Finite Group DatabasebetaFinite Group Databasebeta| order | 34546 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17273 |
| unambiguous semidirect product | C23⋊D751 |
| unambiguous semidirect product | C751⋊D23 |
| Fitting, socle, derived, Hall | C23×C751 ⋊ C2 |
| Sylow | C751 ⋊ D23 |
| Sylow | C23 ⋊ D751 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C751 | C2 |
| LCS | G ▷ C23×C751 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 774 |
| transitive degree | μt(G) = 17273 |
A minimal faithful permutation representation — 2 generators on 774 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);(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(25,774)(26,773)(27,772)(28,771)(29,770)(30,769)(31,768)(32,767)(33,766)(34,765)(35,764)(36,763)(37,762)(38,761)(39,760)(40,759)(41,758)(42,757)(43,756)(44,755)(45,754)(46,753)(47,752)(48,751)(49,750)(50,749)(51,748)(52,747)(53,746)(54,745)(55,744)(56,743)(57,742)(58,741)(59,740)(60,739)(61,738)(62,737)(63,736)(64,735)(65,734)(66,733)(67,732)(68,731)(69,730)(70,729)(71,728)(72,727)(73,726)(74,725)(75,724)(76,723)(77,722)(78,721)(79,720)(80,719)(81,718)(82,717)(83,716)(84,715)(85,714)(86,713)(87,712)(88,711)(89,710)(90,709)(91,708)(92,707)(93,706)(94,705)(95,704)(96,703)(97,702)(98,701)(99,700)(100,699)(101,698)(102,697)(103,696)(104,695)(105,694)(106,693)(107,692)(108,691)(109,690)(110,689)(111,688)(112,687)(113,686)(114,685)(115,684)(116,683)(117,682)(118,681)(119,680)(120,679)(121,678)(122,677)(123,676)(124,675)(125,674)(126,673)(127,672)(128,671)(129,670)(130,669)(131,668)(132,667)(133,666)(134,665)(135,664)(136,663)(137,662)(138,661)(139,660)(140,659)(141,658)(142,657)(143,656)(144,655)(145,654)(146,653)(147,652)(148,651)(149,650)(150,649)(151,648)(152,647)(153,646)(154,645)(155,644)(156,643)(157,642)(158,641)(159,640)(160,639)(161,638)(162,637)(163,636)(164,635)(165,634)(166,633)(167,632)(168,631)(169,630)(170,629)(171,628)(172,627)(173,626)(174,625)(175,624)(176,623)(177,622)(178,621)(179,620)(180,619)(181,618)(182,617)(183,616)(184,615)(185,614)(186,613)(187,612)(188,611)(189,610)(190,609)(191,608)(192,607)(193,606)(194,605)(195,604)(196,603)(197,602)(198,601)(199,600)(200,599)(201,598)(202,597)(203,596)(204,595)(205,594)(206,593)(207,592)(208,591)(209,590)(210,589)(211,588)(212,587)(213,586)(214,585)(215,584)(216,583)(217,582)(218,581)(219,580)(220,579)(221,578)(222,577)(223,576)(224,575)(225,574)(226,573)(227,572)(228,571)(229,570)(230,569)(231,568)(232,567)(233,566)(234,565)(235,564)(236,563)(237,562)(238,561)(239,560)(240,559)(241,558)(242,557)(243,556)(244,555)(245,554)(246,553)(247,552)(248,551)(249,550)(250,549)(251,548)(252,547)(253,546)(254,545)(255,544)(256,543)(257,542)(258,541)(259,540)(260,539)(261,538)(262,537)(263,536)(264,535)(265,534)(266,533)(267,532)(268,531)(269,530)(270,529)(271,528)(272,527)(273,526)(274,525)(275,524)(276,523)(277,522)(278,521)(279,520)(280,519)(281,518)(282,517)(283,516)(284,515)(285,514)(286,513)(287,512)(288,511)(289,510)(290,509)(291,508)(292,507)(293,506)(294,505)(295,504)(296,503)(297,502)(298,501)(299,500)(300,499)(301,498)(302,497)(303,496)(304,495)(305,494)(306,493)(307,492)(308,491)(309,490)(310,489)(311,488)(312,487)(313,486)(314,485)(315,484)(316,483)(317,482)(318,481)(319,480)(320,479)(321,478)(322,477)(323,476)(324,475)(325,474)(326,473)(327,472)(328,471)(329,470)(330,469)(331,468)(332,467)(333,466)(334,465)(335,464)(336,463)(337,462)(338,461)(339,460)(340,459)(341,458)(342,457)(343,456)(344,455)(345,454)(346,453)(347,452)(348,451)(349,450)(350,449)(351,448)(352,447)(353,446)(354,445)(355,444)(356,443)(357,442)(358,441)(359,440)(360,439)(361,438)(362,437)(363,436)(364,435)(365,434)(366,433)(367,432)(368,431)(369,430)(370,429)(371,428)(372,427)(373,426)(374,425)(375,424)(376,423)(377,422)(378,421)(379,420)(380,419)(381,418)(382,417)(383,416)(384,415)(385,414)(386,413)(387,412)(388,411)(389,410)(390,409)(391,408)(392,407)(393,406)(394,405)(395,404)(396,403)(397,402)(398,401)(399,400)Polycyclic presentation:
2,23,751|b^a=b^22,c^a=c^7508638 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34546, 3);