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D8743 #31775748
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1256 points:
(1,2,3,4,5,6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256);(2,7)(3,6)(4,5)(9,1256)(10,1255)(11,1254)(12,1253)(13,1252)(14,1251)(15,1250)(16,1249)(17,1248)(18,1247)(19,1246)(20,1245)(21,1244)(22,1243)(23,1242)(24,1241)(25,1240)(26,1239)(27,1238)(28,1237)(29,1236)(30,1235)(31,1234)(32,1233)(33,1232)(34,1231)(35,1230)(36,1229)(37,1228)(38,1227)(39,1226)(40,1225)(41,1224)(42,1223)(43,1222)(44,1221)(45,1220)(46,1219)(47,1218)(48,1217)(49,1216)(50,1215)(51,1214)(52,1213)(53,1212)(54,1211)(55,1210)(56,1209)(57,1208)(58,1207)(59,1206)(60,1205)(61,1204)(62,1203)(63,1202)(64,1201)(65,1200)(66,1199)(67,1198)(68,1197)(69,1196)(70,1195)(71,1194)(72,1193)(73,1192)(74,1191)(75,1190)(76,1189)(77,1188)(78,1187)(79,1186)(80,1185)(81,1184)(82,1183)(83,1182)(84,1181)(85,1180)(86,1179)(87,1178)(88,1177)(89,1176)(90,1175)(91,1174)(92,1173)(93,1172)(94,1171)(95,1170)(96,1169)(97,1168)(98,1167)(99,1166)(100,1165)(101,1164)(102,1163)(103,1162)(104,1161)(105,1160)(106,1159)(107,1158)(108,1157)(109,1156)(110,1155)(111,1154)(112,1153)(113,1152)(114,1151)(115,1150)(116,1149)(117,1148)(118,1147)(119,1146)(120,1145)(121,1144)(122,1143)(123,1142)(124,1141)(125,1140)(126,1139)(127,1138)(128,1137)(129,1136)(130,1135)(131,1134)(132,1133)(133,1132)(134,1131)(135,1130)(136,1129)(137,1128)(138,1127)(139,1126)(140,1125)(141,1124)(142,1123)(143,1122)(144,1121)(145,1120)(146,1119)(147,1118)(148,1117)(149,1116)(150,1115)(151,1114)(152,1113)(153,1112)(154,1111)(155,1110)(156,1109)(157,1108)(158,1107)(159,1106)(160,1105)(161,1104)(162,1103)(163,1102)(164,1101)(165,1100)(166,1099)(167,1098)(168,1097)(169,1096)(170,1095)(171,1094)(172,1093)(173,1092)(174,1091)(175,1090)(176,1089)(177,1088)(178,1087)(179,1086)(180,1085)(181,1084)(182,1083)(183,1082)(184,1081)(185,1080)(186,1079)(187,1078)(188,1077)(189,1076)(190,1075)(191,1074)(192,1073)(193,1072)(194,1071)(195,1070)(196,1069)(197,1068)(198,1067)(199,1066)(200,1065)(201,1064)(202,1063)(203,1062)(204,1061)(205,1060)(206,1059)(207,1058)(208,1057)(209,1056)(210,1055)(211,1054)(212,1053)(213,1052)(214,1051)(215,1050)(216,1049)(217,1048)(218,1047)(219,1046)(220,1045)(221,1044)(222,1043)(223,1042)(224,1041)(225,1040)(226,1039)(227,1038)(228,1037)(229,1036)(230,1035)(231,1034)(232,1033)(233,1032)(234,1031)(235,1030)(236,1029)(237,1028)(238,1027)(239,1026)(240,1025)(241,1024)(242,1023)(243,1022)(244,1021)(245,1020)(246,1019)(247,1018)(248,1017)(249,1016)(250,1015)(251,1014)(252,1013)(253,1012)(254,1011)(255,1010)(256,1009)(257,1008)(258,1007)(259,1006)(260,1005)(261,1004)(262,1003)(263,1002)(264,1001)(265,1000)(266,999)(267,998)(268,997)(269,996)(270,995)(271,994)(272,993)(273,992)(274,991)(275,990)(276,989)(277,988)(278,987)(279,986)(280,985)(281,984)(282,983)(283,982)(284,981)(285,980)(286,979)(287,978)(288,977)(289,976)(290,975)(291,974)(292,973)(293,972)(294,971)(295,970)(296,969)(297,968)(298,967)(299,966)(300,965)(301,964)(302,963)(303,962)(304,961)(305,960)(306,959)(307,958)(308,957)(309,956