Polytope of Type {8,4,28} with group SmallGroup(1792,200564)

Overview

Group: SmallGroup(1792,200564)
Rank: 4
Schläfli Type: {8,4,28}
Vertices, edges, …: 8, 16, 56, 28
Order of s₀s₁s₂s₃: 56
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: {{8,4|2},{4,28|2}}. if this polytope has another name.

Special Properties

Universal
Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

7-fold

{8,4,4}*256a

8-fold

14-fold

16-fold

28-fold

32-fold

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

Permutation Representation (Magma)

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

References