Finite Group DatabasebetaFinite Group Databasebeta| order | 26354 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D13177 |
| unambiguous semidirect product | C13177⋊C2 |
| Fitting, socle, derived, Sylow | C13177 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13177 | C2 |
| LCS | G ▷ C13177 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13177 |
| transitive degree | μt(G) = 13177 |
A minimal faithful permutation representation — 2 generators on 13177 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1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17)(6363,6816)(6364,6815)(6365,6814)(6366,6813)(6367,6812)(6368,6811)(6369,6810)(6370,6809)(6371,6808)(6372,6807)(6373,6806)(6374,6805)(6375,6804)(6376,6803)(6377,6802)(6378,6801)(6379,6800)(6380,6799)(6381,6798)(6382,6797)(6383,6796)(6384,6795)(6385,6794)(6386,6793)(6387,6792)(6388,6791)(6389,6790)(6390,6789)(6391,6788)(6392,6787)(6393,6786)(6394,6785)(6395,6784)(6396,6783)(6397,6782)(6398,6781)(6399,6780)(6400,6779)(6401,6778)(6402,6777)(6403,6776)(6404,6775)(6405,6774)(6406,6773)(6407,6772)(6408,6771)(6409,6770)(6410,6769)(6411,6768)(6412,6767)(6413,6766)(6414,6765)(6415,6764)(6416,6763)(6417,6762)(6418,6761)(6419,6760)(6420,6759)(6421,6758)(6422,6757)(6423,6756)(6424,6755)(6425,6754)(6426,6753)(6427,6752)(6428,6751)(6429,6750)(6430,6749)(6431,6748)(6432,6747)(6433,6746)(6434,6745)(6435,6744)(6436,6743)(6437,6742)(6438,6741)(6439,6740)(6440,6739)(6441,6738)(6442,6737)(6443,6736)(6444,6735)(6445,6734)(6446,6733)(6447,6732)(6448,6731)(6449,6730)(6450,6729)(6451,6728)(6452,6727)(6453,6726)(6454,6725)(6455,6724)(6456,6723)(6457,6722)(6458,6721)(6459,6720)(6460,6719)(6461,6718)(6462,6717)(6463,6716)(6464,6715)(6465,6714)(6466,6713)(6467,6712)(6468,6711)(6469,6710)(6470,6709)(6471,6708)(6472,6707)(6473,6706)(6474,6705)(6475,6704)(6476,6703)(6477,6702)(6478,6701)(6479,6700)(6480,6699)(6481,6698)(6482,6697)(6483,6696)(6484,6695)(6485,6694)(6486,6693)(6487,6692)(6488,6691)(6489,6690)(6490,6689)(6491,6688)(6492,6687)(6493,6686)(6494,6685)(6495,6684)(6496,6683)(6497,6682)(6498,6681)(6499,6680)(6500,6679)(6501,6678)(6502,6677)(6503,6676)(6504,6675)(6505,6674)(6506,6673)(6507,6672)(6508,6671)(6509,6670)(6510,6669)(6511,6668)(6512,6667)(6513,6666)(6514,6665)(6515,6664)(6516,6663)(6517,6662)(6518,6661)(6519,6660)(6520,6659)(6521,6658)(6522,6657)(6523,6656)(6524,6655)(6525,6654)(6526,6653)(6527,6652)(6528,6651)(6529,6650)(6530,6649)(6531,6648)(6532,6647)(6533,6646)(6534,6645)(6535,6644)(6536,6643)(6537,6642)(6538,6641)(6539,6640)(6540,6639)(6541,6638)(6542,6637)(6543,6636)(6544,6635)(6545,6634)(6546,6633)(6547,6632)(6548,6631)(6549,6630)(6550,6629)(6551,6628)(6552,6627)(6553,6626)(6554,6625)(6555,6624)(6556,6623)(6557,6622)(6558,6621)(6559,6620)(6560,6619)(6561,6618)(6562,6617)(6563,6616)(6564,6615)(6565,6614)(6566,6613)(6567,6612)(6568,6611)(6569,6610)(6570,6609)(6571,6608)(6572,6607)(6573,6606)(6574,6605)(6575,6604)(6576,6603)(6577,6602)(6578,6601)(6579,6600)(6580,6599)(6581,6598)(6582,6597)(6583,6596)(6584,6595)(6585,6594)(6586,6593)(6587,6592)(6588,6591)(6589,6590)Polycyclic presentation:
2,13177|b^a=b^131766590 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26354, 1);