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D5948 #26045331
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1491 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,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80,1117)(381,1116)(382,1115)(383,1114)(384,1113)(385,1112)(386,1111)(387,1110)(388,1109)(389,1108)(390,1107)(391,1106)(392,1105)(393,1104)(394,1103)(395,1102)(396,1101)(397,1100)(398,1099)(399,1098)(400,1097)(401,1096)(402,1095)(403,1094)(404,1093)(405,1092)(406,1091)(407,1090)(408,1089)(409,1088)(410,1087)(411,1086)(412,1085)(413,1084)(414,1083)(415,1082)(416,1081)(417,1080)(418,1079)(419,1078)(420,1077)(421,1076)(422,1075)(423,1074)(424,1073)(425,1072)(426,1071)(427,1070)(428,1069)(429,1068)(430,1067)(431,1066)(432,1065)(433,1064)(434,1063)(435,1062)(436,1061)(437,1060)(438,1059)(439,1058)(440,1057)(441,1056)(442,1055)(443,1054)(444,1053)(445,1052)(446,1051)(447,1050)(448,1049)(449,1048)(450,1047)(451,1046)(452,1045)(453,1044)(454,1043)(455,1042)(456,1041)(457,1040)(458,1039)(459,1038)(460,1037)(461,1036)(462,1035)(463,1034)(464,1033)(465,1032)(466,1031)(467,1030)(468,1029)(469,1028)(470,1027)(471,1026)(472,1025)(473,1024)(474,1023)(475,1022)(476,1021)(477,1020)(478,1019)(479,1018)(480,1017)(481,1016)(482,1015)(483,1014)(484,1013)(485,1012)(486,1011)(487,1010)(488,1009)(489,1008)(490,1007)(491,1006)(492,1005)(493,1004)(494,1003)(495,1002)(496,1001)(497,1000)(498,999)(499,998)(500,997)(501,996)(502,995)(503,994)(504,993)(505,992)(506,991)(507,990)(508,989)(509,988)(510,987)(511,986)(512,985)(513,984)(514,983)(515,982)(516,981)(517,980)(518,979)(519,978)(520,977)(521,976)(522,975)(523,974)(524,973)(525,972)(526,971)(527,970)(528,969)(529,968)(530,967)(531,966)(532,965)(533,964)(534,963)(535,962)(536,961)(537,960)(538,959)(539,958)(540,957)(541,956)(542,955)(543,954)(544,953)(545,952)(546,951)(547,950)(548,949)(549,948)(550,947)(551,946)(552,945)(553,944)(554,943)(555,942)(556,941)(557,940)(558,939)(559,938)(560,937)(561,936)(562,935)(563,934)(564,933)(565,932)(566,931)(567,930)(568,929)(569,928)(570,927)(571,926)(572,925)(573,924)(574,923)(575,922)(576,921)(577,920)(578,919)(579,918)(580,917)(581,916)(582,915)(583,914)(584,913)(585,912)(586,911)(587,910)(588,909)(589,908)(590,907)(591,906)(592,905)(593,904)(594,903)(595,902)(596,901)(597,900)(598,899)(599,898)(600,897)(601,896)(602,895)(603,894)(604,893)(605,892)(606,891)(607,890)(608,889)(609,888)(610,887)(611,886)(612,885)(613,884)(614,883)(615,882)(616,881)(617,880)(618,879)(619,878)(620,877)(621,876)(622,875)(623,874)(624,873)(625,872)(626,871)(627,870)(628,869)(629,868)(630,867)(631,866)(632,865)(633,864)(634,863)(635,862)(636,861)(637,860)(638,859)(639,858)(640,857)(641,856)(642,855)(643,854)(644,853)(645,852)(646,851)(647,850)(648,849)(649,848)(650,847)(651,846)(652,845)(653,844)(654,843)(655,842)(656,841)(657,840)(658,839)(659,838)(660,837)(661,836)(662,835)(663,834)(664,833)(665,832)(666,831)(667,830)(668,829)(669,828)(670,827)(671,826)(672,825)(673,824)(674,823)(675,822)(676,821)(677,820)(678,819)(679,818)(680,817)(681,816)(682,815)(683,814)(684,813)(685,812)(686,811)(687,810)(688,809)(689,808)(690,807)(691,806)(692,805)(693,804)(694,803)(695,802)(696,801)(697,800)(698,799)(699,798)(700,797)(701,796)(702,795)(703,794)(704,793)(705,792)(706,791)(707,790)(708,789)(709,788)(710,787)(711,786)(712,785)(713,784)(714,783)(715,782)(716,781)(717,780)(718,779)(719,778)(720,777)(721,776)(722,775)(723,774)(724,773)(725,772)(726,771)(727,770)(728,769)(729,768)(730,767)(731,766)(732,765)(733,764)(734,763)(735,762)(736,761)(737,760)(738,759)(739,758)(740,757)(741,756)(742,755)(743,754)(744,753)(745,752)(746,751)(747,750)(748,749)
Polycyclic presentation:
2^3,1487|b^a=bc,d^a=d^1486,d^b=d^1486
Conjugacy classes & character table
2977 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11896, 10);
Finite Group Databasebeta