Polytope of Type {150,4} with group SmallGroup(1200,198)

Overview

Group: SmallGroup(1200,198)
Rank: 3
Schläfli Type: {150,4}
Vertices, edges, …: 150, 300, 4
Order of s₀s₁s₂: 150
Order of s₀s₁s₂s₁: 4
Also known as: if this polytope has a name.

Special Properties

Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Flat
Self-Petrie

Quotients maximal quotients in bold

2-fold

{75,4}*600

5-fold

{30,4}*240b

10-fold

{15,4}*120

25-fold

{6,4}*48c

50-fold

{3,4}*24

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 97)( 22, 98)( 23,100)( 24, 99)( 25, 93)( 26, 94)( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)( 33, 85)( 34, 86)( 35, 88)( 36, 87)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 69)( 50, 70)( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)( 59, 64)( 60, 63)(101,201)(102,202)(103,204)(104,203)(105,217)(106,218)(107,220)(108,219)(109,213)(110,214)(111,216)(112,215)(113,209)(114,210)(115,212)(116,211)(117,205)(118,206)(119,208)(120,207)(121,297)(122,298)(123,300)(124,299)(125,293)(126,294)(127,296)(128,295)(129,289)(130,290)(131,292)(132,291)(133,285)(134,286)(135,288)(136,287)(137,281)(138,282)(139,284)(140,283)(141,277)(142,278)(143,280)(144,279)(145,273)(146,274)(147,276)(148,275)(149,269)(150,270)(151,272)(152,271)(153,265)(154,266)(155,268)(156,267)(157,261)(158,262)(159,264)(160,263)(161,257)(162,258)(163,260)(164,259)(165,253)(166,254)(167,256)(168,255)(169,249)(170,250)(171,252)(172,251)(173,245)(174,246)(175,248)(176,247)(177,241)(178,242)(179,244)(180,243)(181,237)(182,238)(183,240)(184,239)(185,233)(186,234)(187,236)(188,235)(189,229)(190,230)(191,232)(192,231)(193,225)(194,226)(195,228)(196,227)(197,221)(198,222)(199,224)(200,223)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,397)(322,398)(323,400)(324,399)(325,393)(326,394)(327,396)(328,395)(329,389)(330,390)(331,392)(332,391)(333,385)(334,386)(335,388)(336,387)(337,381)(338,382)(339,384)(340,383)(341,377)(342,378)(343,380)(344,379)(345,373)(346,374)(347,376)(348,375)(349,369)(350,370)(351,372)(352,371)(353,365)(354,366)(355,368)(356,367)(357,361)(358,362)(359,364)(360,363)(401,501)(402,502)(403,504)(404,503)(405,517)(406,518)(407,520)(408,519)(409,513)(410,514)(411,516)(412,515)(413,509)(414,510)(415,512)(416,511)(417,505)(418,506)(419,508)(420,507)(421,597)(422,598)(423,600)(424,599)(425,593)(426,594)(427,596)(428,595)(429,589)(430,590)(431,592)(432,591)(433,585)(434,586)(435,588)(436,587)(437,581)(438,582)(439,584)(440,583)(441,577)(442,578)(443,580)(444,579)(445,573)(446,574)(447,576)(448,575)(449,569)(450,570)(451,572)(452,571)(453,565)(454,566)(455,568)(456,567)(457,561)(458,562)(459,564)(460,563)(461,557)(462,558)(463,560)(464,559)(465,553)(466,554)(467,556)(468,555)(469,549)(470,550)(471,552)(472,551)(473,545)(474,546)(475,548)(476,547)(477,541)(478,542)(479,544)(480,543)(481,537)(482,538)(483,540)(484,539)(485,533)(486,534)(487,536)(488,535)(489,529)(490,530)(491,532)(492,531)(493,525)(494,526)(495,528)(496,527)(497,521)(498,522)(499,524)(500,523);;
