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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1194 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);(4,7)(5,6)(9,1194)(10,1193)(11,1192)(12,1191)(13,1190)(14,1189)(15,1188)(16,1187)(17,1186)(18,1185)(19,1184)(20,1183)(21,1182)(22,1181)(23,1180)(24,1179)(25,1178)(26,1177)(27,1176)(28,1175)(29,1174)(30,1173)(31,1172)(32,1171)(33,1170)(34,1169)(35,1168)(36,1167)(37,1166)(38,1165)(39,1164)(40,1163)(41,1162)(42,1161)(43,1160)(44,1159)(45,1158)(46,1157)(47,1156)(48,1155)(49,1154)(50,1153)(51,1152)(52,1151)(53,1150)(54,1149)(55,1148)(56,1147)(57,1146)(58,1145)(59,1144)(60,1143)(61,1142)(62,1141)(63,1140)(64,1139)(65,1138)(66,1137)(67,1136)(68,1135)(69,1134)(70,1133)(71,1132)(72,1131)(73,1130)(74,1129)(75,1128)(76,1127)(77,1126)(78,1125)(79,1124)(80,1123)(81,1122)(82,1121)(83,1120)(84,1119)(85,1118)(86,1117)(87,1116)(88,1115)(89,1114)(90,1113)(91,1112)(92,1111)(93,1110)(94,1109)(95,1108)(96,1107)(97,1106)(98,1105)(99,1104)(100,1103)(101,1102)(102,1101)(103,1100)(104,1099)(105,1098)(106,1097)(107,1096)(108,1095)(109,1094)(110,1093)(111,1092)(112,1091)(113,1090)(114,1089)(115,1088)(116,1087)(117,1086)(118,1085)(119,1084)(120,1083)(121,1082)(122,1081)(123,1080)(124,1079)(125,1078)(126,1077)(127,1076)(128,1075)(129,1074)(130,1073)(131,1072)(132,1071)(133,1070)(134,1069)(135,1068)(136,1067)(137,1066)(138,1065)(139,1064)(140,1063)(141,1062)(142,1061)(143,1060)(144,1059)(145,1058)(146,1057)(147,1056)(148,1055)(149,1054)(150,1053)(151,1052)(152,1051)(153,1050)(154,1049)(155,1048)(156,1047)(157,1046)(158,1045)(159,1044)(160,1043)(161,1042)(162,1041)(163,1040)(164,1039)(165,1038)(166,1037)(167,1036)(168,1035)(169,1034)(170,1033)(171,1032)(172,1031)(173,1030)(174,1029)(175,1028)(176,1027)(177,1026)(178,1025)(179,1024)(180,1023)(181,1022)(182,1021)(183,1020)(184,1019)(185,1018)(186,1017)(187,1016)(188,1015)(189,1014)(190,1013)(191,1012)(192,1011)(193,1010)(194,1009)(195,1008)(196,1007)(197,1006)(198,1005)(199,1004)(200,1003)(201,1002)(202,1001)(203,1000)(204,999)(205,998)(206,997)(207,996)(208,995)(209,994)(210,993)(211,992)(212,991)(213,990)(214,989)(215,988)(216,987)(217,986)(218,985)(219,984)(220,983)(221,982)(222,981)(223,980)(224,979)(225,978)(226,977)(227,976)(228,975)(229,974)(230,973)(231,972)(232,971)(233,970)(234,969)(235,968)(236,967)(237,966)(238,965)(239,964)(240,963)(241,962)(242,961)(243,960)(244,959)(245,958)(246,957)(247,956)(248,955)(249,954)(250,953)(251,952)(252,951)(253,950)(254,949)(255,948)(256,947)(257,946)(258,945)(259,944)(260,943)(261,942)(262,941)(263,940)(264,939)(265,938)(266,937)(267,936)(268,935)(269,934)(270,933)(271,932)(272,931)(273,930)(274,929)(275,928)(276,927)(277,926)(278,925)(279,924)(280,923)(281,922)(282,921)(283,920)(284,919)(285,918)(286,917)(287,916)(288,915)(289,914)(290,913)(291,912)(292,911)(293,910)(294,909)(295,908)(296,907)(297