Polytope of Type {14,8,8} with group SmallGroup(1792,150681)

Overview

Group: SmallGroup(1792,150681)
Rank: 4
Schläfli Type: {14,8,8}
Vertices, edges, …: 14, 56, 32, 8
Order of s₀s₁s₂s₃: 56
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

{14,4,4}*448

7-fold

{2,8,8}*256d

8-fold

14-fold

16-fold

28-fold

{2,4,4}*64

32-fold

{7,2,2}*56

56-fold

112-fold

{2,2,2}*16

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  1,113)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)(  8,120)(  9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)( 16,133)( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)( 24,139)( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)( 32,145)( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)( 40,151)( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)( 57,169)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)( 64,176)( 65,182)( 66,181)( 67,180)( 68,179)( 69,178)( 70,177)( 71,183)( 72,189)( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,190)( 79,196)( 80,195)( 81,194)( 82,193)( 83,192)( 84,191)( 85,197)( 86,203)( 87,202)( 88,201)( 89,200)( 90,199)( 91,198)( 92,204)( 93,210)( 94,209)( 95,208)( 96,207)( 97,206)( 98,205)( 99,211)(100,217)(101,216)(102,215)(103,214)(104,213)(105,212)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)(112,219)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)(248,363)(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)(256,369)(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)(264,375)(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)(272,381)(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)(281,393)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)(288,400)(289,406)(290,405)(291,404)(292,403)(293,402)(294,401)(295,407)(296,413)(297,412)(298,411)(299,410)(300,409)(301,408)(302,414)(303,420)(304,419)(305,418)(306,417)(307,416)(308,415)(309,421)(310,427)(311,426)(312,425)(313,424)(314,423)(315,422)(316,428)(317,434)(318,433)(319,432)(320,431)(321,430)(322,429)(323,435)(324,441)(325,440)(326,439)(327,438)(328,437)(329,436)(330,442)(331,448)(332,447)(333,446)(334,445)(335,444)(336,443)(449,561)(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)(457,574)(458,573)(459,572)(460,571)(461,570)(462,569)(463,575)(464,581)(465,580)(466,579)(467,578)(468,577)(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)(476,583)(477,589)(478,595)(479,594)(480,593)(481,592)(482,591)(483,590)(484,596)(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(491,603)(492,609)(493,608)(494,607)(495,606)(496,605)(497,604)(498,610)(499,616)(500,615)(501,614)(502,613)(503,612)(504,611)(505,617)(506,623)(507,622)(508,621)(509,620)(510,619)(511,618)(512,624)(513,630)(514,629)(515,628)(516,627)(517,626)(518,625)(519,631)(520,637)(521,636)(522,635)(523,634)(524,633)(525,632)(526,638)(527,644)(528,643)(529,642)(530,641)(531,640)(532,639)(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)(540,652)(541,658)(542,657)(543,656)(544,655)(545,654)(546,653)(547,659)(548,665)(549,664)(550,663)(551,662)(552,661)(553,660)(554,666)(555,672)(556,671)(557,670)(558,669)(559,668)(560,667)(673,785)(674,791)(675,790)(676,789)(677,788)(678,787)(679,786)(680,792)(681,798)(682,797)(683,796)(684,795)(685,794)(686,793)(687,799)(688,805)(689,804)(690,803)(691,802)(692,801)(693,800)(694,806)(695,812)(696,811)(697,810)(698,809)(699,808)(700,807)(701,813)(702,819)(703,818)(704,817)(705,816)(706,815)(707,814)(708,820)(709,826)(710,825)(711,824)(712,823)(713,822)(714,821)(715,827)(716,833)(717,832)(718,831)(719,830)(720,829)(721,828)(722,834)(723,840)(724,839)(725,838)(726,837)(727,836)(728,835)(729,841)(730,847)(731,846)(732,845)(733,844)(734,843)(735,842)(736,848)(737,854)(738,853)(739,852)(740,851)(741,850)(742,849)(743,855)(744,861)(745,860)(746,859)(747,858)(748,857)(749,856)(750,862)(751,868)(752,867)(753,866)(754,865)(755,864)(756,863)(757,869)(758,875)(759,874)(760,873)(761,872)(762,871)(763,870)(764,876)(765,882)(766,881)(767,880)(768,879)(769,878)(770,877)(771,883)(772,889)(773,888)(774,887)(775,886)(776,885)(777,884)(778,890)(779,896)(780,895)(781,894)(782,893)(783,892)(784,891);;
