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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1200 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);(4,7)(5,6)(9,1200)(10,1199)(11,1198)(12,1197)(13,1196)(14,1195)(15,1194)(16,1193)(17,1192)(18,1191)(19,1190)(20,1189)(21,1188)(22,1187)(23,1186)(24,1185)(25,1184)(26,1183)(27,1182)(28,1181)(29,1180)(30,1179)(31,1178)(32,1177)(33,1176)(34,1175)(35,1174)(36,1173)(37,1172)(38,1171)(39,1170)(40,1169)(41,1168)(42,1167)(43,1166)(44,1165)(45,1164)(46,1163)(47,1162)(48,1161)(49,1160)(50,1159)(51,1158)(52,1157)(53,1156)(54,1155)(55,1154)(56,1153)(57,1152)(58,1151)(59,1150)(60,1149)(61,1148)(62,1147)(63,1146)(64,1145)(65,1144)(66,1143)(67,1142)(68,1141)(69,1140)(70,1139)(71,1138)(72,1137)(73,1136)(74,1135)(75,1134)(76,1133)(77,1132)(78,1131)(79,1130)(80,1129)(81,1128)(82,1127)(83,1126)(84,1125)(85,1124)(86,1123)(87,1122)(88,1121)(89,1120)(90,1119)(91,1118)(92,1117)(93,1116)(94,1115)(95,1114)(96,1113)(97,1112)(98,1111)(99,1110)(100,1109)(101,1108)(102,1107)(103,1106)(104,1105)(105,1104)(106,1103)(107,1102)(108,1101)(109,1100)(110,1099)(111,1098)(112,1097)(113,1096)(114,1095)(115,1094)(116,1093)(117,1092)(118,1091)(119,1090)(120,1089)(121,1088)(122,1087)(123,1086)(124,1085)(125,1084)(126,1083)(127,1082)(128,1081)(129,1080)(130,1079)(131,1078)(132,1077)(133,1076)(134,1075)(135,1074)(136,1073)(137,1072)(138,1071)(139,1070)(140,1069)(141,1068)(142,1067)(143,1066)(144,1065)(145,1064)(146,1063)(147,1062)(148,1061)(149,1060)(150,1059)(151,1058)(152,1057)(153,1056)(154,1055)(155,1054)(156,1053)(157,1052)(158,1051)(159,1050)(160,1049)(161,1048)(162,1047)(163,1046)(164,1045)(165,1044)(166,1043)(167,1042)(168,1041)(169,1040)(170,1039)(171,1038)(172,1037)(173,1036)(174,1035)(175,1034)(176,1033)(177,1032)(178,1031)(179,1030)(180,1029)(181,1028)(182,1027)(183,1026)(184,1025)(185,1024)(186,1023)(187,1022)(188,1021)(189,1020)(190,1019)(191,1018)(192,1017)(193,1016)(194,1015)(195,1014)(196,1013)(197,1012)(198,1011)(199,1010)(200,1009)(201,1008)(202,1007)(203,1006)(204,1005)(205,1004)(206,1003)(207,1002)(208,1001)(209,1000)(210,999)(211,998)(212,997)(213,996)(214,995)(215,994)(216,993)(217,992)(218,991)(219,990)(220,989)(221,988)(222,987)(223,986)(224,985)(225,984)(226,983)(227,982)(228,981)(229,980)(230,979)(231,978)(232,977)(233,976)(234,975)(235,974)(236,973)(237,972)(238,971)(239,970)(240,969)(241,968)(242,967)(243,966)(244,965)(245,964)(246,963)(247,962)(248,961)(249,960)(250,959)(251,958)(252,957)(253,956)(254,955)(255,954)(256,953)(257,952)(258,951)(259,950)(260,949)(261,948)(262,947)(263,946)(264,945)(265,944)(266,943)(267,942)(268,941)(269,940)(270,939)(271,938)(272,937)(273,936)(274,935)(275,934)(276,933)(277,932)(278,931)(279,930)(280,929)(281,928)(282,927)(283,926)(284,925)(285,924)(286,923)(287,922)(288,921)(289,920)(290,919)(291,918)(292,917)(293,916)(294,915)(295,914)(296,913)(297,912)(298