Finite Group DatabasebetaFinite Group Databasebeta| order | 26934 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D4489⋊C3 |
| unambiguous semidirect product | (C4489⋊C3)⋊C2 |
| Fitting, derived, Sylow | C4489 ⋊ C2×C3 |
| Hall | C4489⋊C3 ⋊ C2 |
| Hall | D4489 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C4489 | C2×C3 |
| Frattini, socle | C67 | D67⋊C3 |
| LCS | G ▷ C4489 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 4489 |
| transitive degree | μt(G) = 4489 |
A minimal faithful permutation representation — 2 generators on 4489 points:
(2,11,13,4,5,14)(3,23,25,8,9,27)(6,41,43,16,17,102)(7,53,54,20,21,132)(10,70,72,28,29,164)(12,62,83,24,33,98)(15,96,64,38,39,154)(18,113,115,46,47,253)(19,125,126,50,51,285)(22,140,141,57,58,318)(26,85,35,65,66,88)(30,175,177,75,76,388)(31,107,90,78,44,36)(32,136,137,81,55,68)(34,167,197,71,86,372)(37,60,135,93,94,56)(40,221,169,99,100,376)(42,152,235,63,105,249)(45,246,155,110,111,350)(48,266,268,118,119,554)(49,278,279,122,123,586)(52,296,297,129,130,619)(59,329,330,144,145,674)(61,170,162,149,74,69)(67,237,108,157,158,241)(73,379,89,171,172,203)(77,401,403,180,181,791)(79,260,261,184,116,227)(80,290,291,187,127,303)(82,323,324,189,142,366)(84,420,205,192,193,202)(87,391,437,176,200,773)(91,103,258,206,207,229)(92,133,288,210,211,292)(95,165,321,213,214,328)(97,248,418,183,218,191)(101,475,393,224,225,777)(104,289,358,232,233,160)(106,374,502,168,238,746)(109,216,310,243,244,456)(112,519,377,250,251,751)(114,347,534,153,256,550)(117,547,351,263,264,712)(120,567,569,271,272,1089)(121,579,580,275,276,1121)(124,597,598,282,283,1155)(128,228,147,293,294,336)(131,630,631,300,301,1212)(134,322,360,307,308,161)(138,195,240,312,313,426)(139,217,378,315,316,460)(143,304,148,326,327,339)(146,685,686,333,334,1298)(150,399,400,342,179,367)(151,431,362,344,223,349)(156,381,436,341,199,220)(159,536,259,354,355,540)(163,166,394,363,364,370)(173,757,242,382,383,509)(174,196,311,386,387,428)(178,780,204,395,396,444)(182,741,734,371,406,1362)(185,561,562,409,269,526)(186,591,592,412,280,604)(188,624,625,414,298,659)(190,679,680,416,331,766)(194,826,543,422,423,508)(198,845,446,432,433,443)(201,794,863,402,440,1444)(208,254,559,449,450,528)(209,286,589,453,454,606)(212,319,622,457,458,661)(215,389,677,461,462,768)(219,806,907,408,468,496)(222,521,842,407,473,430)(226,926,796,478,479,1448)(230,939,930,485,486,481)(231,949,950,489,490,637)(234,956,958,493,494,732)(236,964,447,497,498,442)(239,775,981,392,505,1416)(245,471,667,511,512,913)(247,549,821,448,516,419)(252,1007,778,523,524,1421)(255,590,721,531,532,357)(257,748,1035,375,537,1377)(262,514,649,544,545,994)(265,1054,752,551,552,1383)(267,708,1069,348,557,1085)(270,1082,713,564,565,1337)(273,1102,1104,572,573,1930)(274,1114,1115,576,577,1946)(277,1132,1133,583,584,1970)(281,527,337,594,595,692)(284,1166,1167,601,602,2021)(287,623,723,609