C₃×D₅₈₇₃ #47976439

order	35238
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₅₈₇₃
unambiguous semidirect product	C₈₃₉⋊(C₃×D₇)

Splittings

Fitting, socle, Hall	C₃×C₇×C₈₃₉ ⋊ C₂
derived, Hall	C₇×C₈₃₉ ⋊ C₂×C₃
Hall	C₃×C₈₃₉ ⋊ D₇
Sylow	C₈₃₉ ⋊ C₃×D₇
Hall	C₃×C₇ ⋊ D₈₃₉
Sylow	C₇ ⋊ C₃×D₈₃₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₅₈₇₃
commutator, cosocle, hypocenter	C₇×C₈₃₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₈₃₉	C₂
LCS	G ▷ C₇×C₈₃₉
UCS	C₁ ◁ C₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 849
transitive degree	μ_t(G) = 17619

A minimal faithful permutation representation — 2 generators on 849 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);(5,10)(6,9)(7,8)(12,849)(13,848)(14,847)(15,846)(16,845)(17,844)(18,843)(19,842)(20,841)(21,840)(22,839)(23,838)(24,837)(25,836)(26,835)(27,834)(28,833)(29,832)(30,831)(31,830)(32,829)(33,828)(34,827)(35,826)(36,825)(37,824)(38,823)(39,822)(40,821)(41,820)(42,819)(43,818)(44,817)(45,816)(46,815)(47,814)(48,813)(49,812)(50,811)(51,810)(52,809)(53,808)(54,807)(55,806)(56,805)(57,804)(58,803)(59,802)(60,801)(61,800)(62,799)(63,798)(64,797)(65,796)(66,795)(67,794)(68,793)(69,792)(70,791)(71,790)(72,789)(73,788)(74,787)(75,786)(76,785)(77,784)(78,783)(79,782)(80,781)(81,780)(82,779)(83,778)(84,777)(85,776)(86,775)(87,774)(88,773)(89,772)(90,771)(91,770)(92,769)(93,768)(94,767)(95,766)(96,765)(97,764)(98,763)(99,762)(100,761)(101,760)(102,759)(103,758)(104,757)(105,756)(106,755)(107,754)(108,753)(109,752)(110,751)(111,750)(112,749)(113,748)(114,747)(115,746)(116,745)(117,744)(118,743)(119,742)(120,741)(121,740)(122,739)(123,738)(124,737)(125,736)(126,735)(127,734)(128,733)(129,732)(130,731)(131,730)(132,729)(133,728)(134,727)(135,726)(136,725)(137,724)(138,723)(139,722)(140,721)(141,720)(142,719)(143,718)(144,717)(145,716)(146,715)(147,714)(148,713)(149,712)(150,711)(151,710)(152,709)(153,708)(154,707)(155,706)(156,705)(157,704)(158,703)(159,702)(160,701)(161,700)(162,699)(163,698)(164,697)(165,696)(166,695)(167,694)(168,693)(169,692)(170,691)(171,690)(172,689)(173,688)(174,687)(175,686)(176,685)(177,684)(178,683)(179,682)(180,681)(181,680)(182,679)(183,678)(184,677)(185,676)(186,675)(187,674)(188,673)(189,672)(190,671)(191,670)(192,669)(193,668)(194,667)(195,666)(196,665)(197,664)(198,663)(199,662)(200,661)(201,660)(202,659)(203,658)(204,657)(205,656)(206,655)(207,654)(208,653)(209,652)(210,651)(211,650)(212,649)(213,648)(214,647)(215,646)(216,645)(217,644)(218,643)(219,642)(220,641)(221,640)(222,639)(223,638)(224,637)(225,636)(226,635)(227,634)(228,633)(229,632)(230,631)(231,630)(232,629)(233,628)(234,627)(235,626)(236,625)(237,624)(238,623)(239,622)(240,621)(241,620)(242,619)(243,618)(244,617)(245,616)(246,615)(247,614)(248,613)(249,612)(250,611)(251,610)(252,609)(253,608)(254,607)(255,606)(256,605)(257,604)(258,603)(259,602)(260,601)(261,600)(262,599)(263,598)(264,597)(265,596)(266,595)(267,594)(268,593)(269,592)(270,591)(271,590)(272,589)(273,588)(274,587)(275,586)(276,585)(277,584)(278,583)(279,582)(280,581)(281,580)(282,579)(283,578)(284,577)(285,576)(286,575)(287,574)(288,573)(289,572)(290,571)(291,570)(292,569)(293,568)(294,567)(295,566)(296,565)(297,564)(298,563)(299,562)(300,561)(301,560)(302,559)(303,558)(304,557)(305,556)(306,555)(307,554)(308,553)(309,552)(310,551)(311,550)(312,549)(313,548)(314,547)(315,546)(316,545)(317,544)(318,543)(319,542)(320,541)(321,540)(322,539)(323,538)(324,537)(325,536)(326,535)(327,534)(328,533)(329,532)(330,531)(331,530)(332,529)(333,528)(334,527)(335,526)(336,525)(337,524)(338,523)(339,522)(340,521)(341,520)(342,519)(343,518)(344,517)(345,516)(346,515)(347,514)(348,513)(349,512)(350,511)(351,510)(352,509)(353,508)(354,507)(355,506)(356,505)(357,504)(358,503)(359,502)(360,501)(361,500)(362,499)(363,498)(364,497)(365,496)(366,495)(367,494)(368,493)(369,492)(370,491)(371,490)(372,489)(373,488)(374,487)(375,486)(376,485)(377,484)(378,483)(379,482)(380,481)(381,480)(382,479)(383,478)(384,477)(385,476)(386,475)(387,474)(388,473)(389,472)(390,471)(391,470)(392,469)(393,468)(394,467)(395,466)(396,465)(397,464)(398,463)(399,462)(400,461)(401,460)(402,459)(403,458)(404,457)(405,456)(406,455)(407,454)(408,453)(409,452)(410,451)(411,450)(412,449)(413,448)(414,447)(415,446)(416,445)(417,444)(418,443)(419,442)(420,441)(421,440)(422,439)(423,438)(424,437)(425,436)(426,435)(427,434)(428,433)(429,432)(430,431)

Conjugacy classes & character table

8814 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35238, 5);

C3×D5873 #47976439