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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1221 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221);(5,8)(6,7)(10,1221)(11,1220)(12,1219)(13,1218)(14,1217)(15,1216)(16,1215)(17,1214)(18,1213)(19,1212)(20,1211)(21,1210)(22,1209)(23,1208)(24,1207)(25,1206)(26,1205)(27,1204)(28,1203)(29,1202)(30,1201)(31,1200)(32,1199)(33,1198)(34,1197)(35,1196)(36,1195)(37,1194)(38,1193)(39,1192)(40,1191)(41,1190)(42,1189)(43,1188)(44,1187)(45,1186)(46,1185)(47,1184)(48,1183)(49,1182)(50,1181)(51,1180)(52,1179)(53,1178)(54,1177)(55,1176)(56,1175)(57,1174)(58,1173)(59,1172)(60,1171)(61,1170)(62,1169)(63,1168)(64,1167)(65,1166)(66,1165)(67,1164)(68,1163)(69,1162)(70,1161)(71,1160)(72,1159)(73,1158)(74,1157)(75,1156)(76,1155)(77,1154)(78,1153)(79,1152)(80,1151)(81,1150)(82,1149)(83,1148)(84,1147)(85,1146)(86,1145)(87,1144)(88,1143)(89,1142)(90,1141)(91,1140)(92,1139)(93,1138)(94,1137)(95,1136)(96,1135)(97,1134)(98,1133)(99,1132)(100,1131)(101,1130)(102,1129)(103,1128)(104,1127)(105,1126)(106,1125)(107,1124)(108,1123)(109,1122)(110,1121)(111,1120)(112,1119)(113,1118)(114,1117)(115,1116)(116,1115)(117,1114)(118,1113)(119,1112)(120,1111)(121,1110)(122,1109)(123,1108)(124,1107)(125,1106)(126,1105)(127,1104)(128,1103)(129,1102)(130,1101)(131,1100)(132,1099)(133,1098)(134,1097)(135,1096)(136,1095)(137,1094)(138,1093)(139,1092)(140,1091)(141,1090)(142,1089)(143,1088)(144,1087)(145,1086)(146,1085)(147,1084)(148,1083)(149,1082)(150,1081)(151,1080)(152,1079)(153,1078)(154,1077)(155,1076)(156,1075)(157,1074)(158,1073)(159,1072)(160,1071)(161,1070)(162,1069)(163,1068)(164,1067)(165,1066)(166,1065)(167,1064)(168,1063)(169,1062)(170,1061)(171,1060)(172,1059)(173,1058)(174,1057)(175,1056)(176,1055)(177,1054)(178,1053)(179,1052)(180,1051)(181,1050)(182,1049)(183,1048)(184,1047)(185,1046)(186,1045)(187,1044)(188,1043)(189,1042)(190,1041)(191,1040)(192,1039)(193,1038)(194,1037)(195,1036)(196,1035)(197,1034)(198,1033)(199,1032)(200,1031)(201,1030)(202,1029)(203,1028)(204,1027)(205,1026)(206,1025)(207,1024)(208,1023)(209,1022)(210,1021)(211,1020)(212,1019)(213,1018)(214,1017)(215,1016)(216,1015)(217,1014)(218,1013)(219,1012)(220,1011)(221,1010)(222,1009)(223,1008)(224,1007)(225,1006)(226,1005)(227,1004)(228,1003)(229,1002)(230,1001)(231,1000)(232,999)(233,998)(234,997)(235,996)(236,995)(237,994)(238,993)(239,992)(240,991)(241,990)(242,989)(243,988)(244,987)(245,986)(246,985)(247,984)(248,983)(249,982)(250,981)(251,980)(252,979)(253,978)(254,977)(255,976)(256,975)(257,974)(258,973)(259,972)(260,971)(261,970)(262,969)(263,968)(264,967)(265,966)(266,965)(267,964)(268,963)(269,962)(270,961)(271,960)(272,959)(273,958)(274,957)(275,956)(276,955)(277,954)(278,953)(279,952)(280,951)(281,950)(282,949)(283,948)(284,947)(285,946)(286,945)(287,944)(288,943)(289,942)(290,941)(291,940)(292,939)(293,938)(294,937)(295,936)(296,935)(297,934)(298,933)(299,932)(300,931)(301,930)(302,929)