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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1042 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)(480,534,589)(483,537,586)(486,535,583)(489,542,580)(492,545,577)(495,548,574)(498,551,571)(501,554,568)(504,557,565)(507,560,562)(510,563,559)(513,566,556)(516,569,553)(519,572,550)(522,575,547)(525,578,544)(528,581,541)(531,584,539)(533,587,536)(538,592,643)(540,593,640)(543,597,637)(546,599,634)(549,602,631)(552,605,628)(555,608,625)(558,611,622)(561,614,619)(564,617,616)(567,620,613)(570,623,610)(573,626,607)(576,629,604)(579,632,601)(582,635,598)(585,638,596)(588,641,594)(590,644,591)(595,647,692)(600,650,687)(603,652,684)(606,655,681)(609,658,678)(612,661,675)(615,664,672)(618,667,669)(621,670,666)(624,673,663)(627,676,660)(630,679,657)(633,682,654)(636,685,651)(639,688,649)(642,690,648)(645,693,646)(653,698,732)(656,700,729)(659,703,726)(662,706,723)(665,709,720)(668,712,717)(671,715,714)(674,718,711)(677,721,708)(680,724,705)(683,727,702)(686,730,699)(689,733,697)(691,735,696)(694,737,695)(701,742,773)(704,744,770)(707,747,767)(710,750,764)(713,753,761)(716,756,758)(719,759,755)(722,762,752)(725,765,749)(728,768,746)(731,771,743)(734,774,741)(736,776,740)(738,778,739)(745,783,811)(748,785,808)(751,788,805)(754,791,802)(757,794,799)(760,797,796)(763,800,793)(766,803,790)(769,806,787)(772,809,784)(775,812,782)(777,814,781)(779,816,780)(786,821,846)(789,823,843)(792,826,840)(795,829,837)(798,832,834)(801,835,831)(804,838,828)(807,841,825)(810,844,822)(813,847,820)(815,849,819)(817,851,818)(824,856,878)(827,858,875)(830,861,872)(833,864,869)(836,867,866)(839,870,863)(842,873,860)(845,876,857)(848,879,855)(850,881,854)(852,883,853)(859,888,907)(862,890,904)(865,893,901)(868,896,898)(871,899,895)(874,902,892)(877,905,889)(880,908,887)(882,910,886)(884,912,885)(891,917,933)(894,919,930)(897,922,927)(900,925,924)(903,928,921)(906,931,918)(909,934,916)(911,936,915)(913,938,914)(920,943,956)(923,945,953)(926,948,950)(929,951,947)(932,954,944)(935,957,942)(937,959,941)(939,961,940)(946,966,976)(949,968,973)(952,971,970)(955,974,967)(958,977,965)(960,979,964)(962,981,963)(969,986,993)(972,988,990)(975,991,987)(978,994,985)(980,996,984)(982,998,983)(989,1003,1007)(992,1005,1004)(995,1008,1002)(997,1010,1001)(999,1012,1000)(1006,1017,1018)(1009,1019,1016)(1011,1021,1015)(1013,1023,1014)(1020,1028,1027)(1022,1029,1026)(1024,1031,1025)(1030,1035,1034)(1032,1036,1033)(1037,1039,1038)(1041,1042);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,430,332,377,424,473,525,579,633,683,728,769,807,842,874,903,929,952,972,989,998,959,908,844,768,679,572,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,553,607,657,702,743,782,819,853,856,785,703,605,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,558,612,662,707,748,786,816,735,638,527,423,330,373,419,468,520,574,628,678,723,764,802,837,869,898,924,947,967,985,1001,1014,1017,988,948,896,832,756,667,560,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,593,482,378,426,476,528,582,636,686,731,772,810,845,877,906,932,955,975,992,1006,1012,979,934,876,806,724,626,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,550,604,654,699,741,781,818,821,744,655,548,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,561,615,665,710,751,789,824,851,776,688,581,472,374,287,327,370,416,465,517,571,625,675,720,761,799,834,866,895,921,944,965,984,1000,1003,968,922,864,794,712,614,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,540,595,647,537,427,478,531,585,639,689,734,775,813,848,880,909,935,958,978,995,1009,1020,1023,996,957,905,841,765,676,569,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,547,601,651,697,740,780,783,700,602,491,387,295,215,147,177,209,243,280,320,363,409,458,510,564,618,668,713,754,792,827,859,883,814,733,635,524,420,328,247,284,324,367,413,462,514,568,622,672,717,758,796,831,863,892,918,942,964,983,986,945,893,829,753,664,557,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,543,589,643,692,592,479,533,588,642,691,736,777,815,850,882,911,937,960,980,997,1011,1022,1030,1031,1010,977,931,873,803,721,623,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,544,598,649,696,739,742,652,545,436,338,252,178,211,246,283,323,366,412,461,513,567,621,671,716,757,795,830,862,891,912,849,774,685,578,469,371,285,210,244,281,321,364,410,459,511,565,619,669,714,755,793,828,860,889,916,941,963,966,919,861,791,709,611,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,546,600,644,532,586,640,534,590,645,694,738,779,817,852,884,913,939,962,982,999,1013,1024,1032,1037,1036,1021,994,954,902,838,762,673,566,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,541,596,648,695,698,599,488,384,292,212,248,286,326,369,415,464,516,570,624,674,719,760,798,833,865,894,920,938,881,812,730,632,521,417,325,245,176,207,241,278,318,361,407,456,508,562,616,666,711,752,790,825,857,887,915,940,943,890,826,750,661,554,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,549,603,653,693,587,477,529,583,637,687,732,773,811,846,878,907,933,956,976,993,1007,1018,1027,1034,1038,1039,1029,1008,974,928,870,800,718,620,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,594,646,650,542,433,335,249,288,329,372,418,467,519,573,627,677,722,763,801,836,868,897,923,946,961,910,847,771,682,575,466,368,282,208,145,173,204,238,275,315,358,404,453,505,559,613,663,708,749,787,822,855,886,914,917,858,788,706,608,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,552,606,656,701,737,641,530,425,474,526,580,634,684,729,770,808,843,875,904,930,953,973,990,1004,1016,1026,1033,1035,1019,991,951,899,835,759,670,563,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,591,597,485,381,289,331,375,421,470,522,576,630,680,725,766,804,839,871,900,926,949,969,981,936,879,809,727,629,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,556,610,660,705,746,784,820,854,885,888,823,747,658,551,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,555,609,659,704,745,778,690,584,475,376,422,471,523,577,631,681,726,767,805,840,872,901,927,950,970,987,1002,1015,1025,1028,1005,971,925,867,797,715,617,506,402,310,230,162,106,62,30,10)(1040,1041,1042)
Conjugacy classes & character table
1047 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18702, 10);
Finite Group Databasebeta