D₁₆₈₂₉ #46777830

order	33658
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₈₂₉
unambiguous semidirect product	C₁₆₈₂₉⋊C₂

Splittings

Fitting, socle, derived, Sylow

C₁₆₈₂₉ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₆₈₂₉	C₂
LCS	G ▷ C₁₆₈₂₉
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16829
transitive degree	μ_t(G) = 16829

A minimal faithful permutation representation — 2 generators on 16829 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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702)(8130,8701)(8131,8700)(8132,8699)(8133,8698)(8134,8697)(8135,8696)(8136,8695)(8137,8694)(8138,8693)(8139,8692)(8140,8691)(8141,8690)(8142,8689)(8143,8688)(8144,8687)(8145,8686)(8146,8685)(8147,8684)(8148,8683)(8149,8682)(8150,8681)(8151,8680)(8152,8679)(8153,8678)(8154,8677)(8155,8676)(8156,8675)(8157,8674)(8158,8673)(8159,8672)(8160,8671)(8161,8670)(8162,8669)(8163,8668)(8164,8667)(8165,8666)(8166,8665)(8167,8664)(8168,8663)(8169,8662)(8170,8661)(8171,8660)(8172,8659)(8173,8658)(8174,8657)(8175,8656)(8176,8655)(8177,8654)(8178,8653)(8179,8652)(8180,8651)(8181,8650)(8182,8649)(8183,8648)(8184,8647)(8185,8646)(8186,8645)(8187,8644)(8188,8643)(8189,8642)(8190,8641)(8191,8640)(8192,8639)(8193,8638)(8194,8637)(8195,8636)(8196,8635)(8197,8634)(8198,8633)(8199,8632)(8200,8631)(8201,8630)(8202,8629)(8203,8628)(8204,8627)(8205,8626)(8206,8625)(8207,8624)(8208,8623)(8209,8622)(8210,8621)(8211,8620)(8212,8619)(8213,8618)(8214,8617)(8215,8616)(8216,8615)(8217,8614)(8218,8613)(8219,8612)(8220,8611)(8221,8610)(8222,8609)(8223,8608)(8224,8607)(8225,8606)(8226,8605)(8227,8604)(8228,8603)(8229,8602)(8230,8601)(8231,8600)(8232,8599)(8233,8598)(8234,8597)(8235,8596)(8236,8595)(8237,8594)(8238,8593)(8239,8592)(8240,8591)(8241,8590)(8242,8589)(8243,8588)(8244,8587)(8245,8586)(8246,8585)(8247,8584)(8248,8583)(8249,8582)(8250,8581)(8251,8580)(8252,8579)(8253,8578)(8254,8577)(8255,8576)(8256,8575)(8257,8574)(8258,8573)(8259,8572)(8260,8571)(8261,8570)(8262,8569)(8263,8568)(8264,8567)(8265,8566)(8266,8565)(8267,8564)(8268,8563)(8269,8562)(8270,8561)(8271,8560)(8272,8559)(8273,8558)(8274,8557)(8275,8556)(8276,8555)(8277,8554)(8278,8553)(8279,8552)(8280,8551)(8281,8550)(8282,8549)(8283,8548)(8284,8547)(8285,8546)(8286,8545)(8287,8544)(8288,8543)(8289,8542)(8290,8541)(8291,8540)(8292,8539)(8293,8538)(8294,8537)(8295,8536)(8296,8535)(8297,8534)(8298,8533)(8299,8532)(8300,8531)(8301,8530)(8302,8529)(8303,8528)(8304,8527)(8305,8526)(8306,8525)(8307,8524)(8308,8523)(8309,8522)(8310,8521)(8311,8520)(8312,8519)(8313,8518)(8314,8517)(8315,8516)(8316,8515)(8317,8514)(8318,8513)(8319,8512)(8320,8511)(8321,8510)(8322,8509)(8323,8508)(8324,8507)(8325,8506)(8326,8505)(8327,8504)(8328,8503)(8329,8502)(8330,8501)(8331,8500)(8332,8499)(8333,8498)(8334,8497)(8335,8496)(8336,8495)(8337,8494)(8338,8493)(8339,8492)(8340,8491)(8341,8490)(8342,8489)(8343,8488)(8344,8487)(8345,8486)(8346,8485)(8347,8484)(8348,8483)(8349,8482)(8350,8481)(8351,8480)(8352,8479)(8353,8478)(8354,8477)(8355,8476)(8356,8475)(8357,8474)(8358,8473)(8359,8472)(8360,8471)(8361,8470)(8362,8469)(8363,8468)(8364,8467)(8365,8466)(8366,8465)(8367,8464)(8368,8463)(8369,8462)(8370,8461)(8371,8460)(8372,8459)(8373,8458)(8374,8457)(8375,8456)(8376,8455)(8377,8454)(8378,8453)(8379,8452)(8380,8451)(8381,8450)(8382,8449)(8383,8448)(8384,8447)(8385,8446)(8386,8445)(8387,8444)(8388,8443)(8389,8442)(8390,8441)(8391,8440)(8392,8439)(8393,8438)(8394,8437)(8395,8436)(8396,8435)(8397,8434)(8398,8433)(8399,8432)(8400,8431)(8401,8430)(8402,8429)(8403,8428)(8404,8427)(8405,8426)(8406,8425)(8407,8424)(8408,8423)(8409,8422)(8410,8421)(8411,8420)(8412,8419)(8413,8418)(8414,8417)(8415,8416)

Polycyclic presentation:

2,16829|b^a=b^16828

Conjugacy classes & character table

8416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33658, 1);

D16829 #46777830