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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1054 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)(535,592,651)(538,595,648)(541,598,645)(544,601,642)(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)(583,640,603)(586,643,600)(589,646,597)(591,649,594)(593,653,695)(596,655,711)(599,658,708)(602,661,705)(605,664,702)(608,667,699)(611,670,696)(614,673,693)(617,676,690)(620,679,687)(623,682,684)(626,685,681)(629,688,678)(632,691,675)(635,694,672)(638,697,669)(641,700,666)(644,703,663)(647,706,660)(650,709,657)(652,712,654)(656,716,753)(659,718,769)(662,721,766)(665,724,763)(668,727,760)(671,730,757)(674,733,754)(677,735,752)(680,738,749)(683,741,746)(686,744,743)(689,747,740)(692,750,737)(698,755,732)(701,758,729)(704,761,726)(707,764,723)(710,767,720)(713,770,717)(714,756,715)(719,774,807)(722,776,821)(725,779,818)(728,782,815)(731,785,812)(734,788,809)(736,790,808)(739,792,806)(742,795,803)(745,798,800)(748,801,797)(751,804,794)(759,810,787)(762,813,784)(765,816,781)(768,819,778)(771,822,775)(772,811,773)(777,826,855)(780,828,867)(783,831,864)(786,834,861)(789,837,858)(791,839,857)(793,841,856)(796,843,854)(799,846,851)(802,849,848)(805,852,845)(814,859,836)(817,862,833)(820,865,830)(823,868,827)(824,860,825)(829,872,897)(832,874,907)(835,877,904)(838,880,901)(840,882,900)(842,884,899)(844,886,898)(847,888,896)(850,891,893)(853,894,890)(863,902,879)(866,905,876)(869,908,873)(870,903,871)(875,912,933)(878,914,941)(881,917,938)(883,919,937)(885,921,936)(887,923,935)(889,925,934)(892,927,932)(895,930,929)(906,939,916)(909,942,913)(910,940,911)(915,946,963)(918,948,969)(920,950,968)(922,952,967)(924,954,966)(926,956,965)(928,958,964)(931,960,962)(943,970,947)(944,971,945)(949,974,987)(951,975,993)(953,977,992)(955,979,991)(957,981,990)(959,983,989)(961,985,988)(972,994,973)(976,995,1006)(978,996,1011)(980,998,1010)(982,1000,1009)(984,1002,1008)(986,1004,1007)(997,1012,1021)(999,1013,1025)(1001,1015,1024)(1003,1017,1023)(1005,1019,1022)(1014,1026,1033)(1016,1027,1036)(1018,1029,1035)(1020,1031,1034)(1028,1037,1042)(1030,1038,1044)(1032,1040,1043)(1039,1045,1048)(1041,1046,1049)(1047,1050,1051)(1053,1054);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,593,631,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,669,729,784,833,876,913,945,939,862,761,640,524,420,328,247,284,324,367,413,462,514,569,627,687,746,800,848,890,872,776,658,537,427,478,531,586,644,704,762,814,860,770,649,532,587,645,705,763,815,861,901,937,967,991,1009,1023,1034,1026,996,950,880,785,667,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,686,745,799,847,889,926,957,982,1001,1016,1028,1031,1002,956,886,792,676,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,668,728,783,832,875,894,801,685,564,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,594,654,715,694,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,612,672,732,787,836,879,916,947,973,970,905,816,703,582,472,374,287,327,370,416,465,517,572,630,690,749,803,851,893,929,912,828,721,598,482,378,426,476,528,583,641,701,759,811,712,590,648,708,766,818,864,904,938,968,992,1010,1024,1035,1043,1037,1013,977,919,837,730,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,683,742,796,844,887,924,955,980,999,1014,1019,983,925,843,738,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,665,725,780,829,852,747,625,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,657,717,773,755,634,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,615,675,653,714,772,824,870,910,944,972,994,942,865,764,643,527,423,330,373,419,468,520,575,633,693,752,806,854,896,932,962,946,874,779,661,540,430,332,377,424,473,525,580,638,698,756,651,711,769,821,867,907,941,969,993,1011,1025,1036,1044,1049,1045,1027,998,952,882,788,670,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,620,680,739,793,842,885,922,953,978,997,1004,958,888,795,679,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,662,722,777,804,688,567,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,660,720,775,825,810,697,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,678,737,716,592,652,713,771,823,869,909,943,971,908,819,706,585,475,376,422,471,523,578,636,696,754,808,856,898,934,964,988,974,914,831,724,601,485,381,289,331,375,421,470,522,577,635,695,753,807,855,897,933,963,987,1006,1021,1033,1042,1048,1051,1050,1038,1015,979,921,839,733,610,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,617,677,736,791,840,883,920,951,976,985,927,846,741,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,659,719,750,628,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,663,723,778,827,871,859,758,637,521,417,325,245,176,207,241,278,318,361,407,456,508,563,621,681,740,794,774,655,534,591,650,710,768,820,866,906,940,868,767,646,530,425,474,526,581,639,699,757,809,857,899,935,965,989,1007,995,948,877,782,664,543,433,335,249,288,329,372,418,467,519,574,632,692,751,805,853,895,931,961,986,1005,1020,1032,1041,1047,1046,1029,1000,954,884,790,673,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,614,674,734,789,838,881,918,949,960,891,798,682,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,656,691,570,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,666,726,781,830,873,911,902,813,700,579,469,371,285,210,244,281,321,364,410,459,511,566,624,684,743,797,845,826,718,595,479,533,589,647,707,765,817,863,903,822,709,588,477,529,584,642,702,760,812,858,900,936,966,990,1008,1022,1012,975,917,834,727,604,488,384,292,212,248,286,326,369,415,464,516,571,629,689,748,802,850,892,928,959,984,1003,1018,1030,1039,1040,1017,981,923,841,735,613,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,611,671,731,786,835,878,915,930,849,744,622,506,402,310,230,162,106,62,30,10)(1052,1053,1054)
Conjugacy classes & character table
1059 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18918, 10);
Finite Group Databasebeta