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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1266 points:
(1,2)(3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266);(4,7)(5,6)(9,1266)(10,1265)(11,1264)(12,1263)(13,1262)(14,1261)(15,1260)(16,1259)(17,1258)(18,1257)(19,1256)(20,1255)(21,1254)(22,1253)(23,1252)(24,1251)(25,1250)(26,1249)(27,1248)(28,1247)(29,1246)(30,1245)(31,1244)(32,1243)(33,1242)(34,1241)(35,1240)(36,1239)(37,1238)(38,1237)(39,1236)(40,1235)(41,1234)(42,1233)(43,1232)(44,1231)(45,1230)(46,1229)(47,1228)(48,1227)(49,1226)(50,1225)(51,1224)(52,1223)(53,1222)(54,1221)(55,1220)(56,1219)(57,1218)(58,1217)(59,1216)(60,1215)(61,1214)(62,1213)(63,1212)(64,1211)(65,1210)(66,1209)(67,1208)(68,1207)(69,1206)(70,1205)(71,1204)(72,1203)(73,1202)(74,1201)(75,1200)(76,1199)(77,1198)(78,1197)(79,1196)(80,1195)(81,1194)(82,1193)(83,1192)(84,1191)(85,1190)(86,1189)(87,1188)(88,1187)(89,1186)(90,1185)(91,1184)(92,1183)(93,1182)(94,1181)(95,1180)(96,1179)(97,1178)(98,1177)(99,1176)(100,1175)(101,1174)(102,1173)(103,1172)(104,1171)(105,1170)(106,1169)(107,1168)(108,1167)(109,1166)(110,1165)(111,1164)(112,1163)(113,1162)(114,1161)(115,1160)(116,1159)(117,1158)(118,1157)(119,1156)(120,1155)(121,1154)(122,1153)(123,1152)(124,1151)(125,1150)(126,1149)(127,1148)(128,1147)(129,1146)(130,1145)(131,1144)(132,1143)(133,1142)(134,1141)(135,1140)(136,1139)(137,1138)(138,1137)(139,1136)(140,1135)(141,1134)(142,1133)(143,1132)(144,1131)(145,1130)(146,1129)(147,1128)(148,1127)(149,1126)(150,1125)(151,1124)(152,1123)(153,1122)(154,1121)(155,1120)(156,1119)(157,1118)(158,1117)(159,1116)(160,1115)(161,1114)(162,1113)(163,1112)(164,1111)(165,1110)(166,1109)(167,1108)(168,1107)(169,1106)(170,1105)(171,1104)(172,1103)(173,1102)(174,1101)(175,1100)(176,1099)(177,1098)(178,1097)(179,1096)(180,1095)(181,1094)(182,1093)(183,1092)(184,1091)(185,1090)(186,1089)(187,1088)(188,1087)(189,1086)(190,1085)(191,1084)(192,1083)(193,1082)(194,1081)(195,1080)(196,1079)(197,1078)(198,1077)(199,1076)(200,1075)(201,1074)(202,1073)(203,1072)(204,1071)(205,1070)(206,1069)(207,1068)(208,1067)(209,1066)(210,1065)(211,1064)(212,1063)(213,1062)(214,1061)(215,1060)(216,1059)(217,1058)(218,1057)(219,1056)(220,1055)(221,1054)(222,1053)(223,1052)(224,1051)(225,1050)(226,1049)(227,1048)(228,1047)(229,1046)(230,1045)(231,1044)(232,1043)(233,1042)(234,1041)(235,1040)(236,1039)(237,1038)(238,1037)(239,1036)(240,1035)(241,1034)(242,1033)(243,1032)(244,1031)(245,1030)(246,1029)(247,1028)(248,1027)(249,1026)(250,1025)(251,1024)(252,1023)(253,1022)(254,1021)(255,1020)(256,1019)(257,1018)(258,1017)(259,1016)(260,1015)(261,1014)(262,1013)(263,1012)(264,1011)(265,1010)(266,1009)(267,1008)(268,1007)(269,1006)(270,1005)(271,1004)(272,1003)(273,1002)(274,1001)(275,1000)(276,999)(277,998)(278,997)(279,996)(280,995)(281,994)(282,993)(283,992)(284,991)(285,990)(286,989)(287,988)(288,987)(289,986)(290,985)(291,984)(292,983)(293,982)(294,981)(295,980)(296,979)(297,978)(298,977)(299,976)(300,975)(301,974)(302,973)(303,972)(304,971)(305,970)(306,969)(307,968)(308,967)(309,966)(310