D₁₅₇₇₃ #44538754

order	31546
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₇₇₃
unambiguous semidirect product	C₁₅₇₇₃⋊C₂

Splittings

Fitting, socle, derived, Sylow

C₁₅₇₇₃ ⋊ C₂

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₅₇₇₃	C₂
LCS	G ▷ C₁₅₇₇₃
UCS	C₁

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 15773
transitive degree	μ_t(G) = 15773

A minimal faithful permutation representation — 2 generators on 15773 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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(7438,8337)(7439,8336)(7440,8335)(7441,8334)(7442,8333)(7443,8332)(7444,8331)(7445,8330)(7446,8329)(7447,8328)(7448,8327)(7449,8326)(7450,8325)(7451,8324)(7452,8323)(7453,8322)(7454,8321)(7455,8320)(7456,8319)(7457,8318)(7458,8317)(7459,8316)(7460,8315)(7461,8314)(7462,8313)(7463,8312)(7464,8311)(7465,8310)(7466,8309)(7467,8308)(7468,8307)(7469,8306)(7470,8305)(7471,8304)(7472,8303)(7473,8302)(7474,8301)(7475,8300)(7476,8299)(7477,8298)(7478,8297)(7479,8296)(7480,8295)(7481,8294)(7482,8293)(7483,8292)(7484,8291)(7485,8290)(7486,8289)(7487,8288)(7488,8287)(7489,8286)(7490,8285)(7491,8284)(7492,8283)(7493,8282)(7494,8281)(7495,8280)(7496,8279)(7497,8278)(7498,8277)(7499,8276)(7500,8275)(7501,8274)(7502,8273)(7503,8272)(7504,8271)(7505,8270)(7506,8269)(7507,8268)(7508,8267)(7509,8266)(7510,8265)(7511,8264)(7512,8263)(7513,8262)(7514,8261)(7515,8260)(7516,8259)(7517,8258)(7518,8257)(7519,8256)(7520,8255)(7521,8254)(7522,8253)(7523,8252)(7524,8251)(7525,8250)(7526,8249)(7527,8248)(7528,8247)(7529,8246)(7530,8245)(7531,8244)(7532,8243)(7533,8242)(7534,8241)(7535,8240)(7536,8239)(7537,8238)(7538,8237)(7539,8236)(7540,8235)(7541,8234)(7542,8233)(7543,8232)(7544,8231)(7545,8230)(7546,8229)(7547,8228)(7548,8227)(7549,8226)(7550,8225)(7551,8224)(7552,8223)(7553,8222)(7554,8221)(7555,8220)(7556,8219)(7557,8218)(7558,8217)(7559,8216)(7560,8215)(7561,8214)(7562,8213)(7563,8212)(7564,8211)(7565,8210)(7566,8209)(7567,8208)(7568,8207)(7569,8206)(7570,8205)(7571,8204)(7572,8203)(7573,8202)(7574,8201)(7575,8200)(7576,8199)(7577,8198)(7578,8197)(7579,8196)(7580,8195)(7581,8194)(7582,8193)(7583,8192)(7584,8191)(7585,8190)(7586,8189)(7587,8188)(7588,8187)(7589,8186)(7590,8185)(7591,8184)(7592,8183)(7593,8182)(7594,8181)(7595,8180)(7596,8179)(7597,8178)(7598,8177)(7599,8176)(7600,8175)(7601,8174)(7602,8173)(7603,8172)(7604,8171)(7605,8170)(7606,8169)(7607,8168)(7608,8167)(7609,8166)(7610,8165)(7611,8164)(7612,8163)(7613,8162)(7614,8161)(7615,8160)(7616,8159)(7617,8158)(7618,8157)(7619,8156)(7620,8155)(7621,8154)(7622,8153)(7623,8152)(7624,8151)(7625,8150)(7626,8149)(7627,8148)(7628,8147)(7629,8146)(7630,8145)(7631,8144)(7632,8143)(7633,8142)(7634,8141)(7635,8140)(7636,8139)(7637,8138)(7638,8137)(7639,8136)(7640,8135)(7641,8134)(7642,8133)(7643,8132)(7644,8131)(7645,8130)(7646