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D15769 #44538681
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 1226 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,1226)(16,1225)(17,1224)(18,1223)(19,1222)(20,1221)(21,1220)(22,1219)(23,1218)(24,1217)(25,1216)(26,1215)(27,1214)(28,1213)(29,1212)(30,1211)(31,1210)(32,1209)(33,1208)(34,1207)(35,1206)(36,1205)(37,1204)(38,1203)(39,1202)(40,1201)(41,1200)(42,1199)(43,1198)(44,1197)(45,1196)(46,1195)(47,1194)(48,1193)(49,1192)(50,1191)(51,1190)(52,1189)(53,1188)(54,1187)(55,1186)(56,1185)(57,1184)(58,1183)(59,1182)(60,1181)(61,1180)(62,1179)(63,1178)(64,1177)(65,1176)(66,1175)(67,1174)(68,1173)(69,1172)(70,1171)(71,1170)(72,1169)(73,1168)(74,1167)(75,1166)(76,1165)(77,1164)(78,1163)(79,1162)(80,1161)(81,1160)(82,1159)(83,1158)(84,1157)(85,1156)(86,1155)(87,1154)(88,1153)(89,1152)(90,1151)(91,1150)(92,1149)(93,1148)(94,1147)(95,1146)(96,1145)(97,1144)(98,1143)(99,1142)(100,1141)(101,1140)(102,1139)(103,1138)(104,1137)(105,1136)(106,1135)(107,1134)(108,1133)(109,1132)(110,1131)(111,1130)(112,1129)(113,1128)(114,1127)(115,1126)(116,1125)(117,1124)(118,1123)(119,1122)(120,1121)(121,1120)(122,1119)(123,1118)(124,1117)(125,1116)(126,1115)(127,1114)(128,1113)(129,1112)(130,1111)(131,1110)(132,1109)(133,1108)(134,1107)(135,1106)(136,1105)(137,1104)(138,1103)(139,1102)(140,1101)(141,1100)(142,1099)(143,1098)(144,1097)(145,1096)(146,1095)(147,1094)(148,1093)(149,1092)(150,1091)(151,1090)(152,1089)(153,1088)(154,1087)(155,1086)(156,1085)(157,1084)(158,1083)(159,1082)(160,1081)(161,1080)(162,1079)(163,1078)(164,1077)(165,1076)(166,1075)(167,1074)(168,1073)(169,1072)(170,1071)(171,1070)(172,1069)(173,1068)(174,1067)(175,1066)(176,1065)(177,1064)(178,1063)(179,1062)(180,1061)(181,1060)(182,1059)(183,1058)(184,1057)(185,1056)(186,1055)(187,1054)(188,1053)(189,1052)(190,1051)(191,1050)(192,1049)(193,1048)(194,1047)(195,1046)(196,1045)(197,1044)(198,1043)(199,1042)(200,1041)(201,1040)(202,1039)(203,1038)(204,1037)(205,1036)(206,1035)(207,1034)(208,1033)(209,1032)(210,1031)(211,1030)(212,1029)(213,1028)(214,1027)(215,1026)(216,1025)(217,1024)(218,1023)(219,1022)(220,1021)(221,1020)(222,1019)(223,1018)(224,1017)(225,1016)(226,1015)(227,1014)(228,1013)(229,1012)(230,1011)(231,1010)(232,1009)(233,1008)(234,1007)(235,1006)(236,1005)(237,1004)(238,1003)(239,1002)(240,1001)(241,1000)(242,999)(243,998)(244,997)(245,996)(246,995)(247,994)(248,993)(249,992)(250,991)(251,990)(252,989)(253,988)(254,987)(255,986)(256,985)(257,984)(258,983)(259,982)(260,981)(261,980)(262,979)(263,978)(264,977)(265,976)(266,975)(267,974)(268,973)(269,972)(270,971)(271,970)(272,969)(273,968)(274,967)(275,966)(276,965)(277,964)(278,963)(279,962)(280,961)(281,960)(282,959)(283,958)(284,957)(285,956)(286,955)(287,954)(288,953)(289,952)(290,951)(291,950)(292,949)(293,948)(294,947)(295,946)(296,945)(297,944)(298,943)(299,942)(300,941)(301,940)(302,939)(303,938)(304,937)(305,936)(306,935)(307,934)(308,933)(309,932)(310