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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1286 points:
(1,2)(3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286);(4,9)(5,8)(6,7)(11,1286)(12,1285)(13,1284)(14,1283)(15,1282)(16,1281)(17,1280)(18,1279)(19,1278)(20,1277)(21,1276)(22,1275)(23,1274)(24,1273)(25,1272)(26,1271)(27,1270)(28,1269)(29,1268)(30,1267)(31,1266)(32,1265)(33,1264)(34,1263)(35,1262)(36,1261)(37,1260)(38,1259)(39,1258)(40,1257)(41,1256)(42,1255)(43,1254)(44,1253)(45,1252)(46,1251)(47,1250)(48,1249)(49,1248)(50,1247)(51,1246)(52,1245)(53,1244)(54,1243)(55,1242)(56,1241)(57,1240)(58,1239)(59,1238)(60,1237)(61,1236)(62,1235)(63,1234)(64,1233)(65,1232)(66,1231)(67,1230)(68,1229)(69,1228)(70,1227)(71,1226)(72,1225)(73,1224)(74,1223)(75,1222)(76,1221)(77,1220)(78,1219)(79,1218)(80,1217)(81,1216)(82,1215)(83,1214)(84,1213)(85,1212)(86,1211)(87,1210)(88,1209)(89,1208)(90,1207)(91,1206)(92,1205)(93,1204)(94,1203)(95,1202)(96,1201)(97,1200)(98,1199)(99,1198)(100,1197)(101,1196)(102,1195)(103,1194)(104,1193)(105,1192)(106,1191)(107,1190)(108,1189)(109,1188)(110,1187)(111,1186)(112,1185)(113,1184)(114,1183)(115,1182)(116,1181)(117,1180)(118,1179)(119,1178)(120,1177)(121,1176)(122,1175)(123,1174)(124,1173)(125,1172)(126,1171)(127,1170)(128,1169)(129,1168)(130,1167)(131,1166)(132,1165)(133,1164)(134,1163)(135,1162)(136,1161)(137,1160)(138,1159)(139,1158)(140,1157)(141,1156)(142,1155)(143,1154)(144,1153)(145,1152)(146,1151)(147,1150)(148,1149)(149,1148)(150,1147)(151,1146)(152,1145)(153,1144)(154,1143)(155,1142)(156,1141)(157,1140)(158,1139)(159,1138)(160,1137)(161,1136)(162,1135)(163,1134)(164,1133)(165,1132)(166,1131)(167,1130)(168,1129)(169,1128)(170,1127)(171,1126)(172,1125)(173,1124)(174,1123)(175,1122)(176,1121)(177,1120)(178,1119)(179,1118)(180,1117)(181,1116)(182,1115)(183,1114)(184,1113)(185,1112)(186,1111)(187,1110)(188,1109)(189,1108)(190,1107)(191,1106)(192,1105)(193,1104)(194,1103)(195,1102)(196,1101)(197,1100)(198,1099)(199,1098)(200,1097)(201,1096)(202,1095)(203,1094)(204,1093)(205,1092)(206,1091)(207,1090)(208,1089)(209,1088)(210,1087)(211,1086)(212,1085)(213,1084)(214,1083)(215,1082)(216,1081)(217,1080)(218,1079)(219,1078)(220,1077)(221,1076)(222,1075)(223,1074)(224,1073)(225,1072)(226,1071)(227,1070)(228,1069)(229,1068)(230,1067)(231,1066)(232,1065)(233,1064)(234,1063)(235,1062)(236,1061)(237,1060)(238,1059)(239,1058)(240,1057)(241,1056)(242,1055)(243,1054)(244,1053)(245,1052)(246,1051)(247,1050)(248,1049)(249,1048)(250,1047)(251,1046)(252,1045)(253,1044)(254,1043)(255,1042)(256,1041)(257,1040)(258,1039)(259,1038)(260,1037)(261,1036)(262,1035)(263,1034)(264,1033)(265,1032)(266,1031)(267,1030)(268,1029)(269,1028)(270,1027)(271,1026)(272,1025)(273,1024)(274,1023)(275,1022)(276,1021)(277,1020)(278,1019)(279,1018)(280,1017)(281,1016)(282,1015)(283,1014)(284,1013)(285,1012)(286,1011)(287,1010)(288,1009)(289,1008)(290,1007)(291,1006)(292,1005)(293,1004)(294,1003)(295,1002)(296,1001)(297,1000)(298,999)(299,998)(300,997)(301,996)(302,995)(303,994)(304,993)(305,992)(306,991)(307,990)(308,989)(309,988)(310,987)(311,986)(312,985)(313,984)(314,983)(315