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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1160 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);(4,7)(5,6)(9,1160)(10,1159)(11,1158)(12,1157)(13,1156)(14,1155)(15,1154)(16,1153)(17,1152)(18,1151)(19,1150)(20,1149)(21,1148)(22,1147)(23,1146)(24,1145)(25,1144)(26,1143)(27,1142)(28,1141)(29,1140)(30,1139)(31,1138)(32,1137)(33,1136)(34,1135)(35,1134)(36,1133)(37,1132)(38,1131)(39,1130)(40,1129)(41,1128)(42,1127)(43,1126)(44,1125)(45,1124)(46,1123)(47,1122)(48,1121)(49,1120)(50,1119)(51,1118)(52,1117)(53,1116)(54,1115)(55,1114)(56,1113)(57,1112)(58,1111)(59,1110)(60,1109)(61,1108)(62,1107)(63,1106)(64,1105)(65,1104)(66,1103)(67,1102)(68,1101)(69,1100)(70,1099)(71,1098)(72,1097)(73,1096)(74,1095)(75,1094)(76,1093)(77,1092)(78,1091)(79,1090)(80,1089)(81,1088)(82,1087)(83,1086)(84,1085)(85,1084)(86,1083)(87,1082)(88,1081)(89,1080)(90,1079)(91,1078)(92,1077)(93,1076)(94,1075)(95,1074)(96,1073)(97,1072)(98,1071)(99,1070)(100,1069)(101,1068)(102,1067)(103,1066)(104,1065)(105,1064)(106,1063)(107,1062)(108,1061)(109,1060)(110,1059)(111,1058)(112,1057)(113,1056)(114,1055)(115,1054)(116,1053)(117,1052)(118,1051)(119,1050)(120,1049)(121,1048)(122,1047)(123,1046)(124,1045)(125,1044)(126,1043)(127,1042)(128,1041)(129,1040)(130,1039)(131,1038)(132,1037)(133,1036)(134,1035)(135,1034)(136,1033)(137,1032)(138,1031)(139,1030)(140,1029)(141,1028)(142,1027)(143,1026)(144,1025)(145,1024)(146,1023)(147,1022)(148,1021)(149,1020)(150,1019)(151,1018)(152,1017)(153,1016)(154,1015)(155,1014)(156,1013)(157,1012)(158,1011)(159,1010)(160,1009)(161,1008)(162,1007)(163,1006)(164,1005)(165,1004)(166,1003)(167,1002)(168,1001)(169,1000)(170,999)(171,998)(172,997)(173,996)(174,995)(175,994)(176,993)(177,992)(178,991)(179,990)(180,989)(181,988)(182,987)(183,986)(184,985)(185,984)(186,983)(187,982)(188,981)(189,980)(190,979)(191,978)(192,977)(193,976)(194,975)(195,974)(196,973)(197,972)(198,971)(199,970)(200,969)(201,968)(202,967)(203,966)(204,965)(205,964)(206,963)(207,962)(208,961)(209,960)(210,959)(211,958)(212,957)(213,956)(214,955)(215,954)(216,953)(217,952)(218,951)(219,950)(220,949)(221,948)(222,947)(223,946)(224,945)(225,944)(226,943)(227,942)(228,941)(229,940)(230,939)(231,938)(232,937)(233,936)(234,935)(235,934)(236,933)(237,932)(238,931)(239,930)(240,929)(241,928)(242,927)(243,926)(244,925)(245,924)(246,923)(247,922)(248,921)(249,920)(250,919)(251,918)(252,917)(253,916)(254,915)(255,914)(256,913)(257,912)(258,911)(259,910)(260,909)(261,908)(262,907)(263,906)(264,905)(265,904)(266,903)(267,902)(268,901)(269,900)(270,899)(271,898)(272,897)(273,896)(274,895)(275,894)(276,893)(277,892)(278,891)(279,890)(280,889)(281,888)(282,887)(283,886)(284,885)(285,884)(286,883)(287,882)(288,881)(289,880)(290,879