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Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1156 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)(541,593,644)(544,600,641)(547,603,638)(550,606,635)(553,609,632)(556,612,629)(559,615,626)(562,618,623)(565,621,620)(568,624,617)(571,627,614)(574,630,611)(577,633,608)(580,636,605)(583,639,602)(586,642,599)(589,645,597)(591,648,594)(596,653,707)(598,654,704)(601,658,701)(604,660,698)(607,663,695)(610,666,692)(613,669,689)(616,672,686)(619,675,683)(622,678,680)(625,681,677)(628,684,674)(631,687,671)(634,690,668)(637,693,665)(640,696,662)(643,699,659)(646,702,657)(649,705,655)(651,708,652)(656,711,759)(661,714,754)(664,716,751)(667,719,748)(670,722,745)(673,725,742)(676,728,739)(679,731,736)(682,734,733)(685,737,730)(688,740,727)(691,743,724)(694,746,721)(697,749,718)(700,752,715)(703,755,713)(706,757,712)(709,760,710)(717,765,802)(720,767,799)(723,770,796)(726,773,793)(729,776,790)(732,779,787)(735,782,784)(738,785,781)(741,788,778)(744,791,775)(747,794,772)(750,797,769)(753,800,766)(756,803,764)(758,805,763)(761,807,762)(768,812,846)(771,814,843)(774,817,840)(777,820,837)(780,823,834)(783,826,831)(786,829,828)(789,832,825)(792,835,822)(795,838,819)(798,841,816)(801,844,813)(804,847,811)(806,849,810)(808,851,809)(815,856,887)(818,858,884)(821,861,881)(824,864,878)(827,867,875)(830,870,872)(833,873,869)(836,876,866)(839,879,863)(842,882,860)(845,885,857)(848,888,855)(850,890,854)(852,892,853)(859,897,925)(862,899,922)(865,902,919)(868,905,916)(871,908,913)(874,911,910)(877,914,907)(880,917,904)(883,920,901)(886,923,898)(889,926,896)(891,928,895)(893,930,894)(900,935,960)(903,937,957)(906,940,954)(909,943,951)(912,946,948)(915,949,945)(918,952,942)(921,955,939)(924,958,936)(927,961,934)(929,963,933)(931,965,932)(938,970,992)(941,972,989)(944,975,986)(947,978,983)(950,981,980)(953,984,977)(956,987,974)(959,990,971)(962,993,969)(964,995,968)(966,997,967)(973,1002,1021)(976,1004,1018)(979,1007,1015)(982,1010,1012)(985,1013,1009)(988,1016,1006)(991,1019,1003)(994,1022,1001)(996,1024,1000)(998,1026,999)(1005,1031,1047)(1008,1033,1044)(1011,1036,1041)(1014,1039,1038)(1017,1042,1035)(1020,1045,1032)(1023,1048,1030)(1025,1050,1029)(1027,1052,1028)(1034,1057,1070)(1037,1059,1067)(1040,1062,1064)(1043,1065,1061)(1046,1068,1058)(1049,1071,1056)(1051,1073,1055)(1053,1075,1054)(1060,1080,1090)(1063,1082,1087)(1066,1085,1084)(1069,1088,1081)(1072,1091,1079)(1074,1093,1078)(1076,1095,1077)(1083,1100,1107)(1086,1102,1104)(1089,1105,1101)(1092,1108,1099)(1094,1110,1098)(1096,1112,1097)(1103,1117,1121)(1106,1119,1118)(1109,1122,1116)(1111,1124,1115)(1113,1126,1114)(1120,1131,1132)(1123,1133,1130)(1125,1135,1129)(1127,1137,1128)(1134,1142,1141)(1136,1143,1140)(1138,1145,1139)(1144,1149,1148)(1146,1150,1147)(1151,1153,1152)(1155,1156);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,593,482,378,426,476,528,583,640,697,750,798,842,883,921,956,988,1017,1043,1066,1086,1103,1112,1073,1022,958,882,794,690,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,611,668,721,769,813,855,895,932,935,858,770,666,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,619,676,729,777,821,862,900,930,849,755,642,527,423,330,373,419,468,520,575,632,689,742,790,834,875,913,948,980,1009,1035,1058,1079,1098,1114,1117,1082,1036,978,908,826,731,618,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,598,656,711,595,479,533,589,646,703,756,804,848,889,927,962,994,1023,1049,1072,1092,1109,1123,1134,1137,1110,1071,1019,955,879,791,687,570,