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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1236 points:
(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236);(4,7)(5,6)(9,1236)(10,1235)(11,1234)(12,1233)(13,1232)(14,1231)(15,1230)(16,1229)(17,1228)(18,1227)(19,1226)(20,1225)(21,1224)(22,1223)(23,1222)(24,1221)(25,1220)(26,1219)(27,1218)(28,1217)(29,1216)(30,1215)(31,1214)(32,1213)(33,1212)(34,1211)(35,1210)(36,1209)(37,1208)(38,1207)(39,1206)(40,1205)(41,1204)(42,1203)(43,1202)(44,1201)(45,1200)(46,1199)(47,1198)(48,1197)(49,1196)(50,1195)(51,1194)(52,1193)(53,1192)(54,1191)(55,1190)(56,1189)(57,1188)(58,1187)(59,1186)(60,1185)(61,1184)(62,1183)(63,1182)(64,1181)(65,1180)(66,1179)(67,1178)(68,1177)(69,1176)(70,1175)(71,1174)(72,1173)(73,1172)(74,1171)(75,1170)(76,1169)(77,1168)(78,1167)(79,1166)(80,1165)(81,1164)(82,1163)(83,1162)(84,1161)(85,1160)(86,1159)(87,1158)(88,1157)(89,1156)(90,1155)(91,1154)(92,1153)(93,1152)(94,1151)(95,1150)(96,1149)(97,1148)(98,1147)(99,1146)(100,1145)(101,1144)(102,1143)(103,1142)(104,1141)(105,1140)(106,1139)(107,1138)(108,1137)(109,1136)(110,1135)(111,1134)(112,1133)(113,1132)(114,1131)(115,1130)(116,1129)(117,1128)(118,1127)(119,1126)(120,1125)(121,1124)(122,1123)(123,1122)(124,1121)(125,1120)(126,1119)(127,1118)(128,1117)(129,1116)(130,1115)(131,1114)(132,1113)(133,1112)(134,1111)(135,1110)(136,1109)(137,1108)(138,1107)(139,1106)(140,1105)(141,1104)(142,1103)(143,1102)(144,1101)(145,1100)(146,1099)(147,1098)(148,1097)(149,1096)(150,1095)(151,1094)(152,1093)(153,1092)(154,1091)(155,1090)(156,1089)(157,1088)(158,1087)(159,1086)(160,1085)(161,1084)(162,1083)(163,1082)(164,1081)(165,1080)(166,1079)(167,1078)(168,1077)(169,1076)(170,1075)(171,1074)(172,1073)(173,1072)(174,1071)(175,1070)(176,1069)(177,1068)(178,1067)(179,1066)(180,1065)(181,1064)(182,1063)(183,1062)(184,1061)(185,1060)(186,1059)(187,1058)(188,1057)(189,1056)(190,1055)(191,1054)(192,1053)(193,1052)(194,1051)(195,1050)(196,1049)(197,1048)(198,1047)(199,1046)(200,1045)(201,1044)(202,1043)(203,1042)(204,1041)(205,1040)(206,1039)(207,1038)(208,1037)(209,1036)(210,1035)(211,1034)(212,1033)(213,1032)(214,1031)(215,1030)(216,1029)(217,1028)(218,1027)(219,1026)(220,1025)(221,1024)(222,1023)(223,1022)(224,1021)(225,1020)(226,1019)(227,1018)(228,1017)(229,1016)(230,1015)(231,1014)(232,1013)(233,1012)(234,1011)(235,1010)(236,1009)(237,1008)(238,1007)(239,1006)(240,1005)(241,1004)(242,1003)(243,1002)(244,1001)(245,1000)(246,999)(247,998)(248,997)(249,996)(250,995)(251,994)(252,993)(253,992)(254,991)(255,990)(256,989)(257,988)(258,987)(259,986)(260,985)(261,984)(262,983)(263,982)(264,981)(265,980)(266,979)(267,978)(268,977)(269,976)(270,975)(271,974)(272,973)(273,972)(274,971)(275,970)(276,969)(277,968)(278,967)(279,966)(280,965)(281,964)(282,963)(283,962)(284,961)(285,960)(286,959)(287,958)(288,957)(289,956)(290,955)(291,954)(292,953)(293,952)(294,951)(295,950)(296,949)(297,948)(298,947)(299,946)(300,945)(301,944)(302,943)(303,942)(304,941