Finite Group DatabasebetaFinite Group Databasebeta| order | 12807 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C1423 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C1423⋊C3 |
| commutator, hypocenter | C1423 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C1423 | C3 |
| LCS | G ▷ C1423 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1432 |
| transitive degree | μt(G) = 12807 |
A minimal faithful permutation representation — 2 generators on 1432 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,210)(151,181,207)(154,184,204)(157,187,201)(160,190,198)(163,193,195)(166,196,192)(169,199,189)(172,202,186)(175,205,183)(177,208,180)(179,212,247)(182,215,244)(185,218,241)(188,221,238)(191,224,235)(194,227,232)(197,230,229)(200,233,226)(203,236,223)(206,239,220)(209,242,217)(211,245,214)(213,249,287)(216,252,284)(219,255,281)(222,258,278)(225,261,275)(228,264,272)(231,267,269)(234,270,266)(237,273,263)(240,276,260)(243,279,257)(246,282,254)(248,285,251)(250,289,330)(253,292,327)(256,295,324)(259,298,321)(262,301,318)(265,304,315)(268,307,312)(271,310,309)(274,313,306)(277,316,303)(280,319,300)(283,322,297)(286,325,294)(288,328,291)(290,332,376)(293,335,373)(296,338,370)(299,341,367)(302,344,364)(305,347,361)(308,350,358)(311,353,355)(314,356,352)(317,359,349)(320,362,346)(323,365,343)(326,368,340)(329,371,337)(331,374,334)(333,378,425)(336,381,422)(339,384,419)(342,387,416)(345,390,413)(348,393,410)(351,396,407)(354,399,404)(357,402,401)(360,405,398)(363,408,395)(366,411,392)(369,414,389)(372,417,386)(375,420,383)(377,423,380)(379,427,477)(382,430,474)(385,433,471)(388,436,468)(391,439,465)(394,442,462)(397,445,459)(400,448,456)(403,451,453)(406,454,450)(409,457,447)(412,460,444)(415,463,441)(418,466,438)(421,469,435)(424,472,432)(426,475,429)(428,479,532)(431,482,529)(434,485,526)(437,488,523)(440,491,520)(443,494,517)(446,497,514)(449,500,511)(452,503,508)(455,506,505)(458,509,502)(461,512,499)(464,515,496)(467,518,493)(470,521,490)(473,524,487)(476,527,484)(478,530,481)(480,534,590)(483,537,587)(486,540,584)(489,543,581)(492,546,578)(495,549,575)(498,552,572)(501,555,569)(504,558,566)(507,561,563)(510,564,560)(513,567,557)(516,570,554)(519,573,551)(522,576,548)(525,579,545)(528,582,542)(531,585,539)(533,588,536)(535,592,651)(538,595,648)(541,598,645)(544,601,642)(547,604,639)(550,607,636)(553,610,633)(556,613,630)(559,616,627)(562,619,624)(565,622,621)(568,625,618)(571,628,615)(574,631,612)(577,634,609)(580,637,606)(583,640,603)(586,643,600)(589,646,597)(591,649,594)(593,653,715)(596,656,712)(599,659,709)(602,662,706)(605,665,703)(608,668,700)(611,671,697)(614,674,694)(617,677,691)(620,680,688)(623,683,685)(626,686,682)(629,689,679)(632,692,676)(635,695,673)(638,698,670)(641,701,667)(644,704,664)(647,707,661)(650,710,658)(652,713,655)(654,717,782)(657,720,779)(660,723,776)(663,726,773)(666,729,770)(669,732,767)(672,735,764)(675,738,761)(678,741,758)(681,744,755)(684,747,752)(687,750,749)(690,753,746)(693,756,743)(696,759,740)(699,762,737)(702,765,734)(705,768,731)(708,771,728)(711,774,725)(714,777,722)(716,780,719)(718,784,852)(721,787,849)(724,790,846)(727,793,843)(730,796,840)(733,799,837)(736,802,834)(739,805,831)(742,808