s1 := (  1,338)(  2,337)(  3,343)(  4,342)(  5,341)(  6,340)(  7,339)(  8,345)(  9,344)( 10,350)( 11,349)( 12,348)( 13,347)( 14,346)( 15,352)( 16,351)( 17,357)( 18,356)( 19,355)( 20,354)( 21,353)( 22,359)( 23,358)( 24,364)( 25,363)( 26,362)( 27,361)( 28,360)( 29,387)( 30,386)( 31,392)( 32,391)( 33,390)( 34,389)( 35,388)( 36,380)( 37,379)( 38,385)( 39,384)( 40,383)( 41,382)( 42,381)( 43,373)( 44,372)( 45,378)( 46,377)( 47,376)( 48,375)( 49,374)( 50,366)( 51,365)( 52,371)( 53,370)( 54,369)( 55,368)( 56,367)( 57,401)( 58,400)( 59,406)( 60,405)( 61,404)( 62,403)( 63,402)( 64,394)( 65,393)( 66,399)( 67,398)( 68,397)( 69,396)( 70,395)( 71,415)( 72,414)( 73,420)( 74,419)( 75,418)( 76,417)( 77,416)( 78,408)( 79,407)( 80,413)( 81,412)( 82,411)( 83,410)( 84,409)( 85,436)( 86,435)( 87,441)( 88,440)( 89,439)( 90,438)( 91,437)( 92,443)( 93,442)( 94,448)( 95,447)( 96,446)( 97,445)( 98,444)( 99,422)(100,421)(101,427)(102,426)(103,425)(104,424)(105,423)(106,429)(107,428)(108,434)(109,433)(110,432)(111,431)(112,430)(113,226)(114,225)(115,231)(116,230)(117,229)(118,228)(119,227)(120,233)(121,232)(122,238)(123,237)(124,236)(125,235)(126,234)(127,240)(128,239)(129,245)(130,244)(131,243)(132,242)(133,241)(134,247)(135,246)(136,252)(137,251)(138,250)(139,249)(140,248)(141,275)(142,274)(143,280)(144,279)(145,278)(146,277)(147,276)(148,268)(149,267)(150,273)(151,272)(152,271)(153,270)(154,269)(155,261)(156,260)(157,266)(158,265)(159,264)(160,263)(161,262)(162,254)(163,253)(164,259)(165,258)(166,257)(167,256)(168,255)(169,289)(170,288)(171,294)(172,293)(173,292)(174,291)(175,290)(176,282)(177,281)(178,287)(179,286)(180,285)(181,284)(182,283)(183,303)(184,302)(185,308)(186,307)(187,306)(188,305)(189,304)(190,296)(191,295)(192,301)(193,300)(194,299)(195,298)(196,297)(197,324)(198,323)(199,329)(200,328)(201,327)(202,326)(203,325)(204,331)(205,330)(206,336)(207,335)(208,334)(209,333)(210,332)(211,310)(212,309)(213,315)(214,314)(215,313)(216,312)(217,311)(218,317)(219,316)(220,322)(221,321)(222,320)(223,319)(224,318)(449,786)(450,785)(451,791)(452,790)(453,789)(454,788)(455,787)(456,793)(457,792)(458,798)(459,797)(460,796)(461,795)(462,794)(463,800)(464,799)(465,805)(466,804)(467,803)(468,802)(469,801)(470,807)(471,806)(472,812)(473,811)(474,810)(475,809)(476,808)(477,835)(478,834)(479,840)(480,839)(481,838)(482,837)(483,836)(484,828)(485,827)(486,833)(487,832)(488,831)(489,830)(490,829)(491,821)(492,820)(493,826)(494,825)(495,824)(496,823)(497,822)(498,814)(499,813)(500,819)(501,818)(502,817)(503,816)(504,815)(505,849)(506,848)(507,854)(508,853)(509,852)(510,851)(511,850)(512,842)(513,841)(514,847)(515,846)(516,845)(517,844)(518,843)(519,863)(520,862)(521,868)(522,867)(523,866)(524,865)(525,864)(526,856)(527,855)(528,861)(529,860)(530,859)(531,858)(532,857)(533,884)(534,883)(535,889)(536,888)(537,887)(538,886)(539,885)(540,891)(541,890)(542,896)(543,895)(544,894)(545,893)(546,892)(547,870)(548,869)(549,875)(550,874)(551,873)(552,872)(553,871)(554,877)(555,876)(556,882)(557,881)(558,880)(559,879)(560,878)(561,674)(562,673)(563,679)(564,678)(565,677)(566,676)(567,675)(568,681)(569,680)(570,686)(571,685)(572,684)(573,683)(574,682)(575,688)(576,687)(577,693)(578,692)(579,691)(580,690)(581,689)(582,695)(583,694)(584,700)(585,699)(586,698)(587,697)(588,696)(589,723)(590,722)(591,728)(592,727)(593,726)(594,725)(595,724)(596,716)(597,715)(598,721)(599,720)(600,719)(601,718)(602,717)(603,709)(604,708)(605,714)(606,713