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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1226 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);(4,9)(5,8)(6,7)(11,1226)(12,1225)(13,1224)(14,1223)(15,1222)(16,1221)(17,1220)(18,1219)(19,1218)(20,1217)(21,1216)(22,1215)(23,1214)(24,1213)(25,1212)(26,1211)(27,1210)(28,1209)(29,1208)(30,1207)(31,1206)(32,1205)(33,1204)(34,1203)(35,1202)(36,1201)(37,1200)(38,1199)(39,1198)(40,1197)(41,1196)(42,1195)(43,1194)(44,1193)(45,1192)(46,1191)(47,1190)(48,1189)(49,1188)(50,1187)(51,1186)(52,1185)(53,1184)(54,1183)(55,1182)(56,1181)(57,1180)(58,1179)(59,1178)(60,1177)(61,1176)(62,1175)(63,1174)(64,1173)(65,1172)(66,1171)(67,1170)(68,1169)(69,1168)(70,1167)(71,1166)(72,1165)(73,1164)(74,1163)(75,1162)(76,1161)(77,1160)(78,1159)(79,1158)(80,1157)(81,1156)(82,1155)(83,1154)(84,1153)(85,1152)(86,1151)(87,1150)(88,1149)(89,1148)(90,1147)(91,1146)(92,1145)(93,1144)(94,1143)(95,1142)(96,1141)(97,1140)(98,1139)(99,1138)(100,1137)(101,1136)(102,1135)(103,1134)(104,1133)(105,1132)(106,1131)(107,1130)(108,1129)(109,1128)(110,1127)(111,1126)(112,1125)(113,1124)(114,1123)(115,1122)(116,1121)(117,1120)(118,1119)(119,1118)(120,1117)(121,1116)(122,1115)(123,1114)(124,1113)(125,1112)(126,1111)(127,1110)(128,1109)(129,1108)(130,1107)(131,1106)(132,1105)(133,1104)(134,1103)(135,1102)(136,1101)(137,1100)(138,1099)(139,1098)(140,1097)(141,1096)(142,1095)(143,1094)(144,1093)(145,1092)(146,1091)(147,1090)(148,1089)(149,1088)(150,1087)(151,1086)(152,1085)(153,1084)(154,1083)(155,1082)(156,1081)(157,1080)(158,1079)(159,1078)(160,1077)(161,1076)(162,1075)(163,1074)(164,1073)(165,1072)(166,1071)(167,1070)(168,1069)(169,1068)(170,1067)(171,1066)(172,1065)(173,1064)(174,1063)(175,1062)(176,1061)(177,1060)(178,1059)(179,1058)(180,1057)(181,1056)(182,1055)(183,1054)(184,1053)(185,1052)(186,1051)(187,1050)(188,1049)(189,1048)(190,1047)(191,1046)(192,1045)(193,1044)(194,1043)(195,1042)(196,1041)(197,1040)(198,1039)(199,1038)(200,1037)(201,1036)(202,1035)(203,1034)(204,1033)(205,1032)(206,1031)(207,1030)(208,1029)(209,1028)(210,1027)(211,1026)(212,1025)(213,1024)(214,1023)(215,1022)(216,1021)(217,1020)(218,1019)(219,1018)(220,1017)(221,1016)(222,1015)(223,1014)(224,1013)(225,1012)(226,1011)(227,1010)(228,1009)(229,1008)(230,1007)(231,1006)(232,1005)(233,1004)(234,1003)(235,1002)(236,1001)(237,1000)(238,999)(239,998)(240,997)(241,996)(242,995)(243,994)(244,993)(245,992)(246,991)(247,990)(248,989)(249,988)(250,987)(251,986)(252,985)(253,984)(254,983)(255,982)(256,981)(257,980)(258,979)(259,978)(260,977)(261,976)(262,975)(263,974)(264,973)(265,972)(266,971)(267,970)(268,969)(269,968)(270,967)(271,966)(272,965)(273,964)(274,963)(275,962)(276,961)(277,960)(278,959)(279,958)(280,957)(281,956)(282,955)(283,954)(284,953)(285,952)(286,951)(287,950)(288,949)(289,948)(290,947)(291,946)(292,945)(293,944)(294,943)(295,942)(296,941)(297,940)(298,939)(299,938)(300,937)(301,936)(302,935)(303,934)(304,933