D₁₇₃₂₃ #46831354

order	34646
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₃₂₃
unambiguous semidirect product	C₁₇⋊D₁₀₁₉
unambiguous semidirect product	C₁₀₁₉⋊D₁₇

Splittings

Fitting, socle, derived, Hall	C₁₇×C₁₀₁₉ ⋊ C₂
Sylow	C₁₀₁₉ ⋊ D₁₇
Sylow	C₁₇ ⋊ D₁₀₁₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₁₀₁₉	C₂
LCS	G ▷ C₁₇×C₁₀₁₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1036
transitive degree	μ_t(G) = 17323

A minimal faithful permutation representation — 2 generators on 1036 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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,1036)(20,1035)(21,1034)(22,1033)(23,1032)(24,1031)(25,1030)(26,1029)(27,1028)(28,1027)(29,1026)(30,1025)(31,1024)(32,1023)(33,1022)(34,1021)(35,1020)(36,1019)(37,1018)(38,1017)(39,1016)(40,1015)(41,1014)(42,1013)(43,1012)(44,1011)(45,1010)(46,1009)(47,1008)(48,1007)(49,1006)(50,1005)(51,1004)(52,1003)(53,1002)(54,1001)(55,1000)(56,999)(57,998)(58,997)(59,996)(60,995)(61,994)(62,993)(63,992)(64,991)(65,990)(66,989)(67,988)(68,987)(69,986)(70,985)(71,984)(72,983)(73,982)(74,981)(75,980)(76,979)(77,978)(78,977)(79,976)(80,975)(81,974)(82,973)(83,972)(84,971)(85,970)(86,969)(87,968)(88,967)(89,966)(90,965)(91,964)(92,963)(93,962)(94,961)(95,960)(96,959)(97,958)(98,957)(99,956)(100,955)(101,954)(102,953)(103,952)(104,951)(105,950)(106,949)(107,948)(108,947)(109,946)(110,945)(111,944)(112,943)(113,942)(114,941)(115,940)(116,939)(117,938)(118,937)(119,936)(120,935)(121,934)(122,933)(123,932)(124,931)(125,930)(126,929)(127,928)(128,927)(129,926)(130,925)(131,924)(132,923)(133,922)(134,921)(135,920)(136,919)(137,918)(138,917)(139,916)(140,915)(141,914)(142,913)(143,912)(144,911)(145,910)(146,909)(147,908)(148,907)(149,906)(150,905)(151,904)(152,903)(153,902)(154,901)(155,900)(156,899)(157,898)(158,897)(159,896)(160,895)(161,894)(162,893)(163,892)(164,891)(165,890)(166,889)(167,888)(168,887)(169,886)(170,885)(171,884)(172,883)(173,882)(174,881)(175,880)(176,879)(177,878)(178,877)(179,876)(180,875)(181,874)(182,873)(183,872)(184,871)(185,870)(186,869)(187,868)(188,867)(189,866)(190,865)(191,864)(192,863)(193,862)(194,861)(195,860)(196,859)(197,858)(198,857)(199,856)(200,855)(201,854)(202,853)(203,852)(204,851)(205,850)(206,849)(207,848)(208,847)(209,846)(210,845)(211,844)(212,843)(213,842)(214,841)(215,840)(216,839)(217,838)(218,837)(219,836)(220,835)(221,834)(222,833)(223,832)(224,831)(225,830)(226,829)(227,828)(228,827)(229,826)(230,825)(231,824)(232,823)(233,822)(234,821)(235,820)(236,819)(237,818)(238,817)(239,816)(240,815)(241,814)(242,813)(243,812)(244,811)(245,810)(246,809)(247,808)(248,807)(249,806)(250,805)(251,804)(252,803)(253,802)(254,801)(255,800)(256,799)(257,798)(258,797)(259,796)(260,795)(261,794)(262,793)(263,792)(264,791)(265,790)(266,789)(267,788)(268,787)(269,786)(270,785)(271,784)(272,783)(273,782)(274,781)(275,780)(276,779)(277,778)(278,777)(279,776)(280,775)(281,774)(282,773)(283,772)(284,771)(285,770)(286,769)(287,768)(288,767)(289,766)(290,765)(291,764)(292,763)(293,762)(294,761)(295,760)(296,759)(297,758)(298,757)(299,756)(300,755)(301,754)(302,753)(303,752)(304,751)(305,750)(306,749)(307,748)(308,747)(309,746)(310,745)(311,744)(312,743)(313,742)(314,741)(315,740)(316,739)(317,738)(318,737)(319,736)(320,735)(321,734)(322,733)(323,732)(324,731)(325,730)(326,729)(327,728)(328,727)(329,726)(330,725)(331,724)(332,723)(333,722)(334,721)(335,720)(336,719)(337,718)(338,717)(339,716)(340,715)(341,714)(342,713)(343,712)(344,711)(345,710)(346,709)(347,708)(348,707)(349,706)(350,705)(351,704)(352,703)(353,702)(354,701)(355,700)(356,699)(357,698)(358,697)(359,696)(360,695)(361,694)(362,693)(363,692)(364,691)(365,690)(366,689)(367,688)(368,687)(369,686)(370,685)(371,684)(372,683)(373,682)(374,681)(375,680)(376,679)(377,678)(378,677)(379,676)(380,675)(381,674)(382,673)(383,672)(384,671)(385,670)(386,669)(387,668)(388,667)(389,666)(390,665)(391,664)(392,663)(393,662)(394,661)(395,660)(396,659)(397,658)(398,657)(399,656)(400,655)(401,654)(402,653)(403,652)(404,651)(405,650)(406,649)(407,648)(408,647)(409,646)(410,645)(411,644)(412,643)(413,642)(414,641)(415,640)(416,639)(417,638)(418,637)(419,636)(420,635)(421,634)(422,633)(423,632)(424,631)(425,630)(426,629)(427,628)(428,627)(429,626)(430,625)(431,624)(432,623)(433,622)(434,621)(435,620)(436,619)(437,618)(438,617)(439,616)(440,615)(441,614)(442,613)(443,612)(444,611)(445,610)(446,609)(447,608)(448,607)(449,606)(450,605)(451,604)(452,603)(453,602)(454,601)(455,600)(456,599)(457,598)(458,597)(459,596)(460,595)(461,594)(462,593)(463,592)(464,591)(465,590)(466,589)(467,588)(468,587)(469,586)(470,585)(471,584)(472,583)(473,582)(474,581)(475,580)(476,579)(477,578)(478,577)(479,576)(480,575)(481,574)(482,573)(483,572)(484,571)(485,570)(486,569)(487,568)(488,567)(489,566)(490,565)(491,564)(492,563)(493,562)(494,561)(495,560)(496,559)(497,558)(498,557)(499,556)(500,555)(501,554)(502,553)(503,552)(504,551)(505,550)(506,549)(507,548)(508,547)(509,546)(510,545)(511,544)(512,543)(513,542)(514,541)(515,540)(516,539)(517,538)(518,537)(519,536)(520,535)(521,534)(522,533)(523,532)(524,531)(525,530)(526,529)(527,528)

Polycyclic presentation:

2,17,1019|b^a=b^16,c^a=c^1018

Conjugacy classes & character table

8663 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34646, 3);

D17323 #46831354