)(291,878)(292,877)(293,876)(294,875)(295,874)(296,873)(297,872)(298,871)(299,870)(300,869)(301,868)(302,867)(303,866)(304,865)(305,864)(306,863)(307,862)(308,861)(309,860)(310,859)(311,858)(312,857)(313,856)(314,855)(315,854)(316,853)(317,852)(318,851)(319,850)(320,849)(321,848)(322,847)(323,846)(324,845)(325,844)(326,843)(327,842)(328,841)(329,840)(330,839)(331,838)(332,837)(333,836)(334,835)(335,834)(336,833)(337,832)(338,831)(339,830)(340,829)(341,828)(342,827)(343,826)(344,825)(345,824)(346,823)(347,822)(348,821)(349,820)(350,819)(351,818)(352,817)(353,816)(354,815)(355,814)(356,813)(357,812)(358,811)(359,810)(360,809)(361,808)(362,807)(363,806)(364,805)(365,804)(366,803)(367,802)(368,801)(369,800)(370,799)(371,798)(372,797)(373,796)(374,795)(375,794)(376,793)(377,792)(378,791)(379,790)(380,789)(381,788)(382,787)(383,786)(384,785)(385,784)(386,783)(387,782)(388,781)(389,780)(390,779)(391,778)(392,777)(393,776)(394,775)(395,774)(396,773)(397,772)(398,771)(399,770)(400,769)(401,768)(402,767)(403,766)(404,765)(405,764)(406,763)(407,762)(408,761)(409,760)(410,759)(411,758)(412,757)(413,756)(414,755)(415,754)(416,753)(417,752)(418,751)(419,750)(420,749)(421,748)(422,747)(423,746)(424,745)(425,744)(426,743)(427,742)(428,741)(429,740)(430,739)(431,738)(432,737)(433,736)(434,735)(435,734)(436,733)(437,732)(438,731)(439,730)(440,729)(441,728)(442,727)(443,726)(444,725)(445,724)(446,723)(447,722)(448,721)(449,720)(450,719)(451,718)(452,717)(453,716)(454,715)(455,714)(456,713)(457,712)(458,711)(459,710)(460,709)(461,708)(462,707)(463,706)(464,705)(465,704)(466,703)(467,702)(468,701)(469,700)(470,699)(471,698)(472,697)(473,696)(474,695)(475,694)(476,693)(477,692)(478,691)(479,690)(480,689)(481,688)(482,687)(483,686)(484,685)(485,684)(486,683)(487,682)(488,681)(489,680)(490,679)(491,678)(492,677)(493,676)(494,675)(495,674)(496,673)(497,672)(498,671)(499,670)(500,669)(501,668)(502,667)(503,666)(504,665)(505,664)(506,663)(507,662)(508,661)(509,660)(510,659)(511,658)(512,657)(513,656)(514,655)(515,654)(516,653)(517,652)(518,651)(519,650)(520,649)(521,648)(522,647)(523,646)(524,645)(525,644)(526,643)(527,642)(528,641)(529,640)(530,639)(531,638)(532,637)(533,636)(534,635)(535,634)(536,633)(537,632)(538,631)(539,630)(540,629)(541,628)(542,627)(543,626)(544,625)(545,624)(546,623)(547,622)(548,621)(549,620)(550,619)(551,618)(552,617)(553,616)(554,615)(555,614)(556,613)(557,612)(558,611)(559,610)(560,609)(561,608)(562,607)(563,606)(564,605)(565,604)(566,603)(567,602)(568,601)(569,600)(570,599)(571,598)(572,597)(573,596)(574,595)(575,594)(576,593)(577,592)(578,591)(579,590)(580,589)(581,588)(582,587)(583,586)(584,585)
Conjugacy classes & character table
5768 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23060, 15);
Finite Group Databasebeta