,475,376,422,471,523,578,636,694,748,796,838,874,906,935,961,984,1004,1021,993,946,887,815,722,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,681,735,783,825,861,893,922,949,973,994,962,904,833,740,625,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,655,710,755,642,527,423,330,373,419,468,520,575,633,691,745,793,835,871,903,932,958,981,1001,970,917,852,770,665,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,684,738,786,828,864,896,925,951,975,996,1014,985,933,869,788,683,564,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,594,652,700,582,472,374,287,327,370,416,465,517,572,630,688,742,790,832,868,900,929,955,978,944,885,813,719,604,488,384,292,212,248,286,326,369,415,464,516,571,629,687,741,789,831,867,899,928,954,977,998,1016,1031,1005,959,901,830,737,622,506,402,310,230,162,106,62,30,10)(1070,1071,1072)
Conjugacy classes & character table
1077 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19242, 10);
Finite Group Databasebeta