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Dic2878 #26040255
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1447 points:
(1,2,3,4)(5,8,7,6)(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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(404,1053)(405,1052)(406,1051)(407,1050)(408,1049)(409,1048)(410,1047)(411,1046)(412,1045)(413,1044)(414,1043)(415,1042)(416,1041)(417,1040)(418,1039)(419,1038)(420,1037)(421,1036)(422,1035)(423,1034)(424,1033)(425,1032)(426,1031)(427,1030)(428,1029)(429,1028)(430,1027)(431,1026)(432,1025)(433,1024)(434,1023)(435,1022)(436,1021)(437,1020)(438,1019)(439,1018)(440,1017)(441,1016)(442,1015)(443,1014)(444,1013)(445,1012)(446,1011)(447,1010)(448,1009)(449,1008)(450,1007)(451,1006)(452,1005)(453,1004)(454,1003)(455,1002)(456,1001)(457,1000)(458,999)(459,998)(460,997)(461,996)(462,995)(463,994)(464,993)(465,992)(466,991)(467,990)(468,989)(469,988)(470,987)(471,986)(472,985)(473,984)(474,983)(475,982)(476,981)(477,980)(478,979)(479,978)(480,977)(481,976)(482,975)(483,974)(484,973)(485,972)(486,971)(487,970)(488,969)(489,968)(490,967)(491,966)(492,965)(493,964)(494,963)(495,962)(496,961)(497,960)(498,959)(499,958)(500,957)(501,956)(502,955)(503,954)(504,953)(505,952)(506,951)(507,950)(508,949)(509,948)(510,947)(511,946)(512,945)(513,944)(514,943)(515,942)(516,941)(517,940)(518,939)(519,938)(520,937)(521,936)(522,935)(523,934)(524,933)(525,932)(526,931)(527,930)(528,929)(529,928)(530,927)(531,926)(532,925)(533,924)(534,923)(535,922)(536,921)(537,920)(538,919)(539,918)(540,917)(541,916)(542,915)(543,914)(544,913)(545,912)(546,911)(547,910)(548,909)(549,908)(550,907)(551,906)(552,905)(553,904)(554,903)(555,902)(556,901)(557,900)(558,899)(559,898)(560,897)(561,896)(562,895)(563,894)(564,893)(565,892)(566,891)(567,890)(568,889)(569,888)(570,887)(571,886)(572,885)(573,884)(574,883)(575,882)(576,881)(577,880)(578,879)(579,878)(580,877)(581,876)(582,875)(583,874)(584,873)(585,872)(586,871)(587,870)(588,869)(589,868)(590,867)(591,866)(592,865)(593,864)(594,863)(595,862)(596,861)(597,860)(598,859)(599,858)(600,857)(601,856)(602,855)(603,854)(604,853)(605,852)(606,851)(607,850)(608,849)(609,848)(610,847)(611,846)(612,845)(613,844)(614,843)(615,842)(616,841)(617,840)(618,839)(619,838)(620,837)(621,836)(622,835)(623,834)(624,833)(625,832)(626,831)(627,830)(628,829)(629,828)(630,827)(631,826)(632,825)(633,824)(634,823)(635,822)(636,821)(637,820)(638,819)(639,818)(640,817)(641,816)(642,815)(643,814)(644,813)(645,812)(646,811)(647,810)(648,809)(649,808)(650,807)(651,806)(652,805)(653,804)(654,803)(655,802)(656,801)(657,800)(658,799)(659,798)(660,797)(661,796)(662,795)(663,794)(664,793)(665,792)(666,791)(667,790)(668,789)(669,788)(670,787)(671,786)(672,785)(673,784)(674,783)(675,782)(676,781)(677,780)(678,779)(679,778)(680,777)(681,776)(682,775)(683,774)(684,773)(685,772)(686,771)(687,770)(688,769)(689,768)(690,767)(691,766)(692,765)(693,764)(694,763)(695,762)(696,761)(697,760)(698,759)(699,758)(700,757)(701,756)(702,755)(703,754)(704,753)(705,752)(706,751)(707,750)(708,749)(709,748)(710,747)(711,746)(712,745)(713,744)(714,743)(715,742)(716,741)(717,740)(718,739)(719,738)(720,737)(721,736)(722,735)(723,734)(724,733)(725,732)(726,731)(727,730)(728,729)
Polycyclic presentation:
2^3,1439|a^2=c,b^2=c,b^a=bc,d^b=d^1438
Conjugacy classes & character table
2881 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11512, 11);
Finite Group Databasebeta