Finite Group DatabasebetaFinite Group Databasebeta| order | 33826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D16913 |
| unambiguous semidirect product | C13⋊D1301 |
| unambiguous semidirect product | C1301⋊D13 |
| Fitting, socle, derived, Hall | C13×C1301 ⋊ C2 |
| Sylow | C1301 ⋊ D13 |
| Sylow | C13 ⋊ D1301 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C1301 | C2 |
| LCS | G ▷ C13×C1301 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1314 |
| transitive degree | μt(G) = 16913 |
A minimal faithful permutation representation — 2 generators on 1314 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,1314)(16,1313)(17,1312)(18,1311)(19,1310)(20,1309)(21,1308)(22,1307)(23,1306)(24,1305)(25,1304)(26,1303)(27,1302)(28,1301)(29,1300)(30,1299)(31,1298)(32,1297)(33,1296)(34,1295)(35,1294)(36,1293)(37,1292)(38,1291)(39,1290)(40,1289)(41,1288)(42,1287)(43,1286)(44,1285)(45,1284)(46,1283)(47,1282)(48,1281)(49,1280)(50,1279)(51,1278)(52,1277)(53,1276)(54,1275)(55,1274)(56,1273)(57,1272)(58,1271)(59,1270)(60,1269)(61,1268)(62,1267)(63,1266)(64,1265)(65,1264)(66,1263)(67,1262)(68,1261)(69,1260)(70,1259)(71,1258)(72,1257)(73,1256)(74,1255)(75,1254)(76,1253)(77,1252)(78,1251)(79,1250)(80,1249)(81,1248)(82,1247)(83,1246)(84,1245)(85,1244)(86,1243)(87,1242)(88,1241)(89,1240)(90,1239)(91,1238)(92,1237)(93,1236)(94,1235)(95,1234)(96,1233)(97,1232)(98,1231)(99,1230)(100,1229)(101,1228)(102,1227)(103,1226)(104,1225)(105,1224)(106,1223)(107,1222)(108,1221)(109,1220)(110,1219)(111,1218)(112,1217)(113,1216)(114,1215)(115,1214)(116,1213)(117,1212)(118,1211)(119,1210)(120,1209)(121,1208)(122,1207)(123,1206)(124,1205)(125,1204)(126,1203)(127,1202)(128,1201)(129,1200)(130,1199)(131,1198)(132,1197)(133,1196)(134,1195)(135,1194)(136,1193)(137,1192)(138,1191)(139,1190)(140,1189)(141,1188)(142,1187)(143,1186)(144,1185)(145,1184)(146,1183)(147,1182)(148,1181)(149,1180)(150,1179)(151,1178)(152,1177)(153,1176)(154,1175)(155,1174)(156,1173)(157,1172)(158,1171)(159,1170)(160,1169)(161,1168)(162,1167)(163,1166)(164,1165)(165,1164)(166,1163)(167,1162)(168,1161)(169,1160)(170,1159)(171,1158)(172,1157)(173,1156)(174,1155)(175,1154)(176,1153)(177,1152)(178,1151)(179,1150)(180,1149)(181,1148)(182,1147)(183,1146)(184,1145)(185,1144)(186,1143)(187,1142)(188,1141)(189,1140)(190,1139)(191,1138)(192,1137)(193,1136)(194,1135)(195,1134)(196,1133)(197,1132)(198,1131)(199,1130)(200,1129)(201,1128)(202,1127)(203,1126)(204,1125)(205,1124)(206,1123)(207,1122)(208,1121)(209,1120)(210,1119)(211,1118)(212,1117)(213,1116)(214,1115)(215,1114)(216,1113)(217,1112)(218,1111)(219,1110)(220,1109)(221,1108)(222,1107)(223,1106)(224,1105)(225,1104)(226,1103)(227,1102)(228,1101)(229,1100)(230,1099)(231,1098)(232,1097)(233,1096)(234,1095)(235,1094)(236,1093)(237,1092)(238,1091)(239,1090)(240,1089)(241,1088)(242,1087)(243,1086)(244,1085)(245,1084)(246,1083)(247,1082)(248,1081)(249,1080)(250,1079)(251,1078)(252,1077)(253,1076)(254,1075)(255,1074)(256,1073)(257,1072)(258,1071)(259,1070)(260,1069)(261,1068)(262,1067)(263,1066)(264,1065)(265,1064)(266,1063)(267,1062)(268,1061)(269,1060)(270,1059)(271,1058)(272,1057)(273,1056)(274,1055)(275,1054)(276,1053)(277,1052)(278,1051)(279,1050)(280,1049)(281,1048)(282,1047)(283,1046)(284,1045)(285,1044)(286,1043)(287,1042)(288,1041)(289,1040)(290,1039)(291,1038)(292,1037)(293,1036)(294,1035)(295,1034)(296,1033)(297,1032)(298,1031)(299,1030)(300,1029)(301,1028)(302