)(607,712)(608,711)(609,710)(610,702)(611,701)(612,707)(613,706)(614,705)(615,704)(616,703)(617,737)(618,736)(619,742)(620,741)(621,740)(622,739)(623,738)(624,730)(625,729)(626,735)(627,734)(628,733)(629,732)(630,731)(631,751)(632,750)(633,756)(634,755)(635,754)(636,753)(637,752)(638,744)(639,743)(640,749)(641,748)(642,747)(643,746)(644,745)(645,772)(646,771)(647,777)(648,776)(649,775)(650,774)(651,773)(652,779)(653,778)(654,784)(655,783)(656,782)(657,781)(658,780)(659,758)(660,757)(661,763)(662,762)(663,761)(664,760)(665,759)(666,765)(667,764)(668,770)(669,769)(670,768)(671,767)(672,766);;
s2 := ( 29, 50)( 30, 51)( 31, 52)( 32, 53)( 33, 54)( 34, 55)( 35, 56)( 36, 43)( 37, 44)( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 57, 71)( 58, 72)( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 92)( 86, 93)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,204)(198,205)(199,206)(200,207)(201,208)(202,209)(203,210)(211,218)(212,219)(213,220)(214,221)(215,222)(216,223)(217,224)(225,253)(226,254)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)(281,323)(282,324)(283,325)(284,326)(285,327)(286,328)(287,329)(288,330)(289,331)(290,332)(291,333)(292,334)(293,335)(294,336)(295,309)(296,310)(297,311)(298,312)(299,313)(300,314)(301,315)(302,316)(303,317)(304,318)(305,319)(306,320)(307,321)(308,322)(337,365)(338,366)(339,367)(340,368)(341,369)(342,370)(343,371)(344,372)(345,373)(346,374)(347,375)(348,376)(349,377)(350,378)(351,379)(352,380)(353,381)(354,382)(355,383)(356,384)(357,385)(358,386)(359,387)(360,388)(361,389)(362,390)(363,391)(364,392)(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)(420,434)(449,505)(450,506)(451,507)(452,508)(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)(460,516)(461,517)(462,518)(463,519)(464,520)(465,521)(466,522)(467,523)(468,524)(469,525)(470,526)(471,527)(472,528)(473,529)(474,530)(475,531)(476,532)(477,554)(478,555)(479,556)(480,557)(481,558)(482,559)(483,560)(484,547)(485,548)(486,549)(487,550)(488,551)(489,552)(490,553)(491,540)(492,541)(493,542)(494,543)(495,544)(496,545)(497,546)(498,533)(499,534)(500,535)(501,536)(502,537)(503,538)(504,539)(561,617)(562,618)(563,619)(564,620)(565,621)(566,622)(567,623)(568,624)(569,625)(570,626)(571,627)(572,628)(573,629)(574,630)(575,631)(576,632)(577,633)(578,634)(579,635)(580,636)(581,637)(582,638)(583,639)(584,640)(585,641)(586,642)(587,643)(588,644)(589,666)(590,667)(591,668)(592,669)(593,670)(594,671)(595,672)(596,659)(597,660)(598,661)(599,662)(600,663)(601,664)(602,665)(603,652)(604,653)(605,654)(606,655)(607,656)(608,657)(609,658)(610,645)(611,646)(612,647)(613,648)(614,649)(615,650)(616,651)(673,764)(674,765)(675,766)(676,767)(677,768)(678,769)(679,770)(680,757)(681,758)(682,759)(683,760)(684,761)(685,762)(686,763)(687,778)(688,779)(689,780)(690,781)(691,782)(692,783)(693,784)(694,771)(695,772)(696,773)(697,774)(698,775)(699,776)(700,777)(701,736)(702,737)(703,738)(704,739)(705,740)(706,741)(707,742)(708,729)(709,730)(710,731)(711,732)(712,733)(713,734)(714,735)(715,750)(716,751)(717,752)(718,753)(719,754)(720,755)(721,756)(722,743)(723,744)(724,745)(725,746)(726,747)(727,748)(728,749)(785,876)(786,877)(787,878)(788,879)(789,880)(790,881)(791,882)(792,869)(793,870)(794,871)(795,872)(796,873)(797,874)(798,875)(799,890)(800,891)(801,892)(802,893)(803,894)(804,895)(805,896)(806,883)(807,884)(808,885)(809,886)(810,887)(811,888)(812,889)(813,848)(814,849)(815,850)(816,851)(817,852)(818,853)(819,854)(820,841)(821,842)(822,843)(823,844)(824,845)(825,846)(826,847)(827,862)(828,863)(829,864)(830,865)(831,866)(832,867)(833,868)(834,855)(835,856)(836,857)(837,858)(838,859)(839,860)(840,861);;