)(305,932)(306,931)(307,930)(308,929)(309,928)(310,927)(311,926)(312,925)(313,924)(314,923)(315,922)(316,921)(317,920)(318,919)(319,918)(320,917)(321,916)(322,915)(323,914)(324,913)(325,912)(326,911)(327,910)(328,909)(329,908)(330,907)(331,906)(332,905)(333,904)(334,903)(335,902)(336,901)(337,900)(338,899)(339,898)(340,897)(341,896)(342,895)(343,894)(344,893)(345,892)(346,891)(347,890)(348,889)(349,888)(350,887)(351,886)(352,885)(353,884)(354,883)(355,882)(356,881)(357,880)(358,879)(359,878)(360,877)(361,876)(362,875)(363,874)(364,873)(365,872)(366,871)(367,870)(368,869)(369,868)(370,867)(371,866)(372,865)(373,864)(374,863)(375,862)(376,861)(377,860)(378,859)(379,858)(380,857)(381,856)(382,855)(383,854)(384,853)(385,852)(386,851)(387,850)(388,849)(389,848)(390,847)(391,846)(392,845)(393,844)(394,843)(395,842)(396,841)(397,840)(398,839)(399,838)(400,837)(401,836)(402,835)(403,834)(404,833)(405,832)(406,831)(407,830)(408,829)(409,828)(410,827)(411,826)(412,825)(413,824)(414,823)(415,822)(416,821)(417,820)(418,819)(419,818)(420,817)(421,816)(422,815)(423,814)(424,813)(425,812)(426,811)(427,810)(428,809)(429,808)(430,807)(431,806)(432,805)(433,804)(434,803)(435,802)(436,801)(437,800)(438,799)(439,798)(440,797)(441,796)(442,795)(443,794)(444,793)(445,792)(446,791)(447,790)(448,789)(449,788)(450,787)(451,786)(452,785)(453,784)(454,783)(455,782)(456,781)(457,780)(458,779)(459,778)(460,777)(461,776)(462,775)(463,774)(464,773)(465,772)(466,771)(467,770)(468,769)(469,768)(470,767)(471,766)(472,765)(473,764)(474,763)(475,762)(476,761)(477,760)(478,759)(479,758)(480,757)(481,756)(482,755)(483,754)(484,753)(485,752)(486,751)(487,750)(488,749)(489,748)(490,747)(491,746)(492,745)(493,744)(494,743)(495,742)(496,741)(497,740)(498,739)(499,738)(500,737)(501,736)(502,735)(503,734)(504,733)(505,732)(506,731)(507,730)(508,729)(509,728)(510,727)(511,726)(512,725)(513,724)(514,723)(515,722)(516,721)(517,720)(518,719)(519,718)(520,717)(521,716)(522,715)(523,714)(524,713)(525,712)(526,711)(527,710)(528,709)(529,708)(530,707)(531,706)(532,705)(533,704)(534,703)(535,702)(536,701)(537,700)(538,699)(539,698)(540,697)(541,696)(542,695)(543,694)(544,693)(545,692)(546,691)(547,690)(548,689)(549,688)(550,687)(551,686)(552,685)(553,684)(554,683)(555,682)(556,681)(557,680)(558,679)(559,678)(560,677)(561,676)(562,675)(563,674)(564,673)(565,672)(566,671)(567,670)(568,669)(569,668)(570,667)(571,666)(572,665)(573,664)(574,663)(575,662)(576,661)(577,660)(578,659)(579,658)(580,657)(581,656)(582,655)(583,654)(584,653)(585,652)(586,651)(587,650)(588,649)(589,648)(590,647)(591,646)(592,645)(593,644)(594,643)(595,642)(596,641)(597,640)(598,639)(599,638)(600,637)(601,636)(602,635)(603,634)(604,633)(605,632)(606,631)(607,630)(608,629)(609,628)(610,627)(611,626)(612,625)(613,624)(614,623)(615,622)(616,621)(617,620)(618,619)
Conjugacy classes & character table
8522 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34076, 11);
Finite Group Databasebeta