,1027)(303,1026)(304,1025)(305,1024)(306,1023)(307,1022)(308,1021)(309,1020)(310,1019)(311,1018)(312,1017)(313,1016)(314,1015)(315,1014)(316,1013)(317,1012)(318,1011)(319,1010)(320,1009)(321,1008)(322,1007)(323,1006)(324,1005)(325,1004)(326,1003)(327,1002)(328,1001)(329,1000)(330,999)(331,998)(332,997)(333,996)(334,995)(335,994)(336,993)(337,992)(338,991)(339,990)(340,989)(341,988)(342,987)(343,986)(344,985)(345,984)(346,983)(347,982)(348,981)(349,980)(350,979)(351,978)(352,977)(353,976)(354,975)(355,974)(356,973)(357,972)(358,971)(359,970)(360,969)(361,968)(362,967)(363,966)(364,965)(365,964)(366,963)(367,962)(368,961)(369,960)(370,959)(371,958)(372,957)(373,956)(374,955)(375,954)(376,953)(377,952)(378,951)(379,950)(380,949)(381,948)(382,947)(383,946)(384,945)(385,944)(386,943)(387,942)(388,941)(389,940)(390,939)(391,938)(392,937)(393,936)(394,935)(395,934)(396,933)(397,932)(398,931)(399,930)(400,929)(401,928)(402,927)(403,926)(404,925)(405,924)(406,923)(407,922)(408,921)(409,920)(410,919)(411,918)(412,917)(413,916)(414,915)(415,914)(416,913)(417,912)(418,911)(419,910)(420,909)(421,908)(422,907)(423,906)(424,905)(425,904)(426,903)(427,902)(428,901)(429,900)(430,899)(431,898)(432,897)(433,896)(434,895)(435,894)(436,893)(437,892)(438,891)(439,890)(440,889)(441,888)(442,887)(443,886)(444,885)(445,884)(446,883)(447,882)(448,881)(449,880)(450,879)(451,878)(452,877)(453,876)(454,875)(455,874)(456,873)(457,872)(458,871)(459,870)(460,869)(461,868)(462,867)(463,866)(464,865)(465,864)(466,863)(467,862)(468,861)(469,860)(470,859)(471,858)(472,857)(473,856)(474,855)(475,854)(476,853)(477,852)(478,851)(479,850)(480,849)(481,848)(482,847)(483,846)(484,845)(485,844)(486,843)(487,842)(488,841)(489,840)(490,839)(491,838)(492,837)(493,836)(494,835)(495,834)(496,833)(497,832)(498,831)(499,830)(500,829)(501,828)(502,827)(503,826)(504,825)(505,824)(506,823)(507,822)(508,821)(509,820)(510,819)(511,818)(512,817)(513,816)(514,815)(515,814)(516,813)(517,812)(518,811)(519,810)(520,809)(521,808)(522,807)(523,806)(524,805)(525,804)(526,803)(527,802)(528,801)(529,800)(530,799)(531,798)(532,797)(533,796)(534,795)(535,794)(536,793)(537,792)(538,791)(539,790)(540,789)(541,788)(542,787)(543,786)(544,785)(545,784)(546,783)(547,782)(548,781)(549,780)(550,779)(551,778)(552,777)(553,776)(554,775)(555,774)(556,773)(557,772)(558,771)(559,770)(560,769)(561,768)(562,767)(563,766)(564,765)(565,764)(566,763)(567,762)(568,761)(569,760)(570,759)(571,758)(572,757)(573,756)(574,755)(575,754)(576,753)(577,752)(578,751)(579,750)(580,749)(581,748)(582,747)(583,746)(584,745)(585,744)(586,743)(587,742)(588,741)(589,740)(590,739)(591,738)(592,737)(593,736)(594,735)(595,734)(596,733)(597,732)(598,731)(599,730)(600,729)(601,728)(602,727)(603,726)(604,725)(605,724)(606,723)(607,722)(608,721)(609,720)(610,719)(611,718)(612,717)(613,716)(614,715)(615,714)(616,713)(617,712)(618,711)(619,710)(620,709)(621,708)(622,707)(623,706)(624,705)(625,704)(626,703)(627,702)(628,701)(629,700)(630,699)(631,698)(632,697)(633,696)(634,695)(635,694)(636,693)(637,692)(638,691)(639,690)(640,689)(641,688)(642,687)(643,686)(644,685)(645,684)(646,683)(647,682)(648,681)(649,680)(650,679)(651,678)(652,677)(653,676)(654,675)(655,674)(656,673)(657,672)(658,671)(659,670)(660,669)(661,668)(662,667)(663,666)(664,665)Polycyclic presentation:
2,13,1301|b^a=b^12,c^a=c^13008458 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33826, 5);