s3 := (  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)(  8,456)(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,463)( 16,464)( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)( 24,472)( 25,473)( 26,474)( 27,475)( 28,476)( 29,484)( 30,485)( 31,486)( 32,487)( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)( 40,481)( 41,482)( 42,483)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)( 48,503)( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)( 56,497)( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)( 64,526)( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)( 72,506)( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)( 80,514)( 81,515)( 82,516)( 83,517)( 84,518)( 85,554)( 86,555)( 87,556)( 88,557)( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)( 96,551)( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)(112,539)(113,561)(114,562)(115,563)(116,564)(117,565)(118,566)(119,567)(120,568)(121,569)(122,570)(123,571)(124,572)(125,573)(126,574)(127,575)(128,576)(129,577)(130,578)(131,579)(132,580)(133,581)(134,582)(135,583)(136,584)(137,585)(138,586)(139,587)(140,588)(141,596)(142,597)(143,598)(144,599)(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)(152,593)(153,594)(154,595)(155,610)(156,611)(157,612)(158,613)(159,614)(160,615)(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)(168,609)(169,631)(170,632)(171,633)(172,634)(173,635)(174,636)(175,637)(176,638)(177,639)(178,640)(179,641)(180,642)(181,643)(182,644)(183,617)(184,618)(185,619)(186,620)(187,621)(188,622)(189,623)(190,624)(191,625)(192,626)(193,627)(194,628)(195,629)(196,630)(197,666)(198,667)(199,668)(200,669)(201,670)(202,671)(203,672)(204,659)(205,660)(206,661)(207,662)(208,663)(209,664)(210,665)(211,652)(212,653)(213,654)(214,655)(215,656)(216,657)(217,658)(218,645)(219,646)(220,647)(221,648)(222,649)(223,650)(224,651)(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)(232,680)(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,687)(240,688)(241,689)(242,690)(243,691)(244,692)(245,693)(246,694)(247,695)(248,696)(249,697)(250,698)(251,699)(252,700)(253,708)(254,709)(255,710)(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)(288,750)(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)(296,730)(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)(304,738)(305,739)(306,740)(307,741)(308,742)(309,778)(310,779)(311,780)(312,781)(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)(320,775)(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)(328,769)(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)(336,763)(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)(344,792)(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,799)(352,800)(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)(360,808)(361,809)(362,810)(363,811)(364,812)(365,820)(366,821)(367,822)(368,823)(369,824)(370,825)(371,826)(372,813)(373,814)(374,815)(375,816)(376,817)(377,818)(378,819)(379,834)(380,835)(381,836)(382,837)(383,838)(384,839)(385,840)(386,827)(387,828)(388,829)(389,830)(390,831)(391,832)(392,833)(393,855)(394,856)(395,857)(396,858)(397,859)(398,860)(399,861)(400,862)(401,863)(402,864)(403,865)(404,866)(405,867)(406,868)(407,841)(408,842)(409,843)(410,844)(411,845)(412,846)(413,847)(414,848)(415,849)(416,850)(417,851)(418,852)(419,853)(420,854)(421,890)(422,891)(423,892)(424,893)(425,894)(426,895)(427,896)(428,883)(429,884)(430,885)(431,886)(432,887)(433,888)(434,889)(435,876)(436,877)(437,878)(438,879)(439,880)(440,881)(441,882)(442,869)(443,870)(444,871)(445,872)(446,873)(447,874)(448,875);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(896)!