)(305,940)(306,939)(307,938)(308,937)(309,936)(310,935)(311,934)(312,933)(313,932)(314,931)(315,930)(316,929)(317,928)(318,927)(319,926)(320,925)(321,924)(322,923)(323,922)(324,921)(325,920)(326,919)(327,918)(328,917)(329,916)(330,915)(331,914)(332,913)(333,912)(334,911)(335,910)(336,909)(337,908)(338,907)(339,906)(340,905)(341,904)(342,903)(343,902)(344,901)(345,900)(346,899)(347,898)(348,897)(349,896)(350,895)(351,894)(352,893)(353,892)(354,891)(355,890)(356,889)(357,888)(358,887)(359,886)(360,885)(361,884)(362,883)(363,882)(364,881)(365,880)(366,879)(367,878)(368,877)(369,876)(370,875)(371,874)(372,873)(373,872)(374,871)(375,870)(376,869)(377,868)(378,867)(379,866)(380,865)(381,864)(382,863)(383,862)(384,861)(385,860)(386,859)(387,858)(388,857)(389,856)(390,855)(391,854)(392,853)(393,852)(394,851)(395,850)(396,849)(397,848)(398,847)(399,846)(400,845)(401,844)(402,843)(403,842)(404,841)(405,840)(406,839)(407,838)(408,837)(409,836)(410,835)(411,834)(412,833)(413,832)(414,831)(415,830)(416,829)(417,828)(418,827)(419,826)(420,825)(421,824)(422,823)(423,822)(424,821)(425,820)(426,819)(427,818)(428,817)(429,816)(430,815)(431,814)(432,813)(433,812)(434,811)(435,810)(436,809)(437,808)(438,807)(439,806)(440,805)(441,804)(442,803)(443,802)(444,801)(445,800)(446,799)(447,798)(448,797)(449,796)(450,795)(451,794)(452,793)(453,792)(454,791)(455,790)(456,789)(457,788)(458,787)(459,786)(460,785)(461,784)(462,783)(463,782)(464,781)(465,780)(466,779)(467,778)(468,777)(469,776)(470,775)(471,774)(472,773)(473,772)(474,771)(475,770)(476,769)(477,768)(478,767)(479,766)(480,765)(481,764)(482,763)(483,762)(484,761)(485,760)(486,759)(487,758)(488,757)(489,756)(490,755)(491,754)(492,753)(493,752)(494,751)(495,750)(496,749)(497,748)(498,747)(499,746)(500,745)(501,744)(502,743)(503,742)(504,741)(505,740)(506,739)(507,738)(508,737)(509,736)(510,735)(511,734)(512,733)(513,732)(514,731)(515,730)(516,729)(517,728)(518,727)(519,726)(520,725)(521,724)(522,723)(523,722)(524,721)(525,720)(526,719)(527,718)(528,717)(529,716)(530,715)(531,714)(532,713)(533,712)(534,711)(535,710)(536,709)(537,708)(538,707)(539,706)(540,705)(541,704)(542,703)(543,702)(544,701)(545,700)(546,699)(547,698)(548,697)(549,696)(550,695)(551,694)(552,693)(553,692)(554,691)(555,690)(556,689)(557,688)(558,687)(559,686)(560,685)(561,684)(562,683)(563,682)(564,681)(565,680)(566,679)(567,678)(568,677)(569,676)(570,675)(571,674)(572,673)(573,672)(574,671)(575,670)(576,669)(577,668)(578,667)(579,666)(580,665)(581,664)(582,663)(583,662)(584,661)(585,660)(586,659)(587,658)(588,657)(589,656)(590,655)(591,654)(592,653)(593,652)(594,651)(595,650)(596,649)(597,648)(598,647)(599,646)(600,645)(601,644)(602,643)(603,642)(604,641)(605,640)(606,639)(607,638)(608,637)(609,636)(610,635)(611,634)(612,633)(613,632)(614,631)(615,630)(616,629)(617,628)(618,627)(619,626)(620,625)(621,624)(622,623)
Conjugacy classes & character table
6148 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24580, 15);
Finite Group Databasebeta