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Dic6185 #37613205
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1246 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);(1,3,2,4)(6,9)(7,8)(11,1246)(12,1245)(13,1244)(14,1243)(15,1242)(16,1241)(17,1240)(18,1239)(19,1238)(20,1237)(21,1236)(22,1235)(23,1234)(24,1233)(25,1232)(26,1231)(27,1230)(28,1229)(29,1228)(30,1227)(31,1226)(32,1225)(33,1224)(34,1223)(35,1222)(36,1221)(37,1220)(38,1219)(39,1218)(40,1217)(41,1216)(42,1215)(43,1214)(44,1213)(45,1212)(46,1211)(47,1210)(48,1209)(49,1208)(50,1207)(51,1206)(52,1205)(53,1204)(54,1203)(55,1202)(56,1201)(57,1200)(58,1199)(59,1198)(60,1197)(61,1196)(62,1195)(63,1194)(64,1193)(65,1192)(66,1191)(67,1190)(68,1189)(69,1188)(70,1187)(71,1186)(72,1185)(73,1184)(74,1183)(75,1182)(76,1181)(77,1180)(78,1179)(79,1178)(80,1177)(81,1176)(82,1175)(83,1174)(84,1173)(85,1172)(86,1171)(87,1170)(88,1169)(89,1168)(90,1167)(91,1166)(92,1165)(93,1164)(94,1163)(95,1162)(96,1161)(97,1160)(98,1159)(99,1158)(100,1157)(101,1156)(102,1155)(103,1154)(104,1153)(105,1152)(106,1151)(107,1150)(108,1149)(109,1148)(110,1147)(111,1146)(112,1145)(113,1144)(114,1143)(115,1142)(116,1141)(117,1140)(118,1139)(119,1138)(120,1137)(121,1136)(122,1135)(123,1134)(124,1133)(125,1132)(126,1131)(127,1130)(128,1129)(129,1128)(130,1127)(131,1126)(132,1125)(133,1124)(134,1123)(135,1122)(136,1121)(137,1120)(138,1119)(139,1118)(140,1117)(141,1116)(142,1115)(143,1114)(144,1113)(145,1112)(146,1111)(147,1110)(148,1109)(149,1108)(150,1107)(151,1106)(152,1105)(153,1104)(154,1103)(155,1102)(156,1101)(157,1100)(158,1099)(159,1098)(160,1097)(161,1096)(162,1095)(163,1094)(164,1093)(165,1092)(166,1091)(167,1090)(168,1089)(169,1088)(170,1087)(171,1086)(172,1085)(173,1084)(174,1083)(175,1082)(176,1081)(177,1080)(178,1079)(179,1078)(180,1077)(181,1076)(182,1075)(183,1074)(184,1073)(185,1072)(186,1071)(187,1070)(188,1069)(189,1068)(190,1067)(191,1066)(192,1065)(193,1064)(194,1063)(195,1062)(196,1061)(197,1060)(198,1059)(199,1058)(200,1057)(201,1056)(202,1055)(203,1054)(204,1053)(205,1052)(206,1051)(207,1050)(208,1049)(209,1048)(210,1047)(211,1046)(212,1045)(213,1044)(214,1043)(215,1042)(216,1041)(217,1040)(218,1039)(219,1038)(220,1037)(221,1036)(222,1035)(223,1034)(224,1033)(225,1032)(226,1031)(227,1030)(228,1029)(229,1028)(230,1027)(231,1026)(232,1025)(233,1024)(234,1023)(235,1022)(236,1021)(237,1020)(238,1019)(239,1018)(240,1017)(241,1016)(242,1015)(243,1014)(244,1013)(245,1012)(246,1011)(247,1010)(248,1009)(249,1008)(250,1007)(251,1006)(252,1005)(253,1004)(254,1003)(255,1002)(256,1001)(257,1000)(258,999)(259,998)(260,997)(261,996)(262,995)(263,994)(264,993)(265,992)(266,991)(267,990)(268,989)(269,988)(270,987)(271,986)(272,985)(273,984)(274,983)(275,982)(276,981)(277,980)(278,979)(279,978)(280,977)(281,976)(282,975)(283,974)(284,973)(285,972)(286,971)(287,970)(288,969)(289,968)(290,967)(291,966)(292,965)(293,964)(294,963)(295,962)(296,961)(297,960)(298,959)(299,958)(300,957)(301,956)(302,955)(303,954)(304,953)(305,952)(306,951)(307,950)(308,949)(309,948)(310,947