← Prev (#37589606) Next (#37589608) →
Dic6145 #37589607
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1238 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);(1,3,2,4)(6,9)(7,8)(11,1238)(12,1237)(13,1236)(14,1235)(15,1234)(16,1233)(17,1232)(18,1231)(19,1230)(20,1229)(21,1228)(22,1227)(23,1226)(24,1225)(25,1224)(26,1223)(27,1222)(28,1221)(29,1220)(30,1219)(31,1218)(32,1217)(33,1216)(34,1215)(35,1214)(36,1213)(37,1212)(38,1211)(39,1210)(40,1209)(41,1208)(42,1207)(43,1206)(44,1205)(45,1204)(46,1203)(47,1202)(48,1201)(49,1200)(50,1199)(51,1198)(52,1197)(53,1196)(54,1195)(55,1194)(56,1193)(57,1192)(58,1191)(59,1190)(60,1189)(61,1188)(62,1187)(63,1186)(64,1185)(65,1184)(66,1183)(67,1182)(68,1181)(69,1180)(70,1179)(71,1178)(72,1177)(73,1176)(74,1175)(75,1174)(76,1173)(77,1172)(78,1171)(79,1170)(80,1169)(81,1168)(82,1167)(83,1166)(84,1165)(85,1164)(86,1163)(87,1162)(88,1161)(89,1160)(90,1159)(91,1158)(92,1157)(93,1156)(94,1155)(95,1154)(96,1153)(97,1152)(98,1151)(99,1150)(100,1149)(101,1148)(102,1147)(103,1146)(104,1145)(105,1144)(106,1143)(107,1142)(108,1141)(109,1140)(110,1139)(111,1138)(112,1137)(113,1136)(114,1135)(115,1134)(116,1133)(117,1132)(118,1131)(119,1130)(120,1129)(121,1128)(122,1127)(123,1126)(124,1125)(125,1124)(126,1123)(127,1122)(128,1121)(129,1120)(130,1119)(131,1118)(132,1117)(133,1116)(134,1115)(135,1114)(136,1113)(137,1112)(138,1111)(139,1110)(140,1109)(141,1108)(142,1107)(143,1106)(144,1105)(145,1104)(146,1103)(147,1102)(148,1101)(149,1100)(150,1099)(151,1098)(152,1097)(153,1096)(154,1095)(155,1094)(156,1093)(157,1092)(158,1091)(159,1090)(160,1089)(161,1088)(162,1087)(163,1086)(164,1085)(165,1084)(166,1083)(167,1082)(168,1081)(169,1080)(170,1079)(171,1078)(172,1077)(173,1076)(174,1075)(175,1074)(176,1073)(177,1072)(178,1071)(179,1070)(180,1069)(181,1068)(182,1067)(183,1066)(184,1065)(185,1064)(186,1063)(187,1062)(188,1061)(189,1060)(190,1059)(191,1058)(192,1057)(193,1056)(194,1055)(195,1054)(196,1053)(197,1052)(198,1051)(199,1050)(200,1049)(201,1048)(202,1047)(203,1046)(204,1045)(205,1044)(206,1043)(207,1042)(208,1041)(209,1040)(210,1039)(211,1038)(212,1037)(213,1036)(214,1035)(215,1034)(216,1033)(217,1032)(218,1031)(219,1030)(220,1029)(221,1028)(222,1027)(223,1026)(224,1025)(225,1024)(226,1023)(227,1022)(228,1021)(229,1020)(230,1019)(231,1018)(232,1017)(233,1016)(234,1015)(235,1014)(236,1013)(237,1012)(238,1011)(239,1010)(240,1009)(241,1008)(242,1007)(243,1006)(244,1005)(245,1004)(246,1003)(247,1002)(248,1001)(249,1000)(250,999)(251,998)(252,997)(253,996)(254,995)(255,994)(256,993)(257,992)(258,991)(259,990)(260,989)(261,988)(262,987)(263,986)(264,985)(265,984)(266,983)(267,982)(268,981)(269,980)(270,979)(271,978)(272,977)(273,976)(274,975)(275,974)(276,973)(277,972)(278,971)(279,970)(280,969)(281,968)(282,967)(283,966)(284,965)(285,964)(286,963)(287,962)(288,961)(289,960)(290,959)(291,958)(292,957)(293,956)(294,955)(295,954)(296,953)(297,952)(298,951)(299,950)(300,949)(301,948)(302,947)(303,946)(304,945)(305,944)(306,943)(307