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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1170 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);(4,7)(5,6)(9,1170)(10,1169)(11,1168)(12,1167)(13,1166)(14,1165)(15,1164)(16,1163)(17,1162)(18,1161)(19,1160)(20,1159)(21,1158)(22,1157)(23,1156)(24,1155)(25,1154)(26,1153)(27,1152)(28,1151)(29,1150)(30,1149)(31,1148)(32,1147)(33,1146)(34,1145)(35,1144)(36,1143)(37,1142)(38,1141)(39,1140)(40,1139)(41,1138)(42,1137)(43,1136)(44,1135)(45,1134)(46,1133)(47,1132)(48,1131)(49,1130)(50,1129)(51,1128)(52,1127)(53,1126)(54,1125)(55,1124)(56,1123)(57,1122)(58,1121)(59,1120)(60,1119)(61,1118)(62,1117)(63,1116)(64,1115)(65,1114)(66,1113)(67,1112)(68,1111)(69,1110)(70,1109)(71,1108)(72,1107)(73,1106)(74,1105)(75,1104)(76,1103)(77,1102)(78,1101)(79,1100)(80,1099)(81,1098)(82,1097)(83,1096)(84,1095)(85,1094)(86,1093)(87,1092)(88,1091)(89,1090)(90,1089)(91,1088)(92,1087)(93,1086)(94,1085)(95,1084)(96,1083)(97,1082)(98,1081)(99,1080)(100,1079)(101,1078)(102,1077)(103,1076)(104,1075)(105,1074)(106,1073)(107,1072)(108,1071)(109,1070)(110,1069)(111,1068)(112,1067)(113,1066)(114,1065)(115,1064)(116,1063)(117,1062)(118,1061)(119,1060)(120,1059)(121,1058)(122,1057)(123,1056)(124,1055)(125,1054)(126,1053)(127,1052)(128,1051)(129,1050)(130,1049)(131,1048)(132,1047)(133,1046)(134,1045)(135,1044)(136,1043)(137,1042)(138,1041)(139,1040)(140,1039)(141,1038)(142,1037)(143,1036)(144,1035)(145,1034)(146,1033)(147,1032)(148,1031)(149,1030)(150,1029)(151,1028)(152,1027)(153,1026)(154,1025)(155,1024)(156,1023)(157,1022)(158,1021)(159,1020)(160,1019)(161,1018)(162,1017)(163,1016)(164,1015)(165,1014)(166,1013)(167,1012)(168,1011)(169,1010)(170,1009)(171,1008)(172,1007)(173,1006)(174,1005)(175,1004)(176,1003)(177,1002)(178,1001)(179,1000)(180,999)(181,998)(182,997)(183,996)(184,995)(185,994)(186,993)(187,992)(188,991)(189,990)(190,989)(191,988)(192,987)(193,986)(194,985)(195,984)(196,983)(197,982)(198,981)(199,980)(200,979)(201,978)(202,977)(203,976)(204,975)(205,974)(206,973)(207,972)(208,971)(209,970)(210,969)(211,968)(212,967)(213,966)(214,965)(215,964)(216,963)(217,962)(218,961)(219,960)(220,959)(221,958)(222,957)(223,956)(224,955)(225,954)(226,953)(227,952)(228,951)(229,950)(230,949)(231,948)(232,947)(233,946)(234,945)(235,944)(236,943)(237,942)(238,941)(239,940)(240,939)(241,938)(242,937)(243,936)(244,935)(245,934)(246,933)(247,932)(248,931)(249,930)(250,929)(251,928)(252,927)(253,926)(254,925)(255,924)(256,923)(257,922)(258,921)(259,920)(260,919)(261,918)(262,917)(263,916)(264,915)(265,914)(266,913)(267,912)(268,911)(269,910)(270,909)(271,908)(272,907)(273,906)(274,905)(275,904)(276,903)(277,902)(278,901)(279,900)(280,899)(281,898)(282,897)(283,896)(284,895)(285,894)(286,893)(287,892)(288,891)(289,890)(290,889)(291,888)(292,887