)(311,946)(312,945)(313,944)(314,943)(315,942)(316,941)(317,940)(318,939)(319,938)(320,937)(321,936)(322,935)(323,934)(324,933)(325,932)(326,931)(327,930)(328,929)(329,928)(330,927)(331,926)(332,925)(333,924)(334,923)(335,922)(336,921)(337,920)(338,919)(339,918)(340,917)(341,916)(342,915)(343,914)(344,913)(345,912)(346,911)(347,910)(348,909)(349,908)(350,907)(351,906)(352,905)(353,904)(354,903)(355,902)(356,901)(357,900)(358,899)(359,898)(360,897)(361,896)(362,895)(363,894)(364,893)(365,892)(366,891)(367,890)(368,889)(369,888)(370,887)(371,886)(372,885)(373,884)(374,883)(375,882)(376,881)(377,880)(378,879)(379,878)(380,877)(381,876)(382,875)(383,874)(384,873)(385,872)(386,871)(387,870)(388,869)(389,868)(390,867)(391,866)(392,865)(393,864)(394,863)(395,862)(396,861)(397,860)(398,859)(399,858)(400,857)(401,856)(402,855)(403,854)(404,853)(405,852)(406,851)(407,850)(408,849)(409,848)(410,847)(411,846)(412,845)(413,844)(414,843)(415,842)(416,841)(417,840)(418,839)(419,838)(420,837)(421,836)(422,835)(423,834)(424,833)(425,832)(426,831)(427,830)(428,829)(429,828)(430,827)(431,826)(432,825)(433,824)(434,823)(435,822)(436,821)(437,820)(438,819)(439,818)(440,817)(441,816)(442,815)(443,814)(444,813)(445,812)(446,811)(447,810)(448,809)(449,808)(450,807)(451,806)(452,805)(453,804)(454,803)(455,802)(456,801)(457,800)(458,799)(459,798)(460,797)(461,796)(462,795)(463,794)(464,793)(465,792)(466,791)(467,790)(468,789)(469,788)(470,787)(471,786)(472,785)(473,784)(474,783)(475,782)(476,781)(477,780)(478,779)(479,778)(480,777)(481,776)(482,775)(483,774)(484,773)(485,772)(486,771)(487,770)(488,769)(489,768)(490,767)(491,766)(492,765)(493,764)(494,763)(495,762)(496,761)(497,760)(498,759)(499,758)(500,757)(501,756)(502,755)(503,754)(504,753)(505,752)(506,751)(507,750)(508,749)(509,748)(510,747)(511,746)(512,745)(513,744)(514,743)(515,742)(516,741)(517,740)(518,739)(519,738)(520,737)(521,736)(522,735)(523,734)(524,733)(525,732)(526,731)(527,730)(528,729)(529,728)(530,727)(531,726)(532,725)(533,724)(534,723)(535,722)(536,721)(537,720)(538,719)(539,718)(540,717)(541,716)(542,715)(543,714)(544,713)(545,712)(546,711)(547,710)(548,709)(549,708)(550,707)(551,706)(552,705)(553,704)(554,703)(555,702)(556,701)(557,700)(558,699)(559,698)(560,697)(561,696)(562,695)(563,694)(564,693)(565,692)(566,691)(567,690)(568,689)(569,688)(570,687)(571,686)(572,685)(573,684)(574,683)(575,682)(576,681)(577,680)(578,679)(579,678)(580,677)(581,676)(582,675)(583,674)(584,673)(585,672)(586,671)(587,670)(588,669)(589,668)(590,667)(591,666)(592,665)(593,664)(594,663)(595,662)(596,661)(597,660)(598,659)(599,658)(600,657)(601,656)(602,655)(603,654)(604,653)(605,652)(606,651)(607,650)(608,649)(609,648)(610,647)(611,646)(612,645)(613,644)(614,643)(615,642)(616,641)(617,640)(618,639)(619,638)(620,637)(621,636)(622,635)(623,634)(624,633)(625,632)(626,631)(627,630)(628,629)
Polycyclic presentation:
2,5,1237,2|a^2=d,b^a=b^4,c^a=c^1236
Conjugacy classes & character table
6188 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24740, 4);
Finite Group Databasebeta