Finite Group DatabasebetaFinite Group Databasebeta| order | 23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D11943 |
| unambiguous semidirect product | C9⋊D1327 |
| unambiguous semidirect product | C1327⋊D9 |
| Fitting, derived, Hall | C9×C1327 ⋊ C2 |
| Sylow | C1327 ⋊ D9 |
| Sylow | C9 ⋊ D1327 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C1327 | C2 |
| Frattini | C3 | D3981 |
| socle | C3×C1327 | D3 |
| LCS | G ▷ C9×C1327 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1336 |
| transitive degree | μt(G) = 11943 |
A minimal faithful permutation representation — 2 generators on 1336 points:
(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1222,1223,1224,1225,1226,1227,1228,1229,1230,1231,1232,1233,1234,1235,1236,1237,1238,1239,1240,1241,1242,1243,1244,1245,1246,1247,1248,1249,1250,1251,1252,1253,1254,1255,1256,1257,1258,1259,1260,1261,1262,1263,1264,1265,1266,1267,1268,1269,1270,1271,1272,1273,1274,1275,1276,1277,1278,1279,1280,1281,1282,1283,1284,1285,1286,1287,1288,1289,1290,1291,1292,1293,1294,1295,1296,1297,1298,1299,1300,1301,1302,1303,1304,1305,1306,1307,1308,1309,1310,1311,1312,1313,1314,1315,1316,1317,1318,1319,1320,1321,1322,1323,1324,1325,1326,1327,1328,1329,1330,1331,1332,1333,1334,1335,1336);(2,9)(3,8)(4,7)(5,6)(11,1336)(12,1335)(13,1334)(14,1333)(15,1332)(16,1331)(17,1330)(18,1329)(19,1328)(20,1327)(21,1326)(22,1325)(23,1324)(24,1323)(25,1322)(26,1321)(27,1320)(28,1319)(29,1318)(30,1317)(31,1316)(32,1315)(33,1314)(34,1313)(35,1312)(36,1311)(37,1310)(38,1309)(39,1308)(40,1307)(41,1306)(42,1305)(43,1304)(44,1303)(45,1302)(46,1301)(47,1300)(48,1299)(49,1298)(50,1297)(51,1296)(52,1295)(53,1294)(54,1293)(55,1292)(56,1291)(57,1290)(58,1289)(59,1288)(60,1287)(61,1286)(62,1285)(63,1284)(64,1283)(65,1282)(66,1281)(67,1280)(68,1279)(69,1278)(70,1277)(71,1276)(72,1275)(73,1274)(74,1273)(75,1272)(76,1271)(77,1270)(78,1269)(79,1268)(80,1267)(81,1266)(82,1265)(83,1264)(84,1263)(85,1262)(86,1261)(87,1260)(88,1259)(89,1258)(90,1257)(91,1256)(92,1255)(93,1254)(94,1253)(95,1252)(96,1251)(97,1250)(98,1249)(99,1248)(100,1247)(101,1246)(102,1245)(103,1244)(104,1243)(105,1242)(106,1241)(107,1240)(108,1239)(109,1238)(110,1237)(111,1236)(112,1235)(113,1234)(114,1233)(115,1232)(116,1231)(117,1230)(118,1229)(119,1228)(120,1227)(121,1226)(122,1225)(123,1224)(124,1223)(125,1222)(126,1221)(127,1220)(128,1219)(129,1218)(130,1217)(131,1216)(132,1215)(133,1214)(134,1213)(135,1212)(136,1211)(137,1210)(138,1209)(139,1208)(140,1207)(141,1206)(142,1205)(143,1204)(144,1203)(145,1202)(146,1201)(147,1200)(148,1199)(149,1198)(150,1197)(151,1196)(152,1195)(153,1194)(154,1193)(155,1192)(156,1191)(157,1190)(158,1189)(159,1188)(160,1187)(161,1186)(162,1185)(163,1184)(164,1183)(165,1182)(166,1181)(167,1180)(168,1179)(169,1178)(170,1177)(171,1176)(172,1175)(173,1174)(174,1173)(175,1172)(176,1171)(177,1170)(178,1169)(179,1168)(180,1167)(181,1166)(182,1165)(183,1164)(184,1163)(185,1162)(186,1161)(187,1160)(188,1159)(189,1158)(190,1157)(191,1156)(192,1155)(193,1154)(194,1153)(195,1152)(196,1151)(197,1150)(198,1149)(199,1148)(200,1147)(201,1146)(202,1145)(203,1144)(204,1143)(205,1142)(206,1141)(207,1140)(208,1139)(209,1138)(210,1137)(211,1136)(212,1135)(213,1134)(214,1133)(215,1132)(216,1131)(217,1130)(218,1129)(219,1128)(220,1127)(221,1126)(222,1125)(223,1124)(224,1123)(225,1122)(226,1121)(227,1120)(228,1119)(229,1118)(230,1117)(231,1116)(232,1115)(233,1114)(234,1113)(235,1112)(236,1111)(237,1110)(238,1109)(239,1108)(240,1107)(241,1106)(242,1105)(243,1104)(244,1103)(245,1102)(246,1101)(247,1100)(248,1099)(249,1098)(250,1097)(251,1096)(252,1095)(253,1094)(254,1093)(255,1092)(256,1091)(257,1090)(258,1089)(259,1088)(260,1087)(261,1086)(262,1085)(263,1084)(264,1083)(265,1082)(266,1081)(267,1080)(268,1079)(269,1078)(270,1077)(271,1076)(272,1075)(273,1074)(274