Finite Group DatabasebetaFinite Group Databasebeta| order | 25946 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D12973 |
| unambiguous semidirect product | C12973⋊C2 |
| Fitting, socle, derived, Sylow | C12973 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C12973 | C2 |
| LCS | G ▷ C12973 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12973 |
| transitive degree | μt(G) = 12973 |
A minimal faithful permutation representation — 2 generators on 12973 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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(6038,6937)(6039,6936)(6040,6935)(6041,6934)(6042,6933)(6043,6932)(6044,6931)(6045,6930)(6046,6929)(6047,6928)(6048,6927)(6049,6926)(6050,6925)(6051,6924)(6052,6923)(6053,6922)(6054,6921)(6055,6920)(6056,6919)(6057,6918)(6058,6917)(6059,6916)(6060,6915)(6061,6914)(6062,6913)(6063,6912)(6064,6911)(6065,6910)(6066,6909)(6067,6908)(6068,6907)(6069,6906)(6070,6905)(6071,6904)(6072,6903)(6073,6902)(6074,6901)(6075,6900)(6076,6899)(6077,6898)(6078,6897)(6079,6896)(6080,6895)(6081,6894)(6082,6893)(6083,6892)(6084,6891)(6085,6890)(6086,6889)(6087,6888)(6088,6887)(6089,6886)(6090,6885)(6091,6884)(6092,6883)(6093,6882)(6094,6881)(6095,6880)(6096,6879)(6097,6878)(6098,6877)(6099,6876)(6100,6875)(6101,6874)(6102,6873)(6103,6872)(6104,6871)(6105,6870)(6106,6869)(6107,6868)(6108,6867)(6109,6866)(6110,6865)(6111,6864)(6112,6863)(6113,6862)(6114,6861)(6115,6860)(6116,6859)(6117,6858)(6118,6857)(6119,6856)(6120,6855)(6121,6854)(6122,6853)(6123,6852)(6124,6851)(6125,6850)(6126,6849)(6127,6848)(6128,6847)(6129,6846)(6130,6845)(6131,6844)(6132,6843)(6133,6842)(6134,6841)(6135,6840)(6136,6839)(6137,6838)(6138,6837)(6139,6836)(6140,6835)(6141,6834)(6142,6833)(6143,6832)(6144,6831)(6145,6830)(6146,6829)(6147,6828)(6148,6827)(6149,6826)(6150,6825)(6151,6824)(6152,6823)(6153,6822)(6154,6821)(6155,6820)(6156,6819)(6157,6818)(6158,6817)(6159,6816)(6160,6815)(6161,6814)(6162,6813)(6163,6812)(6164,6811)(6165,6810)(6166,6809)(6167,6808)(6168,6807)(6169,6806)(6170,6805)(6171,6804)(6172,6803)(6173,6802)(6174,6801)(6175,6800)(6176,6799)(6177,6798)(6178,6797)(6179,6796)(6180,6795)(6181,6794)(6182,6793)(6183,6792)(6184,6791)(6185,6790)(6186,6789)(6187,6788)(6188,6787)(6189,6786)(6190,6785)(6191,6784)(6192,6783)(6193,6782)(6194,6781)(6195,6780)(6196,6779)(6197,6778)(6198,6777)(6199,6776)(6200,6775)(6201,6774)(6202,6773)(6203,6772)(6204,6771)(6205,6770)(6206,6769)(6207,6768)(6208,6767)(6209,6766)(6210,6765)(6211,6764)(6212,6763)(6213,6762)(6214,6761)(6215,6760)(6216,6759)(6217,6758)(6218,6757)(6219,6756)(6220,6755)(6221,6754)(6222,6753)(6223,6752)(6224,6751)(6225,6750)(6226,6749)(6227,6748)(6228,6747)(6229,6746)(6230,6745)(6231,6744)(6232,6743)(6233,6742)(6234,6741)(6235,6740)(6236,6739)(6237,6738)(6238,6737)(6239,6736)(6240,6735)(6241,6734