(303,928)(304,927)(305,926)(306,925)(307,924)(308,923)(309,922)(310,921)(311,920)(312,919)(313,918)(314,917)(315,916)(316,915)(317,914)(318,913)(319,912)(320,911)(321,910)(322,909)(323,908)(324,907)(325,906)(326,905)(327,904)(328,903)(329,902)(330,901)(331,900)(332,899)(333,898)(334,897)(335,896)(336,895)(337,894)(338,893)(339,892)(340,891)(341,890)(342,889)(343,888)(344,887)(345,886)(346,885)(347,884)(348,883)(349,882)(350,881)(351,880)(352,879)(353,878)(354,877)(355,876)(356,875)(357,874)(358,873)(359,872)(360,871)(361,870)(362,869)(363,868)(364,867)(365,866)(366,865)(367,864)(368,863)(369,862)(370,861)(371,860)(372,859)(373,858)(374,857)(375,856)(376,855)(377,854)(378,853)(379,852)(380,851)(381,850)(382,849)(383,848)(384,847)(385,846)(386,845)(387,844)(388,843)(389,842)(390,841)(391,840)(392,839)(393,838)(394,837)(395,836)(396,835)(397,834)(398,833)(399,832)(400,831)(401,830)(402,829)(403,828)(404,827)(405,826)(406,825)(407,824)(408,823)(409,822)(410,821)(411,820)(412,819)(413,818)(414,817)(415,816)(416,815)(417,814)(418,813)(419,812)(420,811)(421,810)(422,809)(423,808)(424,807)(425,806)(426,805)(427,804)(428,803)(429,802)(430,801)(431,800)(432,799)(433,798)(434,797)(435,796)(436,795)(437,794)(438,793)(439,792)(440,791)(441,790)(442,789)(443,788)(444,787)(445,786)(446,785)(447,784)(448,783)(449,782)(450,781)(451,780)(452,779)(453,778)(454,777)(455,776)(456,775)(457,774)(458,773)(459,772)(460,771)(461,770)(462,769)(463,768)(464,767)(465,766)(466,765)(467,764)(468,763)(469,762)(470,761)(471,760)(472,759)(473,758)(474,757)(475,756)(476,755)(477,754)(478,753)(479,752)(480,751)(481,750)(482,749)(483,748)(484,747)(485,746)(486,745)(487,744)(488,743)(489,742)(490,741)(491,740)(492,739)(493,738)(494,737)(495,736)(496,735)(497,734)(498,733)(499,732)(500,731)(501,730)(502,729)(503,728)(504,727)(505,726)(506,725)(507,724)(508,723)(509,722)(510,721)(511,720)(512,719)(513,718)(514,717)(515,716)(516,715)(517,714)(518,713)(519,712)(520,711)(521,710)(522,709)(523,708)(524,707)(525,706)(526,705)(527,704)(528,703)(529,702)(530,701)(531,700)(532,699)(533,698)(534,697)(535,696)(536,695)(537,694)(538,693)(539,692)(540,691)(541,690)(542,689)(543,688)(544,687)(545,686)(546,685)(547,684)(548,683)(549,682)(550,681)(551,680)(552,679)(553,678)(554,677)(555,676)(556,675)(557,674)(558,673)(559,672)(560,671)(561,670)(562,669)(563,668)(564,667)(565,666)(566,665)(567,664)(568,663)(569,662)(570,661)(571,660)(572,659)(573,658)(574,657)(575,656)(576,655)(577,654)(578,653)(579,652)(580,651)(581,650)(582,649)(583,648)(584,647)(585,646)(586,645)(587,644)(588,643)(589,642)(590,641)(591,640)(592,639)(593,638)(594,637)(595,636)(596,635)(597,634)(598,633)(599,632)(600,631)(601,630)(602,629)(603,628)(604,627)(605,626)(606,625)(607,624)(608,623)(609,622)(610,621)(611,620)(612,619)(613,618)(614,617)(615,616)
Conjugacy classes & character table
9102 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36390, 5);
Finite Group Databasebeta