,942)(308,941)(309,940)(310,939)(311,938)(312,937)(313,936)(314,935)(315,934)(316,933)(317,932)(318,931)(319,930)(320,929)(321,928)(322,927)(323,926)(324,925)(325,924)(326,923)(327,922)(328,921)(329,920)(330,919)(331,918)(332,917)(333,916)(334,915)(335,914)(336,913)(337,912)(338,911)(339,910)(340,909)(341,908)(342,907)(343,906)(344,905)(345,904)(346,903)(347,902)(348,901)(349,900)(350,899)(351,898)(352,897)(353,896)(354,895)(355,894)(356,893)(357,892)(358,891)(359,890)(360,889)(361,888)(362,887)(363,886)(364,885)(365,884)(366,883)(367,882)(368,881)(369,880)(370,879)(371,878)(372,877)(373,876)(374,875)(375,874)(376,873)(377,872)(378,871)(379,870)(380,869)(381,868)(382,867)(383,866)(384,865)(385,864)(386,863)(387,862)(388,861)(389,860)(390,859)(391,858)(392,857)(393,856)(394,855)(395,854)(396,853)(397,852)(398,851)(399,850)(400,849)(401,848)(402,847)(403,846)(404,845)(405,844)(406,843)(407,842)(408,841)(409,840)(410,839)(411,838)(412,837)(413,836)(414,835)(415,834)(416,833)(417,832)(418,831)(419,830)(420,829)(421,828)(422,827)(423,826)(424,825)(425,824)(426,823)(427,822)(428,821)(429,820)(430,819)(431,818)(432,817)(433,816)(434,815)(435,814)(436,813)(437,812)(438,811)(439,810)(440,809)(441,808)(442,807)(443,806)(444,805)(445,804)(446,803)(447,802)(448,801)(449,800)(450,799)(451,798)(452,797)(453,796)(454,795)(455,794)(456,793)(457,792)(458,791)(459,790)(460,789)(461,788)(462,787)(463,786)(464,785)(465,784)(466,783)(467,782)(468,781)(469,780)(470,779)(471,778)(472,777)(473,776)(474,775)(475,774)(476,773)(477,772)(478,771)(479,770)(480,769)(481,768)(482,767)(483,766)(484,765)(485,764)(486,763)(487,762)(488,761)(489,760)(490,759)(491,758)(492,757)(493,756)(494,755)(495,754)(496,753)(497,752)(498,751)(499,750)(500,749)(501,748)(502,747)(503,746)(504,745)(505,744)(506,743)(507,742)(508,741)(509,740)(510,739)(511,738)(512,737)(513,736)(514,735)(515,734)(516,733)(517,732)(518,731)(519,730)(520,729)(521,728)(522,727)(523,726)(524,725)(525,724)(526,723)(527,722)(528,721)(529,720)(530,719)(531,718)(532,717)(533,716)(534,715)(535,714)(536,713)(537,712)(538,711)(539,710)(540,709)(541,708)(542,707)(543,706)(544,705)(545,704)(546,703)(547,702)(548,701)(549,700)(550,699)(551,698)(552,697)(553,696)(554,695)(555,694)(556,693)(557,692)(558,691)(559,690)(560,689)(561,688)(562,687)(563,686)(564,685)(565,684)(566,683)(567,682)(568,681)(569,680)(570,679)(571,678)(572,677)(573,676)(574,675)(575,674)(576,673)(577,672)(578,671)(579,670)(580,669)(581,668)(582,667)(583,666)(584,665)(585,664)(586,663)(587,662)(588,661)(589,660)(590,659)(591,658)(592,657)(593,656)(594,655)(595,654)(596,653)(597,652)(598,651)(599,650)(600,649)(601,648)(602,647)(603,646)(604,645)(605,644)(606,643)(607,642)(608,641)(609,640)(610,639)(611,638)(612,637)(613,636)(614,635)(615,634)(616,633)(617,632)(618,631)(619,630)(620,629)(621,628)(622,627)(623,626)(624,625)
Polycyclic presentation:
2,5,1229,2|a^2=d,b^a=b^4,c^a=c^1228
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, 4);
Finite Group Databasebeta