,828)(745,811,825)(748,814,822)(751,817,819)(754,820,816)(757,823,813)(760,826,810)(763,829,807)(766,832,804)(769,835,801)(772,838,798)(775,841,795)(778,844,792)(781,847,789)(783,850,786)(785,854,875)(788,856,921)(791,859,918)(794,862,915)(797,865,912)(800,868,909)(803,871,906)(806,874,903)(809,877,900)(812,880,897)(815,883,894)(818,886,891)(821,889,888)(824,892,885)(827,895,882)(830,898,879)(833,901,876)(836,904,873)(839,907,870)(842,910,867)(845,913,864)(848,916,861)(851,919,858)(853,922,855)(857,926,943)(860,928,988)(863,931,985)(866,934,982)(869,937,979)(872,940,976)(878,945,971)(881,948,968)(884,951,965)(887,954,962)(890,957,959)(893,960,956)(896,963,953)(899,966,950)(902,969,947)(905,972,944)(908,974,942)(911,977,939)(914,980,936)(917,983,933)(920,986,930)(923,989,927)(924,946,925)(929,993,1007)(932,995,1049)(935,998,1046)(938,1001,1043)(941,1004,1040)(949,1010,1033)(952,1013,1030)(955,1016,1027)(958,1019,1024)(961,1022,1021)(964,1025,1018)(967,1028,1015)(970,1031,1012)(973,1034,1009)(975,1036,1008)(978,1038,1006)(981,1041,1003)(984,1044,1000)(987,1047,997)(990,1050,994)(991,1011,992)(996,1054,1065)(999,1056,1104)(1002,1059,1101)(1005,1062,1098)(1014,1069,1089)(1017,1072,1086)(1020,1075,1083)(1023,1078,1080)(1026,1081,1077)(1029,1084,1074)(1032,1087,1071)(1035,1090,1068)(1037,1092,1067)(1039,1094,1066)(1042,1096,1064)(1045,1099,1061)(1048,1102,1058)(1051,1105,1055)(1052,1070,1053)(1057,1109,1117)(1060,1111,1153)(1063,1114,1150)(1073,1122,1139)(1076,1125,1136)(1079,1128,1133)(1082,1131,1130)(1085,1134,1127)(1088,1137,1124)(1091,1140,1121)(1093,1142,1120)(1095,1144,1119)(1097,1146,1118)(1100,1148,1116)(1103,1151,1113)(1106,1154,1110)(1107,1123,1108)(1112,1158,1163)(1115,1160,1196)(1126,1169,1183)(1129,1172,1180)(1132,1175,1177)(1135,1178,1174)(1138,1181,1171)(1141,1184,1168)(1143,1186,1167)(1145,1188,1166)(1147,1190,1165)(1149,1192,1164)(1152,1194,1162)(1155,1197,1159)(1156,1170,1157)(1161,1201,1203)(1173,1210,1221)(1176,1213,1218)(1179,1216,1215)(1182,1219,1212)(1185,1222,1209)(1187,1224,1208)(1189,1226,1207)(1191,1228,1206)(1193,1230,1205)(1195,1232,1204)(1198,1234,1202)(1199,1211,1200)(1214,1245,1253)(1217,1248,1250)(1220,1251,1247)(1223,1254,1244)(1225,1256,1243)(1227,1258,1242)(1229,1260,1241)(1231,1262,1240)(1233,1264,1239)(1235,1266,1238)(1236,1246,1237)(1249,1277,1282)(1252,1280,1279)(1255,1283,1276)(1257,1285,1275)(1259,1287,1274)(1261,1289,1273)(1263,1291,1272)(1265,1293,1271)(1267,1295,1270)(1268,1278,1269)(1281,1306,1308)(1284,1309,1305)(1286,1311,1304)(1288,1313,1303)(1290,1315,1302)(1292,1317,1301)(1294,1319,1300)(1296,1321,1299)(1297,1307,1298)(1310,1332,1331)(1312,1334,1330)(1314,1336,1329)(1316,1338,1328)(1318,1340,1327)(1320,1342,1326)(1322,1344,1325)(1323,1333,1324)(1335,1354,1353)(1337,1356,1352)(1339,1358,1351)(1341,1360,1350)(1343,1362,1349)(1345,1364,1348)(1346,1355,1347)(1357,1373,1372)(1359,1375,1371)(1361,1377,1370)(1363,1379,1369)(1365,1381,1368)(1366,1374,1367)(1376,1389,1388)(1378,1391,1387)(1380,1393,1386)(1382,1395,1385)(1383,1390,1384)(1392,1402,1401)(1394,1404,1400)(1396,1406,1399)(1397,1403,1398)(1405,1412,1411)(1407,1414,1410)(1408,1413,1409)(1415,1419,1418)(1416,1420,1417)(1421,1423,1422)(1424,1425,1427