(  1,113)(  2,119)(  3,118)(  4,117)(  5,116)(  6,115)(  7,114)(  8,120)(  9,126)( 10,125)( 11,124)( 12,123)( 13,122)( 14,121)( 15,127)( 16,133)( 17,132)( 18,131)( 19,130)( 20,129)( 21,128)( 22,134)( 23,140)( 24,139)( 25,138)( 26,137)( 27,136)( 28,135)( 29,141)( 30,147)( 31,146)( 32,145)( 33,144)( 34,143)( 35,142)( 36,148)( 37,154)( 38,153)( 39,152)( 40,151)( 41,150)( 42,149)( 43,155)( 44,161)( 45,160)( 46,159)( 47,158)( 48,157)( 49,156)( 50,162)( 51,168)( 52,167)( 53,166)( 54,165)( 55,164)( 56,163)( 57,169)( 58,175)( 59,174)( 60,173)( 61,172)( 62,171)( 63,170)( 64,176)( 65,182)( 66,181)( 67,180)( 68,179)( 69,178)( 70,177)( 71,183)( 72,189)( 73,188)( 74,187)( 75,186)( 76,185)( 77,184)( 78,190)( 79,196)( 80,195)( 81,194)( 82,193)( 83,192)( 84,191)( 85,197)( 86,203)( 87,202)( 88,201)( 89,200)( 90,199)( 91,198)( 92,204)( 93,210)( 94,209)( 95,208)( 96,207)( 97,206)( 98,205)( 99,211)(100,217)(101,216)(102,215)(103,214)(104,213)(105,212)(106,218)(107,224)(108,223)(109,222)(110,221)(111,220)(112,219)(225,337)(226,343)(227,342)(228,341)(229,340)(230,339)(231,338)(232,344)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,351)(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,358)(247,364)(248,363)(249,362)(250,361)(251,360)(252,359)(253,365)(254,371)(255,370)(256,369)(257,368)(258,367)(259,366)(260,372)(261,378)(262,377)(263,376)(264,375)(265,374)(266,373)(267,379)(268,385)(269,384)(270,383)(271,382)(272,381)(273,380)(274,386)(275,392)(276,391)(277,390)(278,389)(279,388)(280,387)(281,393)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)(288,400)(289,406)(290,405)(291,404)(292,403)(293,402)(294,401)(295,407)(296,413)(297,412)(298,411)(299,410)(300,409)(301,408)(302,414)(303,420)(304,419)(305,418)(306,417)(307,416)(308,415)(309,421)(310,427)(311,426)(312,425)(313,424)(314,423)(315,422)(316,428)(317,434)(318,433)(319,432)(320,431)(321,430)(322,429)(323,435)(324,441)(325,440)(326,439)(327,438)(328,437)(329,436)(330,442)(331,448)(332,447)(333,446)(334,445)(335,444)(336,443)(449,561)(450,567)(451,566)(452,565)(453,564)(454,563)(455,562)(456,568)(457,574)(458,573)(459,572)(460,571)(461,570)(462,569)(463,575)(464,581)(465,580)(466,579)(467,578)(468,577)(469,576)(470,582)(471,588)(472,587)(473,586)(474,585)(475,584)(476,583)(477,589)(478,595)(479,594)(480,593)(481,592)(482,591)(483,590)(484,596)(485,602)(486,601)(487,600)(488,599)(489,598)(490,597)(491,603)(492,609)(493,608)(494,607)(495,606)(496,605)(497,604)(498,610)(499,616)(500,615)(501,614)(502,613)(503,612)(504,611)(505,617)(506,623)(507,622)(508,621)(509,620)(510,619)(511,618)(512,624)(513,630)(514,629)(515,628)(516,627)(517,626)(518,625)(519,631)(520,637)(521,636)(522,635)(523,634)(524,633)(525,632)(526,638)(527,644)(528,643)(529,642)(530,641)(531,640)(532,639)(533,645)(534,651)(535,650)(536,649)(537,648)(538,647)(539,646)(540,652)(541,658)(542,657)(543,656)(544,655)(545,654)(546,653)(547,659)(548,665)(549,664)(550,663)(551,662)(552,661)(553,660)(554,666)(555,672)(556,671)(557,670)(558,669)(559,668)(560,667)(673,785)(674,791)(675,790)(676,789)(677,788)(678,787)(679,786)(680,792)(681,798)(682,797)(683,796)(684,795)(685,794)(686,793)(687,799)(688,805)(689,804)(690,803)(691,802)(692,801)(693,800)(694,806)(695,812)(696,811)(697,810)(698,809)(699,808)(700,807)(701,813)(702,819)(703,818)(704,817)(705,816)(706,815)(707,814)(708,820)(709,826)(710,825)(711,824)(712,823)(713,822)(714,821)(715,827)(716,833)(717,832)(718,831)(719,830)(720,829)(721,828)(722,834)(723,840)(724,839)(725,838)(726,837)(727,836)(728,835)(729,841)(730,847)(731,846)(732,845)(733,844)(734,843)(735,842)(736,848)(737,854)(738,853)(739,852)(740,851)(741,850)(742,849)(743,855)(744,861)(745,860)(746,859)(747,858)(748,857)(749,856)(750,862)(751,868)(752,867)(753,866)(754,865)(755,864)(756,863)(757,869)(758,875)(759,874)(760,873)(761,872)(762,871)(763,870)(764,876)(765,882)(766,881)(767,880)(768,879)(769,878)(770,877)(771,883)(772,889)(773,888)(774,887)(775,886)(776,885)(777,884)(778,890)(779,896)(780,895)(781,894)(782,893)(783,892)(784,891);