,911)(299,910)(300,909)(301,908)(302,907)(303,906)(304,905)(305,904)(306,903)(307,902)(308,901)(309,900)(310,899)(311,898)(312,897)(313,896)(314,895)(315,894)(316,893)(317,892)(318,891)(319,890)(320,889)(321,888)(322,887)(323,886)(324,885)(325,884)(326,883)(327,882)(328,881)(329,880)(330,879)(331,878)(332,877)(333,876)(334,875)(335,874)(336,873)(337,872)(338,871)(339,870)(340,869)(341,868)(342,867)(343,866)(344,865)(345,864)(346,863)(347,862)(348,861)(349,860)(350,859)(351,858)(352,857)(353,856)(354,855)(355,854)(356,853)(357,852)(358,851)(359,850)(360,849)(361,848)(362,847)(363,846)(364,845)(365,844)(366,843)(367,842)(368,841)(369,840)(370,839)(371,838)(372,837)(373,836)(374,835)(375,834)(376,833)(377,832)(378,831)(379,830)(380,829)(381,828)(382,827)(383,826)(384,825)(385,824)(386,823)(387,822)(388,821)(389,820)(390,819)(391,818)(392,817)(393,816)(394,815)(395,814)(396,813)(397,812)(398,811)(399,810)(400,809)(401,808)(402,807)(403,806)(404,805)(405,804)(406,803)(407,802)(408,801)(409,800)(410,799)(411,798)(412,797)(413,796)(414,795)(415,794)(416,793)(417,792)(418,791)(419,790)(420,789)(421,788)(422,787)(423,786)(424,785)(425,784)(426,783)(427,782)(428,781)(429,780)(430,779)(431,778)(432,777)(433,776)(434,775)(435,774)(436,773)(437,772)(438,771)(439,770)(440,769)(441,768)(442,767)(443,766)(444,765)(445,764)(446,763)(447,762)(448,761)(449,760)(450,759)(451,758)(452,757)(453,756)(454,755)(455,754)(456,753)(457,752)(458,751)(459,750)(460,749)(461,748)(462,747)(463,746)(464,745)(465,744)(466,743)(467,742)(468,741)(469,740)(470,739)(471,738)(472,737)(473,736)(474,735)(475,734)(476,733)(477,732)(478,731)(479,730)(480,729)(481,728)(482,727)(483,726)(484,725)(485,724)(486,723)(487,722)(488,721)(489,720)(490,719)(491,718)(492,717)(493,716)(494,715)(495,714)(496,713)(497,712)(498,711)(499,710)(500,709)(501,708)(502,707)(503,706)(504,705)(505,704)(506,703)(507,702)(508,701)(509,700)(510,699)(511,698)(512,697)(513,696)(514,695)(515,694)(516,693)(517,692)(518,691)(519,690)(520,689)(521,688)(522,687)(523,686)(524,685)(525,684)(526,683)(527,682)(528,681)(529,680)(530,679)(531,678)(532,677)(533,676)(534,675)(535,674)(536,673)(537,672)(538,671)(539,670)(540,669)(541,668)(542,667)(543,666)(544,665)(545,664)(546,663)(547,662)(548,661)(549,660)(550,659)(551,658)(552,657)(553,656)(554,655)(555,654)(556,653)(557,652)(558,651)(559,650)(560,649)(561,648)(562,647)(563,646)(564,645)(565,644)(566,643)(567,642)(568,641)(569,640)(570,639)(571,638)(572,637)(573,636)(574,635)(575,634)(576,633)(577,632)(578,631)(579,630)(580,629)(581,628)(582,627)(583,626)(584,625)(585,624)(586,623)(587,622)(588,621)(589,620)(590,619)(591,618)(592,617)(593,616)(594,615)(595,614)(596,613)(597,612)(598,611)(599,610)(600,609)(601,608)(602,607)(603,606)(604,605)
Conjugacy classes & character table
5968 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23860, 15);
Finite Group Databasebeta