D₁₆₅₇₃ #45684107

order	33146
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₅₇₃
unambiguous semidirect product	C₁₆₅₇₃⋊C₂

Splittings

Fitting, socle, derived, Sylow

C₁₆₅₇₃ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₆₅₇₃	C₂
LCS	G ▷ C₁₆₅₇₃
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16573
transitive degree	μ_t(G) = 16573

A minimal faithful permutation representation — 2 generators on 16573 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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(7838,8737)(7839,8736)(7840,8735)(7841,8734)(7842,8733)(7843,8732)(7844,8731)(7845,8730)(7846,8729)(7847,8728)(7848,8727)(7849,8726)(7850,8725)(7851,8724)(7852,8723)(7853,8722)(7854,8721)(7855,8720)(7856,8719)(7857,8718)(7858,8717)(7859,8716)(7860,8715)(7861,8714)(7862,8713)(7863,8712)(7864,8711)(7865,8710)(7866,8709)(7867,8708)(7868,8707)(7869,8706)(7870,8705)(7871,8704)(7872,8703)(7873,8702)(7874,8701)(7875,8700)(7876,8699)(7877,8698)(7878,8697)(7879,8696)(7880,8695)(7881,8694)(7882,8693)(7883,8692)(7884,8691)(7885,8690)(7886,8689)(7887,8688)(7888,8687)(7889,8686)(7890,8685)(7891,8684)(7892,8683)(7893,8682)(7894,8681)(7895,8680)(7896,8679)(7897,8678)(7898,8677)(7899,8676)(7900,8675)(7901,8674)(7902,8673)(7903,8672)(7904,8671)(7905,8670)(7906,8669)(7907,8668)(7908,8667)(7909,8666)(7910,8665)(7911,8664)(7912,8663)(7913,8662)(7914,8661)(7915,8660)(7916,8659)(7917,8658)(7918,8657)(7919,8656)(7920,8655)(7921,8654)(7922,8653)(7923,8652)(7924,8651)(7925,8650)(7926,8649)(7927,8648)(7928,8647)(7929,8646)(7930,8645)(7931,8644)(7932,8643)(7933,8642)(7934,8641)(7935,8640)(7936,8639)(7937,8638)(7938,8637)(7939,8636)(7940,8635)(7941,8634)(7942,8633)(7943,8632)(7944,8631)(7945,8630)(7946,8629)(7947,8628)(7948,8627)(7949,8626)(7950,8625)(7951,8624)(7952,8623)(7953,8622)(7954,8621)(7955,8620)(7956,8619)(7957,8618)(7958,8617)(7959,8616)(7960,8615)(7961,8614)(7962,8613)(7963,8612)(7964,8611)(7965,8610)(7966,8609)(7967,8608)(7968,8607)(7969,8606)(7970,8605)(7971,8604)(7972,8603)(7973,8602)(7974,8601)(7975,8600)(7976,8599)(7977,8598)(7978,8597)(7979,8596)(7980,8595)(7981,8594)(7982,8593)(7983,8592)(7984,8591)(7985,8590)(7986,8589)(7987,8588)(7988,8587)(7989,8586)(7990,8585)(7991,8584)(7992,8583)(7993,8582)(7994,8581)(7995,8580)(7996,8579)(7997,8578)(7998,8577)(7999,8576)(8000,8575)(8001,8574)(8002,8573)(8003,8572)(8004,8571)(8005,8570)(8006,8569)(8007,8568)(8008,8567)(8009,8566)(8010,8565)(8011,8564)(8012,8563)(8013,8562)(8014,8561)(8015,8560)(8016,8559)(8017,8558)(8018,8557)(8019,8556)(8020,8555)(8021,8554)(8022,8553)(8023,8552)(8024,8551)(8025,8550)(8026,8549)(8027,8548)(8028,8547)(8029,8546)(8030,8545)(8031,8544)(8032,8543)(8033,8542)(8034,8541)(8035,8540)(8036,8539)(8037,8538)(8038,8537)(8039,8536)(8040,8535)(8041,8534)(8042,8533)(8043,8532)(8044,8531)(8045,8530)(8046,8529