)(310,955)(311,954)(312,953)(313,952)(314,951)(315,950)(316,949)(317,948)(318,947)(319,946)(320,945)(321,944)(322,943)(323,942)(324,941)(325,940)(326,939)(327,938)(328,937)(329,936)(330,935)(331,934)(332,933)(333,932)(334,931)(335,930)(336,929)(337,928)(338,927)(339,926)(340,925)(341,924)(342,923)(343,922)(344,921)(345,920)(346,919)(347,918)(348,917)(349,916)(350,915)(351,914)(352,913)(353,912)(354,911)(355,910)(356,909)(357,908)(358,907)(359,906)(360,905)(361,904)(362,903)(363,902)(364,901)(365,900)(366,899)(367,898)(368,897)(369,896)(370,895)(371,894)(372,893)(373,892)(374,891)(375,890)(376,889)(377,888)(378,887)(379,886)(380,885)(381,884)(382,883)(383,882)(384,881)(385,880)(386,879)(387,878)(388,877)(389,876)(390,875)(391,874)(392,873)(393,872)(394,871)(395,870)(396,869)(397,868)(398,867)(399,866)(400,865)(401,864)(402,863)(403,862)(404,861)(405,860)(406,859)(407,858)(408,857)(409,856)(410,855)(411,854)(412,853)(413,852)(414,851)(415,850)(416,849)(417,848)(418,847)(419,846)(420,845)(421,844)(422,843)(423,842)(424,841)(425,840)(426,839)(427,838)(428,837)(429,836)(430,835)(431,834)(432,833)(433,832)(434,831)(435,830)(436,829)(437,828)(438,827)(439,826)(440,825)(441,824)(442,823)(443,822)(444,821)(445,820)(446,819)(447,818)(448,817)(449,816)(450,815)(451,814)(452,813)(453,812)(454,811)(455,810)(456,809)(457,808)(458,807)(459,806)(460,805)(461,804)(462,803)(463,802)(464,801)(465,800)(466,799)(467,798)(468,797)(469,796)(470,795)(471,794)(472,793)(473,792)(474,791)(475,790)(476,789)(477,788)(478,787)(479,786)(480,785)(481,784)(482,783)(483,782)(484,781)(485,780)(486,779)(487,778)(488,777)(489,776)(490,775)(491,774)(492,773)(493,772)(494,771)(495,770)(496,769)(497,768)(498,767)(499,766)(500,765)(501,764)(502,763)(503,762)(504,761)(505,760)(506,759)(507,758)(508,757)(509,756)(510,755)(511,754)(512,753)(513,752)(514,751)(515,750)(516,749)(517,748)(518,747)(519,746)(520,745)(521,744)(522,743)(523,742)(524,741)(525,740)(526,739)(527,738)(528,737)(529,736)(530,735)(531,734)(532,733)(533,732)(534,731)(535,730)(536,729)(537,728)(538,727)(539,726)(540,725)(541,724)(542,723)(543,722)(544,721)(545,720)(546,719)(547,718)(548,717)(549,716)(550,715)(551,714)(552,713)(553,712)(554,711)(555,710)(556,709)(557,708)(558,707)(559,706)(560,705)(561,704)(562,703)(563,702)(564,701)(565,700)(566,699)(567,698)(568,697)(569,696)(570,695)(571,694)(572,693)(573,692)(574,691)(575,690)(576,689)(577,688)(578,687)(579,686)(580,685)(581,684)(582,683)(583,682)(584,681)(585,680)(586,679)(587,678)(588,677)(589,676)(590,675)(591,674)(592,673)(593,672)(594,671)(595,670)(596,669)(597,668)(598,667)(599,666)(600,665)(601,664)(602,663)(603,662)(604,661)(605,660)(606,659)(607,658)(608,657)(609,656)(610,655)(611,654)(612,653)(613,652)(614,651)(615,650)(616,649)(617,648)(618,647)(619,646)(620,645)(621,644)(622,643)(623,642)(624,641)(625,640)(626,639)(627,638)(628,637)(629,636)(630,635)(631,634)(632,633)
Polycyclic presentation:
2,7,1249|b^a=b^6,c^a=c^1248
Conjugacy classes & character table
4373 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17486, 3);
Finite Group Databasebeta