,965)(311,964)(312,963)(313,962)(314,961)(315,960)(316,959)(317,958)(318,957)(319,956)(320,955)(321,954)(322,953)(323,952)(324,951)(325,950)(326,949)(327,948)(328,947)(329,946)(330,945)(331,944)(332,943)(333,942)(334,941)(335,940)(336,939)(337,938)(338,937)(339,936)(340,935)(341,934)(342,933)(343,932)(344,931)(345,930)(346,929)(347,928)(348,927)(349,926)(350,925)(351,924)(352,923)(353,922)(354,921)(355,920)(356,919)(357,918)(358,917)(359,916)(360,915)(361,914)(362,913)(363,912)(364,911)(365,910)(366,909)(367,908)(368,907)(369,906)(370,905)(371,904)(372,903)(373,902)(374,901)(375,900)(376,899)(377,898)(378,897)(379,896)(380,895)(381,894)(382,893)(383,892)(384,891)(385,890)(386,889)(387,888)(388,887)(389,886)(390,885)(391,884)(392,883)(393,882)(394,881)(395,880)(396,879)(397,878)(398,877)(399,876)(400,875)(401,874)(402,873)(403,872)(404,871)(405,870)(406,869)(407,868)(408,867)(409,866)(410,865)(411,864)(412,863)(413,862)(414,861)(415,860)(416,859)(417,858)(418,857)(419,856)(420,855)(421,854)(422,853)(423,852)(424,851)(425,850)(426,849)(427,848)(428,847)(429,846)(430,845)(431,844)(432,843)(433,842)(434,841)(435,840)(436,839)(437,838)(438,837)(439,836)(440,835)(441,834)(442,833)(443,832)(444,831)(445,830)(446,829)(447,828)(448,827)(449,826)(450,825)(451,824)(452,823)(453,822)(454,821)(455,820)(456,819)(457,818)(458,817)(459,816)(460,815)(461,814)(462,813)(463,812)(464,811)(465,810)(466,809)(467,808)(468,807)(469,806)(470,805)(471,804)(472,803)(473,802)(474,801)(475,800)(476,799)(477,798)(478,797)(479,796)(480,795)(481,794)(482,793)(483,792)(484,791)(485,790)(486,789)(487,788)(488,787)(489,786)(490,785)(491,784)(492,783)(493,782)(494,781)(495,780)(496,779)(497,778)(498,777)(499,776)(500,775)(501,774)(502,773)(503,772)(504,771)(505,770)(506,769)(507,768)(508,767)(509,766)(510,765)(511,764)(512,763)(513,762)(514,761)(515,760)(516,759)(517,758)(518,757)(519,756)(520,755)(521,754)(522,753)(523,752)(524,751)(525,750)(526,749)(527,748)(528,747)(529,746)(530,745)(531,744)(532,743)(533,742)(534,741)(535,740)(536,739)(537,738)(538,737)(539,736)(540,735)(541,734)(542,733)(543,732)(544,731)(545,730)(546,729)(547,728)(548,727)(549,726)(550,725)(551,724)(552,723)(553,722)(554,721)(555,720)(556,719)(557,718)(558,717)(559,716)(560,715)(561,714)(562,713)(563,712)(564,711)(565,710)(566,709)(567,708)(568,707)(569,706)(570,705)(571,704)(572,703)(573,702)(574,701)(575,700)(576,699)(577,698)(578,697)(579,696)(580,695)(581,694)(582,693)(583,692)(584,691)(585,690)(586,689)(587,688)(588,687)(589,686)(590,685)(591,684)(592,683)(593,682)(594,681)(595,680)(596,679)(597,678)(598,677)(599,676)(600,675)(601,674)(602,673)(603,672)(604,671)(605,670)(606,669)(607,668)(608,667)(609,666)(610,665)(611,664)(612,663)(613,662)(614,661)(615,660)(616,659)(617,658)(618,657)(619,656)(620,655)(621,654)(622,653)(623,652)(624,651)(625,650)(626,649)(627,648)(628,647)(629,646)(630,645)(631,644)(632,643)(633,642)(634,641)(635,640)(636,639)(637,638)
Conjugacy classes & character table
6298 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25180, 11);
Finite Group Databasebeta