Finite Group Databasebeta

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C₃⋊(D₁₈₄₉⋊C₃) #45685441

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

27 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 1852 points:

(2,3)(5,14,16,7,8,17)(6,26,28,11,12,30)(9,44,46,19,20,105)(10,56,57,23,24,135)(13,73,75,31,32,167)(15,65,86,27,36,101)(18,99,67,41,42,157)(21,116,118,49,50,253)(22,128,129,53,54,285)(25,143,144,60,61,318)(29,88,38,68,69,91)(33,178,180,78,79,384)(34,110,93,81,47,39)(35,139,140,84,58,71)(37,170,197,74,89,369)(40,63,138,96,97,59)(43,221,172,102,103,372)(45,155,235,66,108,249)(48,246,158,113,114,350)(51,266,268,121,122,539)(52,278,279,125,126,570)(55,296,297,132,133,603)(62,329,330,147,148,655)(64,173,165,152,77,72)(70,237,111,160,161,241)(76,375,92,174,175,203)(80,362,367,166,169,389)(82,260,261,184,119,227)(83,290,291,187,130,303)(85,323,324,189,145,363)(87,409,205,192,193,202)(90,386,426,179,200,736)(94,106,258,206,207,229)(95,136,288,210,211,292)(98,168,321,213,214,328)(100,248,407,183,218,191)(104,462,388,224,225,739)(107,289,358,232,233,163)(109,370,487,171,238,712)(112,216,310,243,244,443)(115,504,373,250,251,716)(117,347,519,156,256,535)(120,532,351,263,264,687)(123,551,553,271,272,996)(124,563,564,275,276,1011)(127,581,582,282,283,1038)(131,228,150,293,294,336)(134,614,615,300,301,1086)(137,322,360,307,308,164)(141,195,240,312,313,415)(142,217,374,315,316,447)(146,304,151,326,327,339)(149,665,666,333,334,798)(153,394,395,342,182,364)(154,420,335,344,223,349)(159,377,425,341,199,220)(162,521,259,354,355,525)(176,723,242,378,379,494)(177,196,311,382,383,417)(181,742,204,390,391,431)(185,546,547,398,269,511)(186,575,576,401,280,588)(188,608,609,403,298,641)(190,659,660,405,331,732)(194,771,528,411,412,493)(198,787,433,421,422,430)(201,646,647,361,320,658)(208,254,544,436,437,513)(209,286,573,440,441,590)(212,319,606,444,445,643)(215,385,657,448,449,734)(219,753,833,397,455,481)(222,506,785,396,460,419)(226,784,708,418,465,1148)(230,859,850,470,471,466)(231,869,870,474,475,621)(234,876,878,478,479,701)(236,884,434,482,483,429)(239,737,901,387,490,1215)(245,458,649,496,497,837)(247,534,766,435,501,408)(252,925,740,508,509,1219)(255,574,696,516,517,357)(257,713,951,371,522,1189)(262,499,633,529,530,912)(265,969,717,536,537,1191)(267,684,983,348,542,995)(270,993,688,549,550,1165)(273,722,1004,556,557,1135)(274,1008,1009,560,561,1528)(277,1020,1021,567,568,1540)(281,512,337,578,579,668)(284,1048,933,585,586,1435)(287,607,698,593,594,359)(295,500,718,600,601,915)(299,589,338,611,612,671)(302,1095,1096,618,619,1397)(305,1031,853,624,577,467)(306,1081,1084,627,610,622)(309,1108,1110,630,631,702)(314,485,524,636,637,890)(317,459,741,406,640,840)(325,719,492,650,651,877)(332,642,340,662,663,673)(343,709,710,677,368,733)(345,848,751,679,464,715)(346,895,620,681,507,686)(352,803,804,676,428,711)(353,725,900,675,489,503)(356,984,545,692,693,987)(365,1080,855,703,613,468)(366,1147,432,706,664,623)(376,743,450,700,721,457)(380,1201,526,726,727,957)(381,486,596,730,731,892)(392,1224,495,744,745,907)(393,720,634,748,749,1109)(399,1000,1001,756,554,975)(400,1015,1016,759,565,1023)(402,1042,1043,761,583,1072)(404,1089,1090,763,616,1142)(410,789,796,678,769,765)(413,1256,990,773,774,956)(414,527,874,777,778,477)(416,597,1083,780,781,629)(423,1273,960,790,791,906)(424,768,635,794,795,783)(427,1285,808,799,800,807)(438,540,998,813,814,977)(439,571,1013,817,818,1025)(442,604,1040,821,822,1074)(446,656,1087,826,827,1144)(451,599,857,569,820,469)(452,653,1067,562,825,598)(453,750,1113,559,829,654)(454,786,639,830,831,824)(456,1236,1303,755,835,945)(461,1234,1316,754,843,894)(463,927,1283,752,846,797)(472,1339,1341,862,863,930)(473,1350,1351,866,867,1051)(476,1356,1227,871,872,1122)(480,1367,1369,880,881,1210)(484,1375,1322,886,887,905)(488,1388,809,896,897,806)(491,1077,1078,699,605,1088)(498,845,1146,909,910,1317)(502,1335,1371,860,918,883)(505,970,714,810,923,543)(510,1386,1187,893,929,1646)(514,1437,1323,934,935,851)(515,1446,1447,938,939,1097)(518,1452,1454,942,943,1178)(520,1460,811,946,947,805)(523,1216,1471,738,953,1489)(531,921,1136,961,962,1417)(533,994,587,812,966,767)(538,1494,1220,972,973,1679)(541,1014,1173,980,981,695)(548,964,1114,991,992,1484)(552,1159,1251,685,770,1525)(555,1272,1166,788,1003,828)(558,849,1218,680,1006,1186)(566,976,669,1018,1019,823)(572,1041,1175,1028,1029,697)(580,965,1192,1035,1036,1487)(584,1024,670,1045,1046,819)(591,1536,1326,1054,1055,852)(592,1567,1585,1058,1059,1098)(595,1589,1591,1062,1063,1179)(602,922,1221,882,1071,1420)(617,1073,672,1092,1093,816)(625,1539,1431,1100,1017,931)(626,1570,1571,1103,1044,1052)(628,1614,1615,1105,1091,1123)(632,1313,1196,1112,841,1211)(638,949,986,1118,1119,1464)(644,1566,1328,1125,1126,854)(645,1613,1293,1129,1130,1099)(648,1171,689,1133,1134,1157)(652,1197,955,1138,1139,1473)(661,1222,904,1149,1150,1368)(667,1143,674,1152,1153,815)(682,1427,1232,1161,928,1190)(683,1469,1050,1163,971,1164)(690,1402,1403,1156,903,1188)(691,1203,1470,1155,952,968)(694,1252,999,1170,1007,1521)(704,1572,1433,1180,1047,932)(705,1616,908,1183,1094,1053)(707,1223,1115,1185,1154,1124)(724,1225,1331,1177,1199,920)(728,1674,988,1204,1205,1512)(729,950,1032,1208,1209,1466)(735,1612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Polycyclic presentation:

2,3^2,43^2|d^43=e^42,c^a=c^2,d^a=d^42e,e^a=e^42,d^b=d^36e^34,e^b=e^36

Conjugacy classes & character table

933 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33282, 10);