)(293,886)(294,885)(295,884)(296,883)(297,882)(298,881)(299,880)(300,879)(301,878)(302,877)(303,876)(304,875)(305,874)(306,873)(307,872)(308,871)(309,870)(310,869)(311,868)(312,867)(313,866)(314,865)(315,864)(316,863)(317,862)(318,861)(319,860)(320,859)(321,858)(322,857)(323,856)(324,855)(325,854)(326,853)(327,852)(328,851)(329,850)(330,849)(331,848)(332,847)(333,846)(334,845)(335,844)(336,843)(337,842)(338,841)(339,840)(340,839)(341,838)(342,837)(343,836)(344,835)(345,834)(346,833)(347,832)(348,831)(349,830)(350,829)(351,828)(352,827)(353,826)(354,825)(355,824)(356,823)(357,822)(358,821)(359,820)(360,819)(361,818)(362,817)(363,816)(364,815)(365,814)(366,813)(367,812)(368,811)(369,810)(370,809)(371,808)(372,807)(373,806)(374,805)(375,804)(376,803)(377,802)(378,801)(379,800)(380,799)(381,798)(382,797)(383,796)(384,795)(385,794)(386,793)(387,792)(388,791)(389,790)(390,789)(391,788)(392,787)(393,786)(394,785)(395,784)(396,783)(397,782)(398,781)(399,780)(400,779)(401,778)(402,777)(403,776)(404,775)(405,774)(406,773)(407,772)(408,771)(409,770)(410,769)(411,768)(412,767)(413,766)(414,765)(415,764)(416,763)(417,762)(418,761)(419,760)(420,759)(421,758)(422,757)(423,756)(424,755)(425,754)(426,753)(427,752)(428,751)(429,750)(430,749)(431,748)(432,747)(433,746)(434,745)(435,744)(436,743)(437,742)(438,741)(439,740)(440,739)(441,738)(442,737)(443,736)(444,735)(445,734)(446,733)(447,732)(448,731)(449,730)(450,729)(451,728)(452,727)(453,726)(454,725)(455,724)(456,723)(457,722)(458,721)(459,720)(460,719)(461,718)(462,717)(463,716)(464,715)(465,714)(466,713)(467,712)(468,711)(469,710)(470,709)(471,708)(472,707)(473,706)(474,705)(475,704)(476,703)(477,702)(478,701)(479,700)(480,699)(481,698)(482,697)(483,696)(484,695)(485,694)(486,693)(487,692)(488,691)(489,690)(490,689)(491,688)(492,687)(493,686)(494,685)(495,684)(496,683)(497,682)(498,681)(499,680)(500,679)(501,678)(502,677)(503,676)(504,675)(505,674)(506,673)(507,672)(508,671)(509,670)(510,669)(511,668)(512,667)(513,666)(514,665)(515,664)(516,663)(517,662)(518,661)(519,660)(520,659)(521,658)(522,657)(523,656)(524,655)(525,654)(526,653)(527,652)(528,651)(529,650)(530,649)(531,648)(532,647)(533,646)(534,645)(535,644)(536,643)(537,642)(538,641)(539,640)(540,639)(541,638)(542,637)(543,636)(544,635)(545,634)(546,633)(547,632)(548,631)(549,630)(550,629)(551,628)(552,627)(553,626)(554,625)(555,624)(556,623)(557,622)(558,621)(559,620)(560,619)(561,618)(562,617)(563,616)(564,615)(565,614)(566,613)(567,612)(568,611)(569,610)(570,609)(571,608)(572,607)(573,606)(574,605)(575,604)(576,603)(577,602)(578,601)(579,600)(580,599)(581,598)(582,597)(583,596)(584,595)(585,594)(586,593)(587,592)(588,591)(589,590)
Conjugacy classes & character table
5818 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23260, 11);
Finite Group Databasebeta