Finite Group DatabasebetaFinite Group Databasebeta| order | 11632 |
| automorphism | Aut(G) order 16889664 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2908 |
| Sylow | C727 ⋊ Q16 |
18 conjugacy classes of subgroups.
| minimal degree | μ(G) = 743 |
| transitive degree | μt(G) = 11632 |
A minimal faithful permutation representation — 2 generators on 743 points:
(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(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);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,743)(19,742)(20,741)(21,740)(22,739)(23,738)(24,737)(25,736)(26,735)(27,734)(28,733)(29,732)(30,731)(31,730)(32,729)(33,728)(34,727)(35,726)(36,725)(37,724)(38,723)(39,722)(40,721)(41,720)(42,719)(43,718)(44,717)(45,716)(46,715)(47,714)(48,713)(49,712)(50,711)(51,710)(52,709)(53,708)(54,707)(55,706)(56,705)(57,704)(58,703)(59,702)(60,701)(61,700)(62,699)(63,698)(64,697)(65,696)(66,695)(67,694)(68,693)(69,692)(70,691)(71,690)(72,689)(73,688)(74,687)(75,686)(76,685)(77,684)(78,683)(79,682)(80,681)(81,680)(82,679)(83,678)(84,677)(85,676)(86,675)(87,674)(88,673)(89,672)(90,671)(91,670)(92,669)(93,668)(94,667)(95,666)(96,665)(97,664)(98,663)(99,662)(100,661)(101,660)(102,659)(103,658)(104,657)(105,656)(106,655)(107,654)(108,653)(109,652)(110,651)(111,650)(112,649)(113,648)(114,647)(115,646)(116,645)(117,644)(118,643)(119,642)(120,641)(121,640)(122,639)(123,638)(124,637)(125,636)(126,635)(127,634)(128,633)(129,632)(130,631)(131,630)(132,629)(133,628)(134,627)(135,626)(136,625)(137,624)(138,623)(139,622)(140,621)(141,620)(142,619)(143,618)(144,617)(145,616)(146,615)(147,614)(148,613)(149,612)(150,611)(151,610)(152,609)(153,608)(154,607)(155,606)(156,605)(157,604)(158,603)(159,602)(160,601)(161,600)(162,599)(163,598)(164,597)(165,596)(166,595)(167,594)(168,593)(169,592)(170,591)(171,590)(172,589)(173,588)(174,587)(175,586)(176,585)(177,584)(178,583)(179,582)(180,581)(181,580)(182,579)(183,578)(184,577)(185,576)(186,575)(187,574)(188,573)(189,572)(190,571)(191,570)(192,569)(193,568)(194,567)(195,566)(196,565)(197,564)(198,563)(199,562)(200,561)(201,560)(202,559)(203,558)(204,557)(205,556)(206,555)(207,554)(208,553)(209,552)(210,551)(211,550)(212,549)(213,548)(214,547)(215,546)(216,545)(217,544)(218,543)(219,542)(220,541)(221,540)(222,539)(223,538)(224,537)(225,536)(226,535)(227,534)(228,533)(229,532)(230,531)(231,530)(232,529)(233,528)(234,527)(235,526)(236,525)(237,524)(238,523)(239,522)(240,521)(241,520)(242,519)(243,518)(244,517)(245,516)(246,515)(247,514)(248,513)(249,512)(250,511)(251,510)(252,509)(253,508)(254,507)(255,506)(256,505)(257,504)(258,503)(259,502)(260,501)(261,500)(262,499)(263,498)(264,497)(265,496)(266,495)(267,494)(268,493)(269,492)(270,491)(271,490)(272,489)(273,488)(274,487)(275,486)(276,485)(277,484)(278,483)(279,482)(280,481)(281,480)(282,479)(283,478)(284,477)(285,476)(286,475)(287,474)(288,473)(289,472)(290,471)(291,470)(292,469)(293,468)(294,467)(295,466)(296,465)(297,464)(298,463)(299,462)(300,461)(301,460)(302,459)(303,458)(304,457)(305,456)(306,455)(307,454)(308,453)(309,452)(310,451)(311,450)(312,449)(313,448)(314,447)(315,446)(316,445)(317,444)(318,443)(319,442)(320,441)(321,440)(322,439)(323,438)(324,437)(325,436)(326,435)(327,434)(328,433)(329,432)(330,431)(331,430)(332,429)(333,428)(334,427)(335,426)(336,425)(337,424)(338,423)(339,422)(340,421)(341,420)(342,419)(343,418)(344,417)(345,416)(346,415)(347,414)(348,413)(349,412)(350,411)(351,410)(352,409)(353,408)(354,407)(355,406)(356,405)(357,404)(358,403)(359,402)(360,401)(361,400)(362,399)(363,398)(364,397)(365,396)(366,395)(367,394)(368,393)(369,392)(370,391)(371,390)(372,389)(373,388)(374,387)(375,386)(376,385)(377,384)(378,383)(379,382)(380,381)Polycyclic presentation:
2^4,727|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^726,c^b=cd,e^b=e^7262911 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37551492, #37551493, #37551494, … |
| maximal normal subgroup of | #37551492, #37551493, #37551494, … |
| maximal quotient of | #37551473, #37551482, C2×Dic2908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11632, 31);