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Dic4317 #31772154
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1446 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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(404,1051)(405,1050)(406,1049)(407,1048)(408,1047)(409,1046)(410,1045)(411,1044)(412,1043)(413,1042)(414,1041)(415,1040)(416,1039)(417,1038)(418,1037)(419,1036)(420,1035)(421,1034)(422,1033)(423,1032)(424,1031)(425,1030)(426,1029)(427,1028)(428,1027)(429,1026)(430,1025)(431,1024)(432,1023)(433,1022)(434,1021)(435,1020)(436,1019)(437,1018)(438,1017)(439,1016)(440,1015)(441,1014)(442,1013)(443,1012)(444,1011)(445,1010)(446,1009)(447,1008)(448,1007)(449,1006)(450,1005)(451,1004)(452,1003)(453,1002)(454,1001)(455,1000)(456,999)(457,998)(458,997)(459,996)(460,995)(461,994)(462,993)(463,992)(464,991)(465,990)(466,989)(467,988)(468,987)(469,986)(470,985)(471,984)(472,983)(473,982)(474,981)(475,980)(476,979)(477,978)(478,977)(479,976)(480,975)(481,974)(482,973)(483,972)(484,971)(485,970)(486,969)(487,968)(488,967)(489,966)(490,965)(491,964)(492,963)(493,962)(494,961)(495,960)(496,959)(497,958)(498,957)(499,956)(500,955)(501,954)(502,953)(503,952)(504,951)(505,950)(506,949)(507,948)(508,947)(509,946)(510,945)(511,944)(512,943)(513,942)(514,941)(515,940)(516,939)(517,938)(518,937)(519,936)(520,935)(521,934)(522,933)(523,932)(524,931)(525,930)(526,929)(527,928)(528,927)(529,926)(530,925)(531,924)(532,923)(533,922)(534,921)(535,920)(536,919)(537,918)(538,917)(539,916)(540,915)(541,914)(542,913)(543,912)(544,911)(545,910)(546,909)(547,908)(548,907)(549,906)(550,905)(551,904)(552,903)(553,902)(554,901)(555,900)(556,899)(557,898)(558,897)(559,896)(560,895)(561,894)(562,893)(563,892)(564,891)(565,890)(566,889)(567,888)(568,887)(569,886)(570,885)(571,884)(572,883)(573,882)(574,881)(575,880)(576,879)(577,878)(578,877)(579,876)(580,875)(581,874)(582,873)(583,872)(584,871)(585,870)(586,869)(587,868)(588,867)(589,866)(590,865)(591,864)(592,863)(593,862)(594,861)(595,860)(596,859)(597,858)(598,857)(599,856)(600,855)(601,854)(602,853)(603,852)(604,851)(605,850)(606,849)(607,848)(608,847)(609,846)(610,845)(611,844)(612,843)(613,842)(614,841)(615,840)(616,839)(617,838)(618,837)(619,836)(620,835)(621,834)(622,833)(623,832)(624,831)(625,830)(626,829)(627,828)(628,827)(629,826)(630,825)(631,824)(632,823)(633,822)(634,821)(635,820)(636,819)(637,818)(638,817)(639,816)(640,815)(641,814)(642,813)(643,812)(644,811)(645,810)(646,809)(647,808)(648,807)(649,806)(650,805)(651,804)(652,803)(653,802)(654,801)(655,800)(656,799)(657,798)(658,797)(659,796)(660,795)(661,794)(662,793)(663,792)(664,791)(665,790)(666,789)(667,788)(668,787)(669,786)(670,785)(671,784)(672,783)(673,782)(674,781)(675,780)(676,779)(677,778)(678,777)(679,776)(680,775)(681,774)(682,773)(683,772)(684,771)(685,770)(686,769)(687,768)(688,767)(689,766)(690,765)(691,764)(692,763)(693,762)(694,761)(695,760)(696,759)(697,758)(698,757)(699,756)(700,755)(701,754)(702,753)(703,752)(704,751)(705,750)(706,749)(707,748)(708,747)(709,746)(710,745)(711,744)(712,743)(713,742)(714,741)(715,740)(716,739)(717,738)(718,737)(719,736)(720,735)(721,734)(722,733)(723,732)(724,731)(725,730)(726,729)(727,728)
Polycyclic presentation:
2,3,1439,2|a^2=d,b^a=b^2,c^a=c^1438
Conjugacy classes & character table
4320 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17268, 4);
Finite Group Databasebeta