,906)(298,905)(299,904)(300,903)(301,902)(302,901)(303,900)(304,899)(305,898)(306,897)(307,896)(308,895)(309,894)(310,893)(311,892)(312,891)(313,890)(314,889)(315,888)(316,887)(317,886)(318,885)(319,884)(320,883)(321,882)(322,881)(323,880)(324,879)(325,878)(326,877)(327,876)(328,875)(329,874)(330,873)(331,872)(332,871)(333,870)(334,869)(335,868)(336,867)(337,866)(338,865)(339,864)(340,863)(341,862)(342,861)(343,860)(344,859)(345,858)(346,857)(347,856)(348,855)(349,854)(350,853)(351,852)(352,851)(353,850)(354,849)(355,848)(356,847)(357,846)(358,845)(359,844)(360,843)(361,842)(362,841)(363,840)(364,839)(365,838)(366,837)(367,836)(368,835)(369,834)(370,833)(371,832)(372,831)(373,830)(374,829)(375,828)(376,827)(377,826)(378,825)(379,824)(380,823)(381,822)(382,821)(383,820)(384,819)(385,818)(386,817)(387,816)(388,815)(389,814)(390,813)(391,812)(392,811)(393,810)(394,809)(395,808)(396,807)(397,806)(398,805)(399,804)(400,803)(401,802)(402,801)(403,800)(404,799)(405,798)(406,797)(407,796)(408,795)(409,794)(410,793)(411,792)(412,791)(413,790)(414,789)(415,788)(416,787)(417,786)(418,785)(419,784)(420,783)(421,782)(422,781)(423,780)(424,779)(425,778)(426,777)(427,776)(428,775)(429,774)(430,773)(431,772)(432,771)(433,770)(434,769)(435,768)(436,767)(437,766)(438,765)(439,764)(440,763)(441,762)(442,761)(443,760)(444,759)(445,758)(446,757)(447,756)(448,755)(449,754)(450,753)(451,752)(452,751)(453,750)(454,749)(455,748)(456,747)(457,746)(458,745)(459,744)(460,743)(461,742)(462,741)(463,740)(464,739)(465,738)(466,737)(467,736)(468,735)(469,734)(470,733)(471,732)(472,731)(473,730)(474,729)(475,728)(476,727)(477,726)(478,725)(479,724)(480,723)(481,722)(482,721)(483,720)(484,719)(485,718)(486,717)(487,716)(488,715)(489,714)(490,713)(491,712)(492,711)(493,710)(494,709)(495,708)(496,707)(497,706)(498,705)(499,704)(500,703)(501,702)(502,701)(503,700)(504,699)(505,698)(506,697)(507,696)(508,695)(509,694)(510,693)(511,692)(512,691)(513,690)(514,689)(515,688)(516,687)(517,686)(518,685)(519,684)(520,683)(521,682)(522,681)(523,680)(524,679)(525,678)(526,677)(527,676)(528,675)(529,674)(530,673)(531,672)(532,671)(533,670)(534,669)(535,668)(536,667)(537,666)(538,665)(539,664)(540,663)(541,662)(542,661)(543,660)(544,659)(545,658)(546,657)(547,656)(548,655)(549,654)(550,653)(551,652)(552,651)(553,650)(554,649)(555,648)(556,647)(557,646)(558,645)(559,644)(560,643)(561,642)(562,641)(563,640)(564,639)(565,638)(566,637)(567,636)(568,635)(569,634)(570,633)(571,632)(572,631)(573,630)(574,629)(575,628)(576,627)(577,626)(578,625)(579,624)(580,623)(581,622)(582,621)(583,620)(584,619)(585,618)(586,617)(587,616)(588,615)(589,614)(590,613)(591,612)(592,611)(593,610)(594,609)(595,608)(596,607)(597,606)(598,605)(599,604)(600,603)(601,602)
Conjugacy classes & character table
5938 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23740, 11);
Finite Group Databasebeta