,931)(311,930)(312,929)(313,928)(314,927)(315,926)(316,925)(317,924)(318,923)(319,922)(320,921)(321,920)(322,919)(323,918)(324,917)(325,916)(326,915)(327,914)(328,913)(329,912)(330,911)(331,910)(332,909)(333,908)(334,907)(335,906)(336,905)(337,904)(338,903)(339,902)(340,901)(341,900)(342,899)(343,898)(344,897)(345,896)(346,895)(347,894)(348,893)(349,892)(350,891)(351,890)(352,889)(353,888)(354,887)(355,886)(356,885)(357,884)(358,883)(359,882)(360,881)(361,880)(362,879)(363,878)(364,877)(365,876)(366,875)(367,874)(368,873)(369,872)(370,871)(371,870)(372,869)(373,868)(374,867)(375,866)(376,865)(377,864)(378,863)(379,862)(380,861)(381,860)(382,859)(383,858)(384,857)(385,856)(386,855)(387,854)(388,853)(389,852)(390,851)(391,850)(392,849)(393,848)(394,847)(395,846)(396,845)(397,844)(398,843)(399,842)(400,841)(401,840)(402,839)(403,838)(404,837)(405,836)(406,835)(407,834)(408,833)(409,832)(410,831)(411,830)(412,829)(413,828)(414,827)(415,826)(416,825)(417,824)(418,823)(419,822)(420,821)(421,820)(422,819)(423,818)(424,817)(425,816)(426,815)(427,814)(428,813)(429,812)(430,811)(431,810)(432,809)(433,808)(434,807)(435,806)(436,805)(437,804)(438,803)(439,802)(440,801)(441,800)(442,799)(443,798)(444,797)(445,796)(446,795)(447,794)(448,793)(449,792)(450,791)(451,790)(452,789)(453,788)(454,787)(455,786)(456,785)(457,784)(458,783)(459,782)(460,781)(461,780)(462,779)(463,778)(464,777)(465,776)(466,775)(467,774)(468,773)(469,772)(470,771)(471,770)(472,769)(473,768)(474,767)(475,766)(476,765)(477,764)(478,763)(479,762)(480,761)(481,760)(482,759)(483,758)(484,757)(485,756)(486,755)(487,754)(488,753)(489,752)(490,751)(491,750)(492,749)(493,748)(494,747)(495,746)(496,745)(497,744)(498,743)(499,742)(500,741)(501,740)(502,739)(503,738)(504,737)(505,736)(506,735)(507,734)(508,733)(509,732)(510,731)(511,730)(512,729)(513,728)(514,727)(515,726)(516,725)(517,724)(518,723)(519,722)(520,721)(521,720)(522,719)(523,718)(524,717)(525,716)(526,715)(527,714)(528,713)(529,712)(530,711)(531,710)(532,709)(533,708)(534,707)(535,706)(536,705)(537,704)(538,703)(539,702)(540,701)(541,700)(542,699)(543,698)(544,697)(545,696)(546,695)(547,694)(548,693)(549,692)(550,691)(551,690)(552,689)(553,688)(554,687)(555,686)(556,685)(557,684)(558,683)(559,682)(560,681)(561,680)(562,679)(563,678)(564,677)(565,676)(566,675)(567,674)(568,673)(569,672)(570,671)(571,670)(572,669)(573,668)(574,667)(575,666)(576,665)(577,664)(578,663)(579,662)(580,661)(581,660)(582,659)(583,658)(584,657)(585,656)(586,655)(587,654)(588,653)(589,652)(590,651)(591,650)(592,649)(593,648)(594,647)(595,646)(596,645)(597,644)(598,643)(599,642)(600,641)(601,640)(602,639)(603,638)(604,637)(605,636)(606,635)(607,634)(608,633)(609,632)(610,631)(611,630)(612,629)(613,628)(614,627)(615,626)(616,625)(617,624)(618,623)(619,622)(620,621)
Polycyclic presentation:
2,13,1213|b^a=b^12,c^a=c^1212
Conjugacy classes & character table
7886 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31538, 3);
Finite Group Databasebeta