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,605,662,715,764,810,853,856,767,663,546,436,338,252,178,211,246,283,323,366,412,461,513,568,625,682,735,783,827,868,906,941,973,997,928,847,752,639,524,420,328,247,284,324,367,413,462,514,569,626,683,736,784,828,869,907,942,974,1003,1030,1055,1077,1080,1033,975,905,823,728,615,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,604,661,708,590,647,704,592,651,709,761,808,852,893,931,966,998,1027,1053,1076,1096,1113,1127,1138,1146,1151,1150,1135,1108,1068,1016,952,876,788,684,567,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,599,657,712,762,765,660,543,433,335,249,288,329,372,418,467,519,574,631,688,741,789,833,874,912,947,979,1008,1034,1052,995,926,844,749,636,521,417,325,245,176,207,241,278,318,361,407,456,508,563,620,677,730,778,822,863,901,936,969,1000,1028,1031,972,902,820,725,612,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,610,667,720,768,807,705,588,477,529,584,641,698,751,799,843,884,922,957,989,1018,1044,1067,1087,1104,1118,1130,1140,1147,1149,1133,1105,1065,1013,949,873,785,681,564,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,594,652,658,540,430,332,377,424,473,525,580,637,694,747,795,839,880,918,953,985,1014,1040,1063,1083,1095,1050,993,923,841,746,633,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,614,671,724,772,816,857,896,933,967,970,899,817,722,609,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,616,673,726,774,818,859,892,805,702,585,475,376,422,471,523,578,635,692,745,793,837,878,916,951,983,1012,1038,1061,1081,1099,1115,1128,1131,1102,1062,1010,946,870,782,678,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,654,537,427,478,531,586,643,700,753,801,845,886,924,959,991,1020,1046,1069,1089,1106,1120,1126,1093,1048,990,920,838,743,630,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,551,608,665,718,766,811,854,894,897,814,719,606,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,622,679,732,780,824,865,903,938,965,890,803,699,582,472,374,287,327,370,416,465,517,572,629,686,739,787,831,872,910,945,977,1006,1032,1056,1078,1097,1100,1059,1007,943,867,779,675,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,601,650,707,759,653,534,591,649,706,758,806,850,891,929,964,996,1025,1051,1074,1094,1111,1125,1136,1144,1145,1124,1091,1045,987,917,835,740,627,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,602,659,713,763,809,812,716,603,488,384,292,212,248,286,326,369,415,464,516,571,628,685,738,786,830,871,909,944,976,1005,1026,963,888,800,696,579,469,371,285,210,244,281,321,364,410,459,511,566,623,680,733,781,825,866,904,939,971,1001,1029,1054,1057,1004,940,864,776,672,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,607,664,717,760,648,532,587,644,701,754,802,846,887,925,960,992,1021,1047,1070,1090,1107,1121,1132,1141,1148,1152,1153,1143,1122,1088,1042,984,914,832,737,624,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,655,710,714,600,485,381,289,331,375,421,470,522,577,634,691,744,792,836,877,915,950,982,1011,1037,1060,1075,1024,961,885,797,693,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,617,674,727,775,819,860,898,934,968,999,1002,937,861,773,669,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,613,670,723,771,815,851,757,645,530,425,474,526,581,638,695,748,796,840,881,919,954,986,1015,1041,1064,1084,1101,1116,1129,1139,1142,1119,1085,1039,981,911,829,734,621,506,402,310,230,162,106,62,30,10)(1154,1155,1156)
Conjugacy classes & character table
1161 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20754, 12);
Finite Group Databasebeta