s1 := Sym(896)!(  1,338)(  2,337)(  3,343)(  4,342)(  5,341)(  6,340)(  7,339)(  8,345)(  9,344)( 10,350)( 11,349)( 12,348)( 13,347)( 14,346)( 15,352)( 16,351)( 17,357)( 18,356)( 19,355)( 20,354)( 21,353)( 22,359)( 23,358)( 24,364)( 25,363)( 26,362)( 27,361)( 28,360)( 29,387)( 30,386)( 31,392)( 32,391)( 33,390)( 34,389)( 35,388)( 36,380)( 37,379)( 38,385)( 39,384)( 40,383)( 41,382)( 42,381)( 43,373)( 44,372)( 45,378)( 46,377)( 47,376)( 48,375)( 49,374)( 50,366)( 51,365)( 52,371)( 53,370)( 54,369)( 55,368)( 56,367)( 57,401)( 58,400)( 59,406)( 60,405)( 61,404)( 62,403)( 63,402)( 64,394)( 65,393)( 66,399)( 67,398)( 68,397)( 69,396)( 70,395)( 71,415)( 72,414)( 73,420)( 74,419)( 75,418)( 76,417)( 77,416)( 78,408)( 79,407)( 80,413)( 81,412)( 82,411)( 83,410)( 84,409)( 85,436)( 86,435)( 87,441)( 88,440)( 89,439)( 90,438)( 91,437)( 92,443)( 93,442)( 94,448)( 95,447)( 96,446)( 97,445)( 98,444)( 99,422)(100,421)(101,427)(102,426)(103,425)(104,424)(105,423)(106,429)(107,428)(108,434)(109,433)(110,432)(111,431)(112,430)(113,226)(114,225)(115,231)(116,230)(117,229)(118,228)(119,227)(120,233)(121,232)(122,238)(123,237)(124,236)(125,235)(126,234)(127,240)(128,239)(129,245)(130,244)(131,243)(132,242)(133,241)(134,247)(135,246)(136,252)(137,251)(138,250)(139,249)(140,248)(141,275)(142,274)(143,280)(144,279)(145,278)(146,277)(147,276)(148,268)(149,267)(150,273)(151,272)(152,271)(153,270)(154,269)(155,261)(156,260)(157,266)(158,265)(159,264)(160,263)(161,262)(162,254)(163,253)(164,259)(165,258)(166,257)(167,256)(168,255)(169,289)(170,288)(171,294)(172,293)(173,292)(174,291)(175,290)(176,282)(177,281)(178,287)(179,286)(180,285)(181,284)(182,283)(183,303)(184,302)(185,308)(186,307)(187,306)(188,305)(189,304)(190,296)(191,295)(192,301)(193,300)(194,299)(195,298)(196,297)(197,324)(198,323)(199,329)(200,328)(201,327)(202,326)(203,325)(204,331)(205,330)(206,336)(207,335)(208,334)(209,333)(210,332)(211,310)(212,309)(213,315)(214,314)(215,313)(216,312)(217,311)(218,317)(219,316)(220,322)(221,321)(222,320)(223,319)(224,318)(449,786)(450,785)(451,791)(452,790)(453,789)(454,788)(455,787)(456,793)(457,792)(458,798)(459,797)(460,796)(461,795)(462,794)(463,800)(464,799)(465,805)(466,804)(467,803)(468,802)(469,801)(470,807)(471,806)(472,812)(473,811)(474,810)(475,809)(476,808)(477,835)(478,834)(479,840)(480,839)(481,838)(482,837)(483,836)(484,828)(485,827)(486,833)(487,832)(488,831)(489,830)(490,829)(491,821)(492,820)(493,826)(494,825)(495,824)(496,823)(497,822)(498,814)(499,813)(500,819)(501,818)(502,817)(503,816)(504,815)(505,849)(506,848)(507,854)(508,853)(509,852)(510,851)(511,850)(512,842)(513,841)(514,847)(515,846)(516,845)(517,844)(518,843)(519,863)(520,862)(521,868)(522,867)(523,866)(524,865)(525,864)(526,856)(527,855)(528,861)(529,860)(530,859)(531,858)(532,857)(533,884)(534,883)(535,889)(536,888)(537,887)(538,886)(539,885)(540,891)(541,890)(542,896)(543,895)(544,894)(545,893)(546,892)(547,870)(548,869)(549,875)(550,874)(551,873)(552,872)(553,871)(554,877)(555,876)(556,882)(557,881)(558,880)(559,879)(560,878)(561,674)(562,673)(563,679)(564,678)(565,677)(566,676)(567,675)(568,681)(569,680)(570,686)(571,685)(572,684)(573,683)(574,682)(575,688)(576,687)(577,693)(578,692)(579,691)(580,690)(581,689)(582,695)(583,694)(584,700)(585,699)(586,698)(587,697)(588,696)(589,723)(590,722)(591,728)(592,727)(593,726)(594,725)(595,724)(596,716)(597,715)(598,721)(599,720)(600,719)(601,718)(602,717)(603,709)(604,708)(605,714)(606,713)(607,712)(608,711)(609,710)(610,702)(611,701)(612,707)(613,706)(614,705)(615,704)(616,703)(617,737)(618,736)(619,742)(620,741)(621,740)(622,739)(623,738)(624,730)(625,729)(626,735)(627,734)(628,733)(629,732)(630,731)(631,751)(632,750)(633,756)(634,755)(635,754)(636,753)(637,752)(638,744)(639,743)(640,749)(641,748)(642,747)(643,746)(644,745)(645,772)(646,771)(647,777)(648,776)(649,775)(650,774)(651,773)(652,779)(653,778)(654,784)(655,783)(656,782)(657,781)(658,780)(659,758)(660,757)(661,763)(662,762)(663,761)(664,760)(665,759)(666,765)(667,764)(668,770)(669,769)(670,768)(671,767)(672,766);