)(6242,6733)(6243,6732)(6244,6731)(6245,6730)(6246,6729)(6247,6728)(6248,6727)(6249,6726)(6250,6725)(6251,6724)(6252,6723)(6253,6722)(6254,6721)(6255,6720)(6256,6719)(6257,6718)(6258,6717)(6259,6716)(6260,6715)(6261,6714)(6262,6713)(6263,6712)(6264,6711)(6265,6710)(6266,6709)(6267,6708)(6268,6707)(6269,6706)(6270,6705)(6271,6704)(6272,6703)(6273,6702)(6274,6701)(6275,6700)(6276,6699)(6277,6698)(6278,6697)(6279,6696)(6280,6695)(6281,6694)(6282,6693)(6283,6692)(6284,6691)(6285,6690)(6286,6689)(6287,6688)(6288,6687)(6289,6686)(6290,6685)(6291,6684)(6292,6683)(6293,6682)(6294,6681)(6295,6680)(6296,6679)(6297,6678)(6298,6677)(6299,6676)(6300,6675)(6301,6674)(6302,6673)(6303,6672)(6304,6671)(6305,6670)(6306,6669)(6307,6668)(6308,6667)(6309,6666)(6310,6665)(6311,6664)(6312,6663)(6313,6662)(6314,6661)(6315,6660)(6316,6659)(6317,6658)(6318,6657)(6319,6656)(6320,6655)(6321,6654)(6322,6653)(6323,6652)(6324,6651)(6325,6650)(6326,6649)(6327,6648)(6328,6647)(6329,6646)(6330,6645)(6331,6644)(6332,6643)(6333,6642)(6334,6641)(6335,6640)(6336,6639)(6337,6638)(6338,6637)(6339,6636)(6340,6635)(6341,6634)(6342,6633)(6343,6632)(6344,6631)(6345,6630)(6346,6629)(6347,6628)(6348,6627)(6349,6626)(6350,6625)(6351,6624)(6352,6623)(6353,6622)(6354,6621)(6355,6620)(6356,6619)(6357,6618)(6358,6617)(6359,6616)(6360,6615)(6361,6614)(6362,6613)(6363,6612)(6364,6611)(6365,6610)(6366,6609)(6367,6608)(6368,6607)(6369,6606)(6370,6605)(6371,6604)(6372,6603)(6373,6602)(6374,6601)(6375,6600)(6376,6599)(6377,6598)(6378,6597)(6379,6596)(6380,6595)(6381,6594)(6382,6593)(6383,6592)(6384,6591)(6385,6590)(6386,6589)(6387,6588)(6388,6587)(6389,6586)(6390,6585)(6391,6584)(6392,6583)(6393,6582)(6394,6581)(6395,6580)(6396,6579)(6397,6578)(6398,6577)(6399,6576)(6400,6575)(6401,6574)(6402,6573)(6403,6572)(6404,6571)(6405,6570)(6406,6569)(6407,6568)(6408,6567)(6409,6566)(6410,6565)(6411,6564)(6412,6563)(6413,6562)(6414,6561)(6415,6560)(6416,6559)(6417,6558)(6418,6557)(6419,6556)(6420,6555)(6421,6554)(6422,6553)(6423,6552)(6424,6551)(6425,6550)(6426,6549)(6427,6548)(6428,6547)(6429,6546)(6430,6545)(6431,6544)(6432,6543)(6433,6542)(6434,6541)(6435,6540)(6436,6539)(6437,6538)(6438,6537)(6439,6536)(6440,6535)(6441,6534)(6442,6533)(6443,6532)(6444,6531)(6445,6530)(6446,6529)(6447,6528)(6448,6527)(6449,6526)(6450,6525)(6451,6524)(6452,6523)(6453,6522)(6454,6521)(6455,6520)(6456,6519)(6457,6518)(6458,6517)(6459,6516)(6460,6515)(6461,6514)(6462,6513)(6463,6512)(6464,6511)(6465,6510)(6466,6509)(6467,6508)(6468,6507)(6469,6506)(6470,6505)(6471,6504)(6472,6503)(6473,6502)(6474,6501)(6475,6500)(6476,6499)(6477,6498)(6478,6497)(6479,6496)(6480,6495)(6481,6494)(6482,6493)(6483,6492)(6484,6491)(6485,6490)(6486,6489)(6487,6488)Polycyclic presentation:
2,12973|b^a=b^129726488 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25946, 1);