Finite Group DatabasebetaFinite Group Databasebeta| order | 31974 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D5329⋊C3 |
| unambiguous semidirect product | (C5329⋊C3)⋊C2 |
| Fitting, derived, Sylow | C5329 ⋊ C2×C3 |
| Hall | C5329⋊C3 ⋊ C2 |
| Hall | D5329 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5329 | C2×C3 |
| Frattini, socle | C73 | D73⋊C3 |
| LCS | G ▷ C5329 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 5329 |
| transitive degree | μt(G) = 5329 |
A minimal faithful permutation representation — 2 generators on 5329 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)(77,401,403,180,181,792)(79,260,261,184,116,227)(80,290,291,187,127,303)(82,323,324,189,142,366)(84,420,205,192,193,202)(87,391,437,176,200,774)(91,103,258,206,207,229)(92,133,288,210,211,292)(95,165,321,213,214,328)(97,248,418,183,218,191)(101,475,393,224,225,778)(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)(117,547,351,263,264,710)(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)(146,685,686,333,334,1300)(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)(173,758,242,382,383,509)(174,196,311,386,387,428)(178,781,204,395,396,444)(182,405,768,343,406,803)(185,561,562,409,269,526)(186,591,592,412,280,604)(188,624,625,414,298,659)(190,679,680,416,331,767)(194,826,543,422,423,508)(198,845,446,432,433,443)(201,795,863,402,440,1454)(208,254,559,449,450,528)(209,286,589,453,454,606)(212,319,622,457,458,661)(215,389,677,461,462,769)(219,806,907,408,468,496)(222,521,842,407,473,430)(226,926,797,478,479,1458)(230,939,930,485,486,481)(231,949,950,489,490,637)(234,956,958,493,494,730)(236,964,447,497,498,442)(239,776,981,392,505,1426)(245,471,667,511,512,913)(247,549,821,448,516,419)(252,1007,779,523,524,1431)(255,590,718,531,532,357)(257,748,1035,375,537,1380)(262,514,649,544,545,994)(265,1054,752,551,552,1386)(267,706,1069,348,557,1085)(270,1082,711,564,565,1333)(273,1102,1104,572,573,1947)(274,1114,1115,576,577,1978)(277,1132,1133,583,584,2013)(281,527,337,594,595,692)(284,1166,1167,601,602,2073)(287,623,720,609,610,359)(295,515,753,616,617,997)(299,605,338,627,628,695)(302,1223,1224,634,635,2163)(305,1147,933,640,593,482)(306,1206,1209,643,626,638)(309,1243,1245,646,647,731)(314,500,539,652,653,970)(317,472,780,656,657,916)(320,678,722,664,665,361)(325,754,507,669,670,957)(332,660,340,682,683,697)(335,865,1310,689,690,1556)(345,925,791,701,477,750)(346,975,724,703,522,709)(352,861,862,691,439,742)(353,760,980,699,504,518)(356,1071,560,714,715,1075)(365,390,798,727,728,772)(368,1205,935,733,629,483)(369,1293,1233,736,684,639)(371,1368,1358,739,740,732)(373,856,725,743,744,708)(380,783,911,726,756,470)(384,1399,541,761,762,1042)(385,501,612,765,766,972)(397,1438,510,784,785,989)(398,755,650,788,789,1244)(404,1461,445,799,800,870)(410,1096,1097,809,570,1061)(411,1126,1127,812,581,1139)(413,1160,1161,814,599,1197)(415,1217,1218,816,632,1284)(417,1305,1306,818,687,1449)(421,847,854,700,824,820)(424,1500,1078,828,829,1041)(425,542,954,832,833,492)(427,613,1208,835,836,645)(429,668,1295,839,840,738)(434,1527,1045,848,849,988)(435,823,651,852,853,838)(438,1540,872,857,858,869)(441,688,1285,698,866,1308)(451,555,1094,877,878,1063)(452,587,1124,881,882,1141)(455,620,1158,885,886,1199)(459,675,1215,890,891,1286)(463,793,1303,894,895,1450)(464,615,937,897,884,484)(465,672,1190,900,889,614)(466,790,1282,902,893,673)(467,844,655,904,905,888)(469,1476,1604,808,909,1029)(474,1474,1625,807,919,974)(476,1009,1537,805,923,855)(480,1247,1409,648,929,2196)(487,1660,1662,942,943,1014)(488,1671,1672,946,947,1173)(491,1677,1678,951,952,1260)(495,1690,1692,960,961,1408)(499,1702,1642,966,967,987)(503,1719,873,976,977,868)(506,1456,1737,796,984,2461)(513,921,1292,991,992,1629)(517,1655,1697,940,1000,963)(520,1056,1521,874,1005,843)(525,1781,1459,1011,1012,2465)(529,1794,1643,1018,1019,931)(530,1804,1805,1022,1023,1230)(533,1811,1813,1026,1027,1355)(535,1819,875,1030,1031,867)(538,1428,1836,777,1038,2422)(546,1003,1275,1046,1047,1768)(548,1084,1492,876,1051,822)(553,1865,1432,1058,1059,2428)(556,1125,1341,1066,1067,717)(558,1382,1893,749,1072,2360)(563,1049,1248,1079,1080,1852)(566,1912,1387,1086,1087,2367)(568,1328,1927,707,1092,1943)(571,1940,1334,1099,1100,2305)(574,1960,1962,1107,1108,3180)(575,1971,1972,1111,1112,3193)(578,1989,1990,1118,1119,3225)(582,1062,693,1129,1130,1312)(585,2024,2025,1136,1137,3284)(588,1159,1343,1144,1145,719)(596,1050,1388,1152,1153,1855)(600,1140,694,1163,1164,1315)(603,2084,2085,1170,1171,3373)(607,2004,1646,1177,1178,932)(608,2064,2105,1181,1182,1231)(611,2110,2112,1185,1186,1356)(618,1004,1433,1194,1195,1771)(621,1216,1345,1202,1203,721)(633,1198,696,1220,1221,1317)(636,1739,2173,1227,1228,2832)(641,2007,1788,1235,1128,1015)(642,2067,2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presentation:
2,3,73^2|c^73=d^72,c^a=c^72d,d^a=d^72,c^b=c^8d^43,d^b=d^8894 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31974, 2);