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Dic7405 #44444166
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1490 points:
(1,2)(3,4)(5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,122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83,1118)(384,1117)(385,1116)(386,1115)(387,1114)(388,1113)(389,1112)(390,1111)(391,1110)(392,1109)(393,1108)(394,1107)(395,1106)(396,1105)(397,1104)(398,1103)(399,1102)(400,1101)(401,1100)(402,1099)(403,1098)(404,1097)(405,1096)(406,1095)(407,1094)(408,1093)(409,1092)(410,1091)(411,1090)(412,1089)(413,1088)(414,1087)(415,1086)(416,1085)(417,1084)(418,1083)(419,1082)(420,1081)(421,1080)(422,1079)(423,1078)(424,1077)(425,1076)(426,1075)(427,1074)(428,1073)(429,1072)(430,1071)(431,1070)(432,1069)(433,1068)(434,1067)(435,1066)(436,1065)(437,1064)(438,1063)(439,1062)(440,1061)(441,1060)(442,1059)(443,1058)(444,1057)(445,1056)(446,1055)(447,1054)(448,1053)(449,1052)(450,1051)(451,1050)(452,1049)(453,1048)(454,1047)(455,1046)(456,1045)(457,1044)(458,1043)(459,1042)(460,1041)(461,1040)(462,1039)(463,1038)(464,1037)(465,1036)(466,1035)(467,1034)(468,1033)(469,1032)(470,1031)(471,1030)(472,1029)(473,1028)(474,1027)(475,1026)(476,1025)(477,1024)(478,1023)(479,1022)(480,1021)(481,1020)(482,1019)(483,1018)(484,1017)(485,1016)(486,1015)(487,1014)(488,1013)(489,1012)(490,1011)(491,1010)(492,1009)(493,1008)(494,1007)(495,1006)(496,1005)(497,1004)(498,1003)(499,1002)(500,1001)(501,1000)(502,999)(503,998)(504,997)(505,996)(506,995)(507,994)(508,993)(509,992)(510,991)(511,990)(512,989)(513,988)(514,987)(515,986)(516,985)(517,984)(518,983)(519,982)(520,981)(521,980)(522,979)(523,978)(524,977)(525,976)(526,975)(527,974)(528,973)(529,972)(530,971)(531,970)(532,969)(533,968)(534,967)(535,966)(536,965)(537,964)(538,963)(539,962)(540,961)(541,960)(542,959)(543,958)(544,957)(545,956)(546,955)(547,954)(548,953)(549,952)(550,951)(551,950)(552,949)(553,948)(554,947)(555,946)(556,945)(557,944)(558,943)(559,942)(560,941)(561,940)(562,939)(563,938)(564,937)(565,936)(566,935)(567,934)(568,933)(569,932)(570,931)(571,930)(572,929)(573,928)(574,927)(575,926)(576,925)(577,924)(578,923)(579,922)(580,921)(581,920)(582,919)(583,918)(584,917)(585,916)(586,915)(587,914)(588,913)(589,912)(590,911)(591,910)(592,909)(593,908)(594,907)(595,906)(596,905)(597,904)(598,903)(599,902)(600,901)(601,900)(602,899)(603,898)(604,897)(605,896)(606,895)(607,894)(608,893)(609,892)(610,891)(611,890)(612,889)(613,888)(614,887)(615,886)(616,885)(617,884)(618,883)(619,882)(620,881)(621,880)(622,879)(623,878)(624,877)(625,876)(626,875)(627,874)(628,873)(629,872)(630,871)(631,870)(632,869)(633,868)(634,867)(635,866)(636,865)(637,864)(638,863)(639,862)(640,861)(641,860)(642,859)(643,858)(644,857)(645,856)(646,855)(647,854)(648,853)(649,852)(650,851)(651,850)(652,849)(653,848)(654,847)(655,846)(656,845)(657,844)(658,843)(659,842)(660,841)(661,840)(662,839)(663,838)(664,837)(665,836)(666,835)(667,834)(668,833)(669,832)(670,831)(671,830)(672,829)(673,828)(674,827)(675,826)(676,825)(677,824)(678,823)(679,822)(680,821)(681,820)(682,819)(683,818)(684,817)(685,816)(686,815)(687,814)(688,813)(689,812)(690,811)(691,810)(692,809)(693,808)(694,807)(695,806)(696,805)(697,804)(698,803)(699,802)(700,801)(701,800)(702,799)(703,798)(704,797)(705,796)(706,795)(707,794)(708,793)(709,792)(710,791)(711,790)(712,789)(713,788)(714,787)(715,786)(716,785)(717,784)(718,783)(719,782)(720,781)(721,780)(722,779)(723,778)(724,777)(725,776)(726,775)(727,774)(728,773)(729,772)(730,771)(731,770)(732,769)(733,768)(734,767)(735,766)(736,765)(737,764)(738,763)(739,762)(740,761)(741,760)(742,759)(743,758)(744,757)(745,756)(746,755)(747,754)(748,753)(749,752)(750,751)
Polycyclic presentation:
2,5,1481,2|a^2=d,b^a=b^4,c^a=c^1480
Conjugacy classes & character table
7408 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29620, 6);
Finite Group Databasebeta