s2 := Sym(896)!( 29, 50)( 30, 51)( 31, 52)( 32, 53)( 33, 54)( 34, 55)( 35, 56)( 36, 43)( 37, 44)( 38, 45)( 39, 46)( 40, 47)( 41, 48)( 42, 49)( 57, 71)( 58, 72)( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 92)( 86, 93)( 87, 94)( 88, 95)( 89, 96)( 90, 97)( 91, 98)( 99,106)(100,107)(101,108)(102,109)(103,110)(104,111)(105,112)(141,162)(142,163)(143,164)(144,165)(145,166)(146,167)(147,168)(148,155)(149,156)(150,157)(151,158)(152,159)(153,160)(154,161)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,204)(198,205)(199,206)(200,207)(201,208)(202,209)(203,210)(211,218)(212,219)(213,220)(214,221)(215,222)(216,223)(217,224)(225,253)(226,254)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,267)(240,268)(241,269)(242,270)(243,271)(244,272)(245,273)(246,274)(247,275)(248,276)(249,277)(250,278)(251,279)(252,280)(281,323)(282,324)(283,325)(284,326)(285,327)(286,328)(287,329)(288,330)(289,331)(290,332)(291,333)(292,334)(293,335)(294,336)(295,309)(296,310)(297,311)(298,312)(299,313)(300,314)(301,315)(302,316)(303,317)(304,318)(305,319)(306,320)(307,321)(308,322)(337,365)(338,366)(339,367)(340,368)(341,369)(342,370)(343,371)(344,372)(345,373)(346,374)(347,375)(348,376)(349,377)(350,378)(351,379)(352,380)(353,381)(354,382)(355,383)(356,384)(357,385)(358,386)(359,387)(360,388)(361,389)(362,390)(363,391)(364,392)(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)(420,434)(449,505)(450,506)(451,507)(452,508)(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)(460,516)(461,517)(462,518)(463,519)(464,520)(465,521)(466,522)(467,523)(468,524)(469,525)(470,526)(471,527)(472,528)(473,529)(474,530)(475,531)(476,532)(477,554)(478,555)(479,556)(480,557)(481,558)(482,559)(483,560)(484,547)(485,548)(486,549)(487,550)(488,551)(489,552)(490,553)(491,540)(492,541)(493,542)(494,543)(495,544)(496,545)(497,546)(498,533)(499,534)(500,535)(501,536)(502,537)(503,538)(504,539)(561,617)(562,618)(563,619)(564,620)(565,621)(566,622)(567,623)(568,624)(569,625)(570,626)(571,627)(572,628)(573,629)(574,630)(575,631)(576,632)(577,633)(578,634)(579,635)(580,636)(581,637)(582,638)(583,639)(584,640)(585,641)(586,642)(587,643)(588,644)(589,666)(590,667)(591,668)(592,669)(593,670)(594,671)(595,672)(596,659)(597,660)(598,661)(599,662)(600,663)(601,664)(602,665)(603,652)(604,653)(605,654)(606,655)(607,656)(608,657)(609,658)(610,645)(611,646)(612,647)(613,648)(614,649)(615,650)(616,651)(673,764)(674,765)(675,766)(676,767)(677,768)(678,769)(679,770)(680,757)(681,758)(682,759)(683,760)(684,761)(685,762)(686,763)(687,778)(688,779)(689,780)(690,781)(691,782)(692,783)(693,784)(694,771)(695,772)(696,773)(697,774)(698,775)(699,776)(700,777)(701,736)(702,737)(703,738)(704,739)(705,740)(706,741)(707,742)(708,729)(709,730)(710,731)(711,732)(712,733)(713,734)(714,735)(715,750)(716,751)(717,752)(718,753)(719,754)(720,755)(721,756)(722,743)(723,744)(724,745)(725,746)(726,747)(727,748)(728,749)(785,876)(786,877)(787,878)(788,879)(789,880)(790,881)(791,882)(792,869)(793,870)(794,871)(795,872)(796,873)(797,874)(798,875)(799,890)(800,891)(801,892)(802,893)(803,894)(804,895)(805,896)(806,883)(807,884)(808,885)(809,886)(810,887)(811,888)(812,889)(813,848)(814,849)(815,850)(816,851)(817,852)(818,853)(819,854)(820,841)(821,842)(822,843)(823,844)(824,845)(825,846)(826,847)(827,862)(828,863)(829,864)(830,865)(831,866)(832,867)(833,868)(834,855)(835,856)(836,857)(837,858)(838,859)(839,860)(840,861);