s1 := (  1,421)(  2,424)(  3,423)(  4,422)(  5,437)(  6,440)(  7,439)(  8,438)(  9,433)( 10,436)( 11,435)( 12,434)( 13,429)( 14,432)( 15,431)( 16,430)( 17,425)( 18,428)( 19,427)( 20,426)( 21,401)( 22,404)( 23,403)( 24,402)( 25,417)( 26,420)( 27,419)( 28,418)( 29,413)( 30,416)( 31,415)( 32,414)( 33,409)( 34,412)( 35,411)( 36,410)( 37,405)( 38,408)( 39,407)( 40,406)( 41,497)( 42,500)( 43,499)( 44,498)( 45,493)( 46,496)( 47,495)( 48,494)( 49,489)( 50,492)( 51,491)( 52,490)( 53,485)( 54,488)( 55,487)( 56,486)( 57,481)( 58,484)( 59,483)( 60,482)( 61,477)( 62,480)( 63,479)( 64,478)( 65,473)( 66,476)( 67,475)( 68,474)( 69,469)( 70,472)( 71,471)( 72,470)( 73,465)( 74,468)( 75,467)( 76,466)( 77,461)( 78,464)( 79,463)( 80,462)( 81,457)( 82,460)( 83,459)( 84,458)( 85,453)( 86,456)( 87,455)( 88,454)( 89,449)( 90,452)( 91,451)( 92,450)( 93,445)( 94,448)( 95,447)( 96,446)( 97,441)( 98,444)( 99,443)(100,442)(101,321)(102,324)(103,323)(104,322)(105,337)(106,340)(107,339)(108,338)(109,333)(110,336)(111,335)(112,334)(113,329)(114,332)(115,331)(116,330)(117,325)(118,328)(119,327)(120,326)(121,301)(122,304)(123,303)(124,302)(125,317)(126,320)(127,319)(128,318)(129,313)(130,316)(131,315)(132,314)(133,309)(134,312)(135,311)(136,310)(137,305)(138,308)(139,307)(140,306)(141,397)(142,400)(143,399)(144,398)(145,393)(146,396)(147,395)(148,394)(149,389)(150,392)(151,391)(152,390)(153,385)(154,388)(155,387)(156,386)(157,381)(158,384)(159,383)(160,382)(161,377)(162,380)(163,379)(164,378)(165,373)(166,376)(167,375)(168,374)(169,369)(170,372)(171,371)(172,370)(173,365)(174,368)(175,367)(176,366)(177,361)(178,364)(179,363)(180,362)(181,357)(182,360)(183,359)(184,358)(185,353)(186,356)(187,355)(188,354)(189,349)(190,352)(191,351)(192,350)(193,345)(194,348)(195,347)(196,346)(197,341)(198,344)(199,343)(200,342)(201,521)(202,524)(203,523)(204,522)(205,537)(206,540)(207,539)(208,538)(209,533)(210,536)(211,535)(212,534)(213,529)(214,532)(215,531)(216,530)(217,525)(218,528)(219,527)(220,526)(221,501)(222,504)(223,503)(224,502)(225,517)(226,520)(227,519)(228,518)(229,513)(230,516)(231,515)(232,514)(233,509)(234,512)(235,511)(236,510)(237,505)(238,508)(239,507)(240,506)(241,597)(242,600)(243,599)(244,598)(245,593)(246,596)(247,595)(248,594)(249,589)(250,592)(251,591)(252,590)(253,585)(254,588)(255,587)(256,586)(257,581)(258,584)(259,583)(260,582)(261,577)(262,580)(263,579)(264,578)(265,573)(266,576)(267,575)(268,574)(269,569)(270,572)(271,571)(272,570)(273,565)(274,568)(275,567)(276,566)(277,561)(278,564)(279,563)(280,562)(281,557)(282,560)(283,559)(284,558)(285,553)(286,556)(287,555)(288,554)(289,549)(290,552)(291,551)(292,550)(293,545)(294,548)(295,547)(296,546)(297,541)(298,544)(299,543)(300,542);;
s2 := (  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);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s1*s0*s2*s1*s2*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*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*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*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*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*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*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*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*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*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*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(600)!