,8129)(7647,8128)(7648,8127)(7649,8126)(7650,8125)(7651,8124)(7652,8123)(7653,8122)(7654,8121)(7655,8120)(7656,8119)(7657,8118)(7658,8117)(7659,8116)(7660,8115)(7661,8114)(7662,8113)(7663,8112)(7664,8111)(7665,8110)(7666,8109)(7667,8108)(7668,8107)(7669,8106)(7670,8105)(7671,8104)(7672,8103)(7673,8102)(7674,8101)(7675,8100)(7676,8099)(7677,8098)(7678,8097)(7679,8096)(7680,8095)(7681,8094)(7682,8093)(7683,8092)(7684,8091)(7685,8090)(7686,8089)(7687,8088)(7688,8087)(7689,8086)(7690,8085)(7691,8084)(7692,8083)(7693,8082)(7694,8081)(7695,8080)(7696,8079)(7697,8078)(7698,8077)(7699,8076)(7700,8075)(7701,8074)(7702,8073)(7703,8072)(7704,8071)(7705,8070)(7706,8069)(7707,8068)(7708,8067)(7709,8066)(7710,8065)(7711,8064)(7712,8063)(7713,8062)(7714,8061)(7715,8060)(7716,8059)(7717,8058)(7718,8057)(7719,8056)(7720,8055)(7721,8054)(7722,8053)(7723,8052)(7724,8051)(7725,8050)(7726,8049)(7727,8048)(7728,8047)(7729,8046)(7730,8045)(7731,8044)(7732,8043)(7733,8042)(7734,8041)(7735,8040)(7736,8039)(7737,8038)(7738,8037)(7739,8036)(7740,8035)(7741,8034)(7742,8033)(7743,8032)(7744,8031)(7745,8030)(7746,8029)(7747,8028)(7748,8027)(7749,8026)(7750,8025)(7751,8024)(7752,8023)(7753,8022)(7754,8021)(7755,8020)(7756,8019)(7757,8018)(7758,8017)(7759,8016)(7760,8015)(7761,8014)(7762,8013)(7763,8012)(7764,8011)(7765,8010)(7766,8009)(7767,8008)(7768,8007)(7769,8006)(7770,8005)(7771,8004)(7772,8003)(7773,8002)(7774,8001)(7775,8000)(7776,7999)(7777,7998)(7778,7997)(7779,7996)(7780,7995)(7781,7994)(7782,7993)(7783,7992)(7784,7991)(7785,7990)(7786,7989)(7787,7988)(7788,7987)(7789,7986)(7790,7985)(7791,7984)(7792,7983)(7793,7982)(7794,7981)(7795,7980)(7796,7979)(7797,7978)(7798,7977)(7799,7976)(7800,7975)(7801,7974)(7802,7973)(7803,7972)(7804,7971)(7805,7970)(7806,7969)(7807,7968)(7808,7967)(7809,7966)(7810,7965)(7811,7964)(7812,7963)(7813,7962)(7814,7961)(7815,7960)(7816,7959)(7817,7958)(7818,7957)(7819,7956)(7820,7955)(7821,7954)(7822,7953)(7823,7952)(7824,7951)(7825,7950)(7826,7949)(7827,7948)(7828,7947)(7829,7946)(7830,7945)(7831,7944)(7832,7943)(7833,7942)(7834,7941)(7835,7940)(7836,7939)(7837,7938)(7838,7937)(7839,7936)(7840,7935)(7841,7934)(7842,7933)(7843,7932)(7844,7931)(7845,7930)(7846,7929)(7847,7928)(7848,7927)(7849,7926)(7850,7925)(7851,7924)(7852,7923)(7853,7922)(7854,7921)(7855,7920)(7856,7919)(7857,7918)(7858,7917)(7859,7916)(7860,7915)(7861,7914)(7862,7913)(7863,7912)(7864,7911)(7865,7910)(7866,7909)(7867,7908)(7868,7907)(7869,7906)(7870,7905)(7871,7904)(7872,7903)(7873,7902)(7874,7901)(7875,7900)(7876,7899)(7877,7898)(7878,7897)(7879,7896)(7880,7895)(7881,7894)(7882,7893)(7883,7892)(7884,7891)(7885,7890)(7886,7889)(7887,7888)

Polycyclic presentation:

2,15773|b^a=b^15772

Conjugacy classes & character table

7888 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31546, 1);

D15773 #44538754