Finite Group DatabasebetaFinite Group Databasebeta| order | 24498 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12249 |
| unambiguous semidirect product | C9⋊D1361 |
| unambiguous semidirect product | C1361⋊D9 |
| Fitting, derived, Hall | C9×C1361 ⋊ C2 |
| Sylow | C1361 ⋊ D9 |
| Sylow | C9 ⋊ D1361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C1361 | C2 |
| Frattini | C3 | D4083 |
| socle | C3×C1361 | D3 |
| LCS | G ▷ C9×C1361 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 1370 |
| transitive degree | μt(G) = 12249 |
A minimal faithful permutation representation — 2 generators on 1370 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,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450,931)(451,930)(452,929)(453,928)(454,927)(455,926)(456,925)(457,924)(458,923)(459,922)(460,921)(461,920)(462,919)(463,918)(464,917)(465,916)(466,915)(467,914)(468,913)(469,912)(470,911)(471,910)(472,909)(473,908)(474,907)(475,906)(476,905)(477,904)(478,903)(479,902)(480,901)(481,900)(482,899)(483,898)(484,897)(485,896)(486,895)(487,894)(488,893)(489,892)(490,891)(491,890)(492,889)(493,888)(494,887)(495,886)(496,885)(497,884)(498,883)(499,882)(500,881)(501,880)(502,879)(503,878)(504,877)(505,876)(506,875)(507,874)(508,873)(509,872)(510,871)(511,870)(512,869)(513,868)(514,867)(515,866)(516,865)(517,864)(518,863)(519,862)(520,861)(521,860)(522,859)(523,858)(524,857)(525,856)(526,855)(527,854)(528,853)(529,852)(530,851)(531,850)(532,849)(533,848)(534,847)(535,846)(536,845)(537,844)(538,843)(539,842)(540,841)(541,840)(542,839)(543,838)(544,837)(545,836)(546,835)(547,834)(548,833)(549,832)(550,831)(551,830)(552,829)(553,828)(554,827)(555,826)(556,825)(557,824)(558,823)(559,822)(560,821)(561,820)(562,819)(563,818)(564,817)(565,816)(566,815)(567,814)(568,813)(569,812)(570,811)(571,810)(572,809)(573,808)(574,807)(575,806)(576,805)(577,804)(578,803)(579,802)(580,801)(581,800)(582,799)(583,798)(584,797)(585,796)(586,795)(587,794)(588,793)(589,792)(590,791)(591,790)(592,789)(593,788)(594,787)(595,786)(596,785)(597,784)(598,783)(599,782)(600,781)(601,780)(602,779)(603,778)(604,777)(605,776)(606,775)(607,774)(608,773)(609,772)(610,771)(611,770)(612,769)(613,768)(614,767)(615,766)(616,765)(617,764)(618,763)(619,762)(620,761)(621,760)(622,759)(623,758)(624,757)(625,756)(626,755)(627,754)(628,753)(629,752)(630,751)(631,750)(632,749)(633,748)(634,747)(635,746)(636,745)(637,744)(638,743)(639,742)(640,741)(641,740)(642,739)(643,738)(644,737)(645,736)(646,735)(647,734)(648,733)(649,732)(650,731)(651,730)(652,729)(653,728)(654,727)(655,726)(656,725)(657,724)(658,723)(659,722)(660,721)(661,720)(662,719)(663,718)(664,717)(665,716)(666,715)(667,714)(668,713)(669,712)(670,711)(671,710)(672,709)(673,708)(674,707)(675,706)(676,705)(677,704)(678,703)(679,702)(680,701)(681,700)(682,699)(683,698)(684,697)(685,696)(686,695)(687,694)(688,693)(689,692)(690,691)Polycyclic presentation:
2,3,1361,3|b^3=d^2,b^a=b^2d,c^a=c^1360,d^a=d^26126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24498, 4);