s3 := Sym(896)!(  1,449)(  2,450)(  3,451)(  4,452)(  5,453)(  6,454)(  7,455)(  8,456)(  9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,463)( 16,464)( 17,465)( 18,466)( 19,467)( 20,468)( 21,469)( 22,470)( 23,471)( 24,472)( 25,473)( 26,474)( 27,475)( 28,476)( 29,484)( 30,485)( 31,486)( 32,487)( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)( 40,481)( 41,482)( 42,483)( 43,498)( 44,499)( 45,500)( 46,501)( 47,502)( 48,503)( 49,504)( 50,491)( 51,492)( 52,493)( 53,494)( 54,495)( 55,496)( 56,497)( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)( 64,526)( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)( 72,506)( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)( 80,514)( 81,515)( 82,516)( 83,517)( 84,518)( 85,554)( 86,555)( 87,556)( 88,557)( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)( 96,551)( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)(112,539)(113,561)(114,562)(115,563)(116,564)(117,565)(118,566)(119,567)(120,568)(121,569)(122,570)(123,571)(124,572)(125,573)(126,574)(127,575)(128,576)(129,577)(130,578)(131,579)(132,580)(133,581)(134,582)(135,583)(136,584)(137,585)(138,586)(139,587)(140,588)(141,596)(142,597)(143,598)(144,599)(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)(152,593)(153,594)(154,595)(155,610)(156,611)(157,612)(158,613)(159,614)(160,615)(161,616)(162,603)(163,604)(164,605)(165,606)(166,607)(167,608)(168,609)(169,631)(170,632)(171,633)(172,634)(173,635)(174,636)(175,637)(176,638)(177,639)(178,640)(179,641)(180,642)(181,643)(182,644)(183,617)(184,618)(185,619)(186,620)(187,621)(188,622)(189,623)(190,624)(191,625)(192,626)(193,627)(194,628)(195,629)(196,630)(197,666)(198,667)(199,668)(200,669)(201,670)(202,671)(203,672)(204,659)(205,660)(206,661)(207,662)(208,663)(209,664)(210,665)(211,652)(212,653)(213,654)(214,655)(215,656)(216,657)(217,658)(218,645)(219,646)(220,647)(221,648)(222,649)(223,650)(224,651)(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)(232,680)(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,687)(240,688)(241,689)(242,690)(243,691)(244,692)(245,693)(246,694)(247,695)(248,696)(249,697)(250,698)(251,699)(252,700)(253,708)(254,709)(255,710)(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)(265,706)(266,707)(267,722)(268,723)(269,724)(270,725)(271,726)(272,727)(273,728)(274,715)(275,716)(276,717)(277,718)(278,719)(279,720)(280,721)(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)(288,750)(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)(296,730)(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)(304,738)(305,739)(306,740)(307,741)(308,742)(309,778)(310,779)(311,780)(312,781)(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)(320,775)(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)(328,769)(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)(336,763)(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)(344,792)(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,799)(352,800)(353,801)(354,802)(355,803)(356,804)(357,805)(358,806)(359,807)(360,808)(361,809)(362,810)(363,811)(364,812)(365,820)(366,821)(367,822)(368,823)(369,824)(370,825)(371,826)(372,813)(373,814)(374,815)(375,816)(376,817)(377,818)(378,819)(379,834)(380,835)(381,836)(382,837)(383,838)(384,839)(385,840)(386,827)(387,828)(388,829)(389,830)(390,831)(391,832)(392,833)(393,855)(394,856)(395,857)(396,858)(397,859)(398,860)(399,861)(400,862)(401,863)(402,864)(403,865)(404,866)(405,867)(406,868)(407,841)(408,842)(409,843)(410,844)(411,845)(412,846)(413,847)(414,848)(415,849)(416,850)(417,851)(418,852)(419,853)(420,854)(421,890)(422,891)(423,892)(424,893)(425,894)(426,895)(427,896)(428,883)(429,884)(430,885)(431,886)(432,887)(433,888)(434,889)(435,876)(436,877)(437,878)(438,879)(439,880)(440,881)(441,882)(442,869)(443,870)(444,871)(445,872)(446,873)(447,874)(448,875);
poly := sub<Sym(896)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s1*s3*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References