)(8047,8528)(8048,8527)(8049,8526)(8050,8525)(8051,8524)(8052,8523)(8053,8522)(8054,8521)(8055,8520)(8056,8519)(8057,8518)(8058,8517)(8059,8516)(8060,8515)(8061,8514)(8062,8513)(8063,8512)(8064,8511)(8065,8510)(8066,8509)(8067,8508)(8068,8507)(8069,8506)(8070,8505)(8071,8504)(8072,8503)(8073,8502)(8074,8501)(8075,8500)(8076,8499)(8077,8498)(8078,8497)(8079,8496)(8080,8495)(8081,8494)(8082,8493)(8083,8492)(8084,8491)(8085,8490)(8086,8489)(8087,8488)(8088,8487)(8089,8486)(8090,8485)(8091,8484)(8092,8483)(8093,8482)(8094,8481)(8095,8480)(8096,8479)(8097,8478)(8098,8477)(8099,8476)(8100,8475)(8101,8474)(8102,8473)(8103,8472)(8104,8471)(8105,8470)(8106,8469)(8107,8468)(8108,8467)(8109,8466)(8110,8465)(8111,8464)(8112,8463)(8113,8462)(8114,8461)(8115,8460)(8116,8459)(8117,8458)(8118,8457)(8119,8456)(8120,8455)(8121,8454)(8122,8453)(8123,8452)(8124,8451)(8125,8450)(8126,8449)(8127,8448)(8128,8447)(8129,8446)(8130,8445)(8131,8444)(8132,8443)(8133,8442)(8134,8441)(8135,8440)(8136,8439)(8137,8438)(8138,8437)(8139,8436)(8140,8435)(8141,8434)(8142,8433)(8143,8432)(8144,8431)(8145,8430)(8146,8429)(8147,8428)(8148,8427)(8149,8426)(8150,8425)(8151,8424)(8152,8423)(8153,8422)(8154,8421)(8155,8420)(8156,8419)(8157,8418)(8158,8417)(8159,8416)(8160,8415)(8161,8414)(8162,8413)(8163,8412)(8164,8411)(8165,8410)(8166,8409)(8167,8408)(8168,8407)(8169,8406)(8170,8405)(8171,8404)(8172,8403)(8173,8402)(8174,8401)(8175,8400)(8176,8399)(8177,8398)(8178,8397)(8179,8396)(8180,8395)(8181,8394)(8182,8393)(8183,8392)(8184,8391)(8185,8390)(8186,8389)(8187,8388)(8188,8387)(8189,8386)(8190,8385)(8191,8384)(8192,8383)(8193,8382)(8194,8381)(8195,8380)(8196,8379)(8197,8378)(8198,8377)(8199,8376)(8200,8375)(8201,8374)(8202,8373)(8203,8372)(8204,8371)(8205,8370)(8206,8369)(8207,8368)(8208,8367)(8209,8366)(8210,8365)(8211,8364)(8212,8363)(8213,8362)(8214,8361)(8215,8360)(8216,8359)(8217,8358)(8218,8357)(8219,8356)(8220,8355)(8221,8354)(8222,8353)(8223,8352)(8224,8351)(8225,8350)(8226,8349)(8227,8348)(8228,8347)(8229,8346)(8230,8345)(8231,8344)(8232,8343)(8233,8342)(8234,8341)(8235,8340)(8236,8339)(8237,8338)(8238,8337)(8239,8336)(8240,8335)(8241,8334)(8242,8333)(8243,8332)(8244,8331)(8245,8330)(8246,8329)(8247,8328)(8248,8327)(8249,8326)(8250,8325)(8251,8324)(8252,8323)(8253,8322)(8254,8321)(8255,8320)(8256,8319)(8257,8318)(8258,8317)(8259,8316)(8260,8315)(8261,8314)(8262,8313)(8263,8312)(8264,8311)(8265,8310)(8266,8309)(8267,8308)(8268,8307)(8269,8306)(8270,8305)(8271,8304)(8272,8303)(8273,8302)(8274,8301)(8275,8300)(8276,8299)(8277,8298)(8278,8297)(8279,8296)(8280,8295)(8281,8294)(8282,8293)(8283,8292)(8284,8291)(8285,8290)(8286,8289)(8287,8288)

Polycyclic presentation:

2,16573|b^a=b^16572

Conjugacy classes & character table

8288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33146, 1);

D16573 #45684107