,610,359)(295,515,753,616,617,997)(299,605,338,627,628,695)(302,1222,1223,634,635,2097)(305,1147,933,640,593,482)(306,1206,1209,643,626,638)(309,1242,1244,646,647,733)(314,500,539,652,653,970)(317,472,779,656,657,916)(320,678,725,664,665,361)(325,754,507,669,670,957)(332,660,340,682,683,697)(335,1309,1310,689,690,2209)(343,802,803,701,405,767)(345,925,790,703,477,750)(346,975,727,705,522,711)(352,861,862,700,439,742)(353,759,980,699,504,518)(356,1071,560,717,718,1075)(365,390,797,729,730,771)(368,1205,935,735,629,483)(369,1291,1232,738,684,639)(373,856,728,743,744,710)(380,782,911,691,756,470)(384,1393,541,760,761,1042)(385,501,612,764,765,972)(397,1428,510,783,784,989)(398,755,650,787,788,1243)(404,1451,445,798,799,870)(410,1096,1097,809,570,1061)(411,1126,1127,812,581,1139)(413,1160,1161,814,599,1197)(415,1217,1218,816,632,1282)(417,1303,1304,818,687,1439)(421,847,854,702,824,820)(424,1491,1078,828,829,1041)(425,542,954,832,833,492)(427,613,1208,835,836,645)(429,668,1293,839,840,740)(434,1518,1045,848,849,988)(435,823,651,852,853,838)(438,1531,872,857,858,869)(441,1308,1263,739,866,2148)(451,555,1094,877,878,1063)(452,587,1124,881,882,1141)(455,620,1158,885,886,1199)(459,675,1215,890,891,1284)(463,792,1301,894,895,1440)(464,615,937,897,884,484)(465,672,1190,900,889,614)(466,789,1280,902,893,673)(467,844,655,904,905,888)(469,1467,1599,808,909,1029)(474,1465,1615,807,919,974)(476,1009,1528,805,923,855)(480,1272,1361,666,929,2162)(487,1652,1654,942,943,1014)(488,1663,1664,946,947,1173)(491,1669,1670,951,952,1261)(495,1682,1684,960,961,1402)(499,1694,1634,966,967,987)(503,1711,873,976,977,868)(506,1446,1729,795,984,2355)(513,921,1290,991,992,1619)(517,1647,1689,940,1000,963)(520,1056,1512,874,1005,843)(525,1771,1449,1011,1012,2359)(529,1783,1635,1018,1019,931)(530,1793,1794,1022,1023,1229)(533,1800,1802,1026,1027,1359)(535,1808,875,1030,1031,867)(538,1418,1825,776,1038,2322)(546,1003,1273,1046,1047,1759)(548,1084,1483,876,1051,822)(553,1854,1422,1058,1059,1659)(556,1125,1346,1066,1067,720)(558,1379,1882,749,1072,2278)(563,1049,1249,1079,1080,1841)(566,1900,1384,1086,1087,1179)(568,1332,1914,709,1092,1929)(571,1926,1338,1099,1100,2082)(574,1175,737,1107,1108,1367)(575,1645,1620,1111,1112,2542)(578,1952,1953,1118,1119,2945)(582,1062,693,1129,1130,1313)(585,1981,1982,1136,1137,2985)(588,1159,1348,1144,1145,722)(596,1050,1385,1152,1153,1844)(600,1140,694,1163,1164,1316)(603,2031,2032,1170,1171,3048)(607,1101,1638,1177,1178,932)(608,2013,2046,1181,1182,1230)(611,2051,2053,1185,1186,1360)(618,1004,1423,1194,1195,1658)(621,1216,1350,1202,1203,724)(633,1198,696,1220,1221,1318)(636,2108,2109,1226,1227,3136)(641,1925,1777,1234,1128,1015)(642,2016,2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presentation:
2,3,67^2|c^67=d^66,c^a=c^66d,d^a=d^66,c^b=c^37d^11,d^b=d^37754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26934, 2);