,982)(316,981)(317,980)(318,979)(319,978)(320,977)(321,976)(322,975)(323,974)(324,973)(325,972)(326,971)(327,970)(328,969)(329,968)(330,967)(331,966)(332,965)(333,964)(334,963)(335,962)(336,961)(337,960)(338,959)(339,958)(340,957)(341,956)(342,955)(343,954)(344,953)(345,952)(346,951)(347,950)(348,949)(349,948)(350,947)(351,946)(352,945)(353,944)(354,943)(355,942)(356,941)(357,940)(358,939)(359,938)(360,937)(361,936)(362,935)(363,934)(364,933)(365,932)(366,931)(367,930)(368,929)(369,928)(370,927)(371,926)(372,925)(373,924)(374,923)(375,922)(376,921)(377,920)(378,919)(379,918)(380,917)(381,916)(382,915)(383,914)(384,913)(385,912)(386,911)(387,910)(388,909)(389,908)(390,907)(391,906)(392,905)(393,904)(394,903)(395,902)(396,901)(397,900)(398,899)(399,898)(400,897)(401,896)(402,895)(403,894)(404,893)(405,892)(406,891)(407,890)(408,889)(409,888)(410,887)(411,886)(412,885)(413,884)(414,883)(415,882)(416,881)(417,880)(418,879)(419,878)(420,877)(421,876)(422,875)(423,874)(424,873)(425,872)(426,871)(427,870)(428,869)(429,868)(430,867)(431,866)(432,865)(433,864)(434,863)(435,862)(436,861)(437,860)(438,859)(439,858)(440,857)(441,856)(442,855)(443,854)(444,853)(445,852)(446,851)(447,850)(448,849)(449,848)(450,847)(451,846)(452,845)(453,844)(454,843)(455,842)(456,841)(457,840)(458,839)(459,838)(460,837)(461,836)(462,835)(463,834)(464,833)(465,832)(466,831)(467,830)(468,829)(469,828)(470,827)(471,826)(472,825)(473,824)(474,823)(475,822)(476,821)(477,820)(478,819)(479,818)(480,817)(481,816)(482,815)(483,814)(484,813)(485,812)(486,811)(487,810)(488,809)(489,808)(490,807)(491,806)(492,805)(493,804)(494,803)(495,802)(496,801)(497,800)(498,799)(499,798)(500,797)(501,796)(502,795)(503,794)(504,793)(505,792)(506,791)(507,790)(508,789)(509,788)(510,787)(511,786)(512,785)(513,784)(514,783)(515,782)(516,781)(517,780)(518,779)(519,778)(520,777)(521,776)(522,775)(523,774)(524,773)(525,772)(526,771)(527,770)(528,769)(529,768)(530,767)(531,766)(532,765)(533,764)(534,763)(535,762)(536,761)(537,760)(538,759)(539,758)(540,757)(541,756)(542,755)(543,754)(544,753)(545,752)(546,751)(547,750)(548,749)(549,748)(550,747)(551,746)(552,745)(553,744)(554,743)(555,742)(556,741)(557,740)(558,739)(559,738)(560,737)(561,736)(562,735)(563,734)(564,733)(565,732)(566,731)(567,730)(568,729)(569,728)(570,727)(571,726)(572,725)(573,724)(574,723)(575,722)(576,721)(577,720)(578,719)(579,718)(580,717)(581,716)(582,715)(583,714)(584,713)(585,712)(586,711)(587,710)(588,709)(589,708)(590,707)(591,706)(592,705)(593,704)(594,703)(595,702)(596,701)(597,700)(598,699)(599,698)(600,697)(601,696)(602,695)(603,694)(604,693)(605,692)(606,691)(607,690)(608,689)(609,688)(610,687)(611,686)(612,685)(613,684)(614,683)(615,682)(616,681)(617,680)(618,679)(619,678)(620,677)(621,676)(622,675)(623,674)(624,673)(625,672)(626,671)(627,670)(628,669)(629,668)(630,667)(631,666)(632,665)(633,664)(634,663)(635,662)(636,661)(637,660)(638,659)(639,658)(640,657)(641,656)(642,655)(643,654)(644,653)(645,652)(646,651)(647,650)(648,649)
Conjugacy classes & character table
8942 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35756, 11);
Finite Group Databasebeta