,1426,1428,1430,1429,1431,1432);(1,2,4,8,15,25,38,54,73,95,120,148,179,213,250,290,333,379,428,480,535,593,654,718,785,802,668,546,436,338,252,178,211,246,283,323,366,412,461,513,568,626,687,751,818,887,955,1017,1073,1123,1050,919,780,651,712,776,843,912,979,1040,993,856,717,783,851,920,987,1048,1103,1152,1195,1233,1265,1294,1320,1343,1363,1380,1394,1405,1413,1395,1362,1317,1260,1188,1092,972,832,698,576,466,368,282,208,145,173,204,238,275,315,358,404,453,505,560,618,679,743,810,879,947,1009,1067,1119,1165,1205,1239,1270,1298,1277,1213,1128,1019,886,747,619,503,399,307,227,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,219,256,296,339,385,434,486,541,599,660,724,791,860,929,940,799,665,543,433,335,249,288,329,372,418,467,519,574,632,693,757,824,893,961,1023,1079,1129,1173,1211,1154,1047,916,777,649,532,587,645,706,770,837,906,854,924,991,1052,1107,1156,1199,1236,1268,1297,1323,1346,1366,1383,1397,1408,1416,1421,1423,1414,1393,1360,1315,1258,1186,1090,969,829,695,573,463,365,279,205,143,92,114,139,167,198,232,269,309,352,398,447,499,554,612,673,737,804,873,942,1006,1064,1116,1162,1202,1237,1210,1125,1016,883,744,616,500,396,304,224,156,100,56,24,36,50,66,85,107,132,160,191,225,262,302,345,391,440,492,547,605,666,730,797,866,935,999,1057,1062,937,796,662,540,430,332,377,424,473,525,580,638,699,763,830,899,967,1029,1085,1135,1179,1217,1249,1278,1234,1151,1044,913,774,646,530,425,474,526,581,639,700,764,831,900,968,1030,1086,1136,1180,1218,1250,1279,1305,1330,1352,1371,1387,1400,1410,1417,1412,1391,1358,1313,1256,1184,1087,966,826,692,570,460,362,276,202,140,90,51,67,86,108,133,161,192,226,263,303,346,392,441,493,548,606,667,731,798,867,936,1000,1058,1110,1157,1122,1013,880,741,613,497,393,301,221,153,97,53,71,91,113,138,166,197,231,268,308,351,397,446,498,553,611,672,736,803,872,941,1005,1063,1115,1161,1160,1059,934,793,659,537,427,478,531,586,644,705,769,836,905,973,1035,1091,1141,1185,1223,1255,1284,1310,1333,1295,1232,1148,1041,910,771,643,527,423,330,373,419,468,520,575,633,694,758,825,894,962,1024,1080,1130,1174,1212,1244,1275,1303,1328,1350,1369,1385,1398,1389,1356,1311,1254,1181,1084,963,823,689,567,457,359,273,199,137,87,49,22,32,45,61,80,102,127,155,186,220,257,297,340,386,435,487,542,600,661,725,792,861,930,994,1053,1010,877,738,610,494,390,298,218,150,94,118,144,172,203,237,274,314,357,403,452,504,559,617,678,742,809,878,946,852,921,988,1049,1104,1153,1196,1158,1056,931,790,656,534,591,650,711,775,842,911,978,1039,1095,1145,1189,1227,1259,1288,1314,1337,1357,1374,1344,1293,1230,1146,1038,907,768,640,524,420,328,247,284,324,367,413,462,514,569,627,688,752,819,888,956,1018,1074,1124,1168,1208,1242,1273,1301,1326,1348,1367,1354,1309,1251,1178,1081,960,820,686,564,454,356,270,196,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,214,251,291,334,380,429,481,536,594,655,719,786,855,925,874,735,607,491,387,295,215,147,177,209,243,280,320,363,409,458,510,565,623,684,748,815,884,952,1014,1070,989,850,715,779,846,915,982,1043,1098,1054,928,787,653,716,781,848,917,984,1045,1100,1149,1193,1231,1263,1292,1318,1341,1361,1378,1392,1403,1381,1342,1291,1228,1144,1036,904,765,637,521,417,325,245,176,207,241,278,318,361,407,456,508,563,621,682,