D₃₂₀₀₃ #71044809

order	64006
automorphism	Aut(G) order 1024160006
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral

D₃₂₀₀₃

Splittings

Fitting, socle, derived, Sylow

C₃₂₀₀₃ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₂₀₀₃	C₂
LCS	G ▷ C₃₂₀₀₃
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 32003
transitive degree	μ_t(G) = 32003

A minimal faithful permutation representation — 2 generators on 32003 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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220)(15786,16219)(15787,16218)(15788,16217)(15789,16216)(15790,16215)(15791,16214)(15792,16213)(15793,16212)(15794,16211)(15795,16210)(15796,16209)(15797,16208)(15798,16207)(15799,16206)(15800,16205)(15801,16204)(15802,16203)(15803,16202)(15804,16201)(15805,16200)(15806,16199)(15807,16198)(15808,16197)(15809,16196)(15810,16195)(15811,16194)(15812,16193)(15813,16192)(15814,16191)(15815,16190)(15816,16189)(15817,16188)(15818,16187)(15819,16186)(15820,16185)(15821,16184)(15822,16183)(15823,16182)(15824,16181)(15825,16180)(15826,16179)(15827,16178)(15828,16177)(15829,16176)(15830,16175)(15831,16174)(15832,16173)(15833,16172)(15834,16171)(15835,16170)(15836,16169)(15837,16168)(15838,16167)(15839,16166)(15840,16165)(15841,16164)(15842,16163)(15843,16162)(15844,16161)(15845,16160)(15846,16159)(15847,16158)(15848,16157)(15849,16156)(15850,16155)(15851,16154)(15852,16153)(15853,16152)(15854,16151)(15855,16150)(15856,16149)(15857,16148)(15858,16147)(15859,16146)(15860,16145)(15861,16144)(15862,16143)(15863,16142)(15864,16141)(15865,16140)(15866,16139)(15867,16138)(15868,16137)(15869,16136)(15870,16135)(15871,16134)(15872,16133)(15873,16132)(15874,16131)(15875,16130)(15876,16129)(15877,16128)(15878,16127)(15879,16126)(15880,16125)(15881,16124)(15882,16123)(15883,16122)(15884,16121)(15885,16120)(15886,16119)(15887,16118)(15888,16117)(15889,16116)(15890,16115)(15891,16114)(15892,16113)(15893,16112)(15894,16111)(15895,16110)(15896,16109)(15897,16108)(15898,16107)(15899,16106)(15900,16105)(15901,16104)(15902,16103)(15903,16102)(15904,16101)(15905,16100)(15906,16099)(15907,16098)(15908,16097)(15909,16096)(15910,16095)(15911,16094)(15912,16093)(15913,16092)(15914,16091)(15915,16090)(15916,16089)(15917,16088)(15918,16087)(15919,16086)(15920,16085)(15921,16084)(15922,16083)(15923,16082)(15924,16081)(15925,16080)(15926,16079)(15927,16078)(15928,16077)(15929,16076)(15930,16075)(15931,16074)(15932,16073)(15933,16072)(15934,16071)(15935,16070)(15936,16069)(15937,16068)(15938,16067)(15939,16066)(15940,16065)(15941,16064)(15942,16063)(15943,16062)(15944,16061)(15945,16060)(15946,16059)(15947,16058)(15948,16057)(15949,16056)(15950,16055)(15951,16054)(15952,16053)(15953,16052)(15954,16051)(15955,16050)(15956,16049)(15957,16048)(15958,16047)(15959,16046)(15960,16045)(15961,16044)(15962,16043)(15963,16042)(15964,16041)(15965,16040)(15966,16039)(15967,16038)(15968,16037)(15969,16036)(15970,16035)(15971,16034)(15972,16033)(15973,16032)(15974,16031)(15975,16030)(15976,16029)(15977,16028)(15978,16027)(15979,16026)(15980,16025)(15981,16024)(15982,16023)(15983,16022)(15984,16021)(15985,16020)(15986,16019)(15987,16018)(15988,16017)(15989,16016)(15990,16015)(15991,16014)(15992,16013)(15993,16012)(15994,16011)(15995,16010)(15996,16009)(15997,16008)(15998,16007)(15999,16006)(16000,16005)(16001,16004)(16002,16003)

Polycyclic presentation:

2,32003|b^a=b^32002

Conjugacy classes & character table

16003 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(64006, 1);

D32003 #71044809