,1073)(275,1072)(276,1071)(277,1070)(278,1069)(279,1068)(280,1067)(281,1066)(282,1065)(283,1064)(284,1063)(285,1062)(286,1061)(287,1060)(288,1059)(289,1058)(290,1057)(291,1056)(292,1055)(293,1054)(294,1053)(295,1052)(296,1051)(297,1050)(298,1049)(299,1048)(300,1047)(301,1046)(302,1045)(303,1044)(304,1043)(305,1042)(306,1041)(307,1040)(308,1039)(309,1038)(310,1037)(311,1036)(312,1035)(313,1034)(314,1033)(315,1032)(316,1031)(317,1030)(318,1029)(319,1028)(320,1027)(321,1026)(322,1025)(323,1024)(324,1023)(325,1022)(326,1021)(327,1020)(328,1019)(329,1018)(330,1017)(331,1016)(332,1015)(333,1014)(334,1013)(335,1012)(336,1011)(337,1010)(338,1009)(339,1008)(340,1007)(341,1006)(342,1005)(343,1004)(344,1003)(345,1002)(346,1001)(347,1000)(348,999)(349,998)(350,997)(351,996)(352,995)(353,994)(354,993)(355,992)(356,991)(357,990)(358,989)(359,988)(360,987)(361,986)(362,985)(363,984)(364,983)(365,982)(366,981)(367,980)(368,979)(369,978)(370,977)(371,976)(372,975)(373,974)(374,973)(375,972)(376,971)(377,970)(378,969)(379,968)(380,967)(381,966)(382,965)(383,964)(384,963)(385,962)(386,961)(387,960)(388,959)(389,958)(390,957)(391,956)(392,955)(393,954)(394,953)(395,952)(396,951)(397,950)(398,949)(399,948)(400,947)(401,946)(402,945)(403,944)(404,943)(405,942)(406,941)(407,940)(408,939)(409,938)(410,937)(411,936)(412,935)(413,934)(414,933)(415,932)(416,931)(417,930)(418,929)(419,928)(420,927)(421,926)(422,925)(423,924)(424,923)(425,922)(426,921)(427,920)(428,919)(429,918)(430,917)(431,916)(432,915)(433,914)(434,913)(435,912)(436,911)(437,910)(438,909)(439,908)(440,907)(441,906)(442,905)(443,904)(444,903)(445,902)(446,901)(447,900)(448,899)(449,898)(450,897)(451,896)(452,895)(453,894)(454,893)(455,892)(456,891)(457,890)(458,889)(459,888)(460,887)(461,886)(462,885)(463,884)(464,883)(465,882)(466,881)(467,880)(468,879)(469,878)(470,877)(471,876)(472,875)(473,874)(474,873)(475,872)(476,871)(477,870)(478,869)(479,868)(480,867)(481,866)(482,865)(483,864)(484,863)(485,862)(486,861)(487,860)(488,859)(489,858)(490,857)(491,856)(492,855)(493,854)(494,853)(495,852)(496,851)(497,850)(498,849)(499,848)(500,847)(501,846)(502,845)(503,844)(504,843)(505,842)(506,841)(507,840)(508,839)(509,838)(510,837)(511,836)(512,835)(513,834)(514,833)(515,832)(516,831)(517,830)(518,829)(519,828)(520,827)(521,826)(522,825)(523,824)(524,823)(525,822)(526,821)(527,820)(528,819)(529,818)(530,817)(531,816)(532,815)(533,814)(534,813)(535,812)(536,811)(537,810)(538,809)(539,808)(540,807)(541,806)(542,805)(543,804)(544,803)(545,802)(546,801)(547,800)(548,799)(549,798)(550,797)(551,796)(552,795)(553,794)(554,793)(555,792)(556,791)(557,790)(558,789)(559,788)(560,787)(561,786)(562,785)(563,784)(564,783)(565,782)(566,781)(567,780)(568,779)(569,778)(570,777)(571,776)(572,775)(573,774)(574,773)(575,772)(576,771)(577,770)(578,769)(579,768)(580,767)(581,766)(582,765)(583,764)(584,763)(585,762)(586,761)(587,760)(588,759)(589,758)(590,757)(591,756)(592,755)(593,754)(594,753)(595,752)(596,751)(597,750)(598,749)(599,748)(600,747)(601,746)(602,745)(603,744)(604,743)(605,742)(606,741)(607,740)(608,739)(609,738)(610,737)(611,736)(612,735)(613,734)(614,733)(615,732)(616,731)(617,730)(618,729)(619,728)(620,727)(621,726)(622,725)(623,724)(624,723)(625,722)(626,721)(627,720)(628,719)(629,718)(630,717)(631,716)(632,715)(633,714)(634,713)(635,712)(636,711)(637,710)(638,709)(639,708)(640,707)(641,706)(642,705)(643,704)(644,703)(645,702)(646,701)(647,700)(648,699)(649,698)(650,697)(651,696)(652,695)(653,694)(654,693)(655,692)(656,691)(657,690)(658,689)(659,688)(660,687)(661,686)(662,685)(663,684)(664,683)(665,682)(666,681)(667,680)(668,679)(669,678)(670,677)(671,676)(672,675)(673,674)Polycyclic presentation:
2,3,1327,3|b^3=d^2,b^a=b^2d,c^a=c^1326,d^a=d^25973 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23886, 6);