746,813,882,950,1012,1068,1120,1166,1206,1240,1271,1299,1324,1306,1248,1175,1078,957,817,683,561,451,353,267,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,216,253,293,336,382,431,483,538,596,657,721,788,857,871,732,604,488,384,292,212,248,286,326,369,415,464,516,571,629,690,754,821,890,958,1020,1076,1126,1170,1105,986,847,713,590,648,709,773,840,909,976,926,784,853,923,990,1051,1106,1155,1198,1235,1267,1296,1322,1345,1365,1382,1396,1407,1415,1420,1406,1379,1340,1289,1226,1142,1034,901,762,634,518,414,322,242,174,117,142,170,201,235,272,312,355,401,450,502,557,615,676,740,807,876,944,1008,1066,1118,1164,1204,1238,1269,1245,1172,1075,954,814,680,558,448,350,264,190,128,78,40,14,23,34,47,63,82,104,129,157,188,222,259,299,342,388,437,489,544,602,663,727,794,863,932,996,1004,868,729,601,485,381,289,331,375,421,470,522,577,635,696,760,827,896,964,1026,1082,1132,1176,1214,1246,1197,1102,983,844,710,588,477,529,584,642,703,767,834,903,971,1033,1089,1139,1183,1221,1253,1282,1308,1331,1353,1372,1388,1401,1411,1418,1422,1419,1404,1377,1338,1287,1224,1140,1031,898,759,631,515,411,319,239,171,115,70,89,111,136,164,195,229,266,306,349,395,444,496,551,609,670,734,801,870,939,1003,1061,1113,1159,1200,1169,1072,951,811,677,555,445,347,261,187,125,75,37,52,69,88,110,135,163,194,228,265,305,348,394,443,495,550,608,669,733,800,869,938,1002,1060,1112,1114,1001,865,726,598,482,378,426,476,528,583,641,702,766,833,902,970,1032,1088,1138,1182,1220,1252,1281,1307,1266,1194,1099,980,841,707,585,475,376,422,471,523,578,636,697,761,828,897,965,1027,1083,1133,1177,1215,1247,1276,1304,1329,1351,1370,1386,1399,1409,1402,1375,1336,1285,1222,1137,1028,895,756,628,512,408,316,236,168,112,68,35,48,64,83,105,130,158,189,223,260,300,343,389,438,490,545,603,664,728,795,864,933,997,1055,1108,1069,948,808,674,552,442,344,258,184,122,72,93,116,141,169,200,234,271,311,354,400,449,501,556,614,675,739,806,875,943,1007,1065,1117,1163,1203,1201,1111,998,862,723,595,479,533,589,647,708,772,839,908,975,1037,1093,1143,1187,1225,1257,1286,1312,1335,1355,1321,1264,1192,1096,977,838,704,582,472,374,287,327,370,416,465,517,572,630,691,755,822,891,959,1021,1077,1127,1171,1209,1243,1274,1302,1327,1349,1368,1384,1373,1334,1283,1219,1134,1025,892,753,625,509,405,313,233,165,109,65,33,12,19,29,42,58,77,99,124,152,183,217,254,294,337,383,432,484,539,597,658,722,789,858,927,992,945,805,671,549,439,341,255,181,119,146,175,206,240,277,317,360,406,455,507,562,620,681,745,812,881,949,1011,922,782,849,918,985,1046,1101,1150,1109,995,859,720,592,652,714,778,845,914,981,1042,1097,1147,1191,1229,1261,1290,1316,1339,1359,1376,1390,1364,1319,1262,1190,1094,974,835,701,579,469,371,285,210,244,281,321,364,410,459,511,566,624,685,749,816,885,953,1015,1071,1121,1167,1207,1241,1272,1300,1325,1347,1332,1280,1216,1131,1022,889,750,622,506,402,310,230,162,106,62,30,10)Polycyclic presentation:
3^2,1423|a^3=b,c^a=c^7791431 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27165409⋊C2, C2×#27165409, C9×C1423⋊C3, … |
| maximal normal subgroup of | #27165409⋊C2, C2×#27165409, C9×C1423⋊C3, … |
| maximal quotient of | C2×#27165409, #50307462, C3×#27165409 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12807, 1);