(  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 97)( 22, 98)( 23,100)( 24, 99)( 25, 93)( 26, 94)( 27, 96)( 28, 95)( 29, 89)( 30, 90)( 31, 92)( 32, 91)( 33, 85)( 34, 86)( 35, 88)( 36, 87)( 37, 81)( 38, 82)( 39, 84)( 40, 83)( 41, 77)( 42, 78)( 43, 80)( 44, 79)( 45, 73)( 46, 74)( 47, 76)( 48, 75)( 49, 69)( 50, 70)( 51, 72)( 52, 71)( 53, 65)( 54, 66)( 55, 68)( 56, 67)( 57, 61)( 58, 62)( 59, 64)( 60, 63)(101,201)(102,202)(103,204)(104,203)(105,217)(106,218)(107,220)(108,219)(109,213)(110,214)(111,216)(112,215)(113,209)(114,210)(115,212)(116,211)(117,205)(118,206)(119,208)(120,207)(121,297)(122,298)(123,300)(124,299)(125,293)(126,294)(127,296)(128,295)(129,289)(130,290)(131,292)(132,291)(133,285)(134,286)(135,288)(136,287)(137,281)(138,282)(139,284)(140,283)(141,277)(142,278)(143,280)(144,279)(145,273)(146,274)(147,276)(148,275)(149,269)(150,270)(151,272)(152,271)(153,265)(154,266)(155,268)(156,267)(157,261)(158,262)(159,264)(160,263)(161,257)(162,258)(163,260)(164,259)(165,253)(166,254)(167,256)(168,255)(169,249)(170,250)(171,252)(172,251)(173,245)(174,246)(175,248)(176,247)(177,241)(178,242)(179,244)(180,243)(181,237)(182,238)(183,240)(184,239)(185,233)(186,234)(187,236)(188,235)(189,229)(190,230)(191,232)(192,231)(193,225)(194,226)(195,228)(196,227)(197,221)(198,222)(199,224)(200,223)(303,304)(305,317)(306,318)(307,320)(308,319)(309,313)(310,314)(311,316)(312,315)(321,397)(322,398)(323,400)(324,399)(325,393)(326,394)(327,396)(328,395)(329,389)(330,390)(331,392)(332,391)(333,385)(334,386)(335,388)(336,387)(337,381)(338,382)(339,384)(340,383)(341,377)(342,378)(343,380)(344,379)(345,373)(346,374)(347,376)(348,375)(349,369)(350,370)(351,372)(352,371)(353,365)(354,366)(355,368)(356,367)(357,361)(358,362)(359,364)(360,363)(401,501)(402,502)(403,504)(404,503)(405,517)(406,518)(407,520)(408,519)(409,513)(410,514)(411,516)(412,515)(413,509)(414,510)(415,512)(416,511)(417,505)(418,506)(419,508)(420,507)(421,597)(422,598)(423,600)(424,599)(425,593)(426,594)(427,596)(428,595)(429,589)(430,590)(431,592)(432,591)(433,585)(434,586)(435,588)(436,587)(437,581)(438,582)(439,584)(440,583)(441,577)(442,578)(443,580)(444,579)(445,573)(446,574)(447,576)(448,575)(449,569)(450,570)(451,572)(452,571)(453,565)(454,566)(455,568)(456,567)(457,561)(458,562)(459,564)(460,563)(461,557)(462,558)(463,560)(464,559)(465,553)(466,554)(467,556)(468,555)(469,549)(470,550)(471,552)(472,551)(473,545)(474,546)(475,548)(476,547)(477,541)(478,542)(479,544)(480,543)(481,537)(482,538)(483,540)(484,539)(485,533)(486,534)(487,536)(488,535)(489,529)(490,530)(491,532)(492,531)(493,525)(494,526)(495,528)(496,527)(497,521)(498,522)(499,524)(500,523);
s1 := Sym(600)!(  1,421)(  2,424)(  3,423)(  4,422)(  5,437)(  6,440)(  7,439)(  8,438)(  9,433)( 10,436)( 11,435)( 12,434)( 13,429)( 14,432)( 15,431)( 16,430)( 17,425)( 18,428)( 19,427)( 20,426)( 21,401)( 22,404)( 23,403)( 24,402)( 25,417)( 26,420)( 27,419)( 28,418)( 29,413)( 30,416)( 31,415)( 32,414)( 33,409)( 34,412)( 35,411)( 36,410)( 37,405)( 38,408)( 39,407)( 40,406)( 41,497)( 42,500)( 43,499)( 44,498)( 45,493)( 46,496)( 47,495)( 48,494)( 49,489)( 50,492)( 51,491)( 52,490)( 53,485)( 54,488)( 55,487)( 56,486)( 57,481)( 58,484)( 59,483)( 60,482)( 61,477)( 62,480)( 63,479)( 64,478)( 65,473)( 66,476)( 67,475)( 68,474)( 69,469)( 70,472)( 71,471)( 72,470)( 73,465)( 74,468)( 75,467)( 76,466)( 77,461)( 78,464)( 79,463)( 80,462)( 81,457)( 82,460)( 83,459)( 84,458)( 85,453)( 86,456)( 87,455)( 88,454)( 89,449)( 90,452)( 91,451)( 92,450)( 93,445)( 94,448)( 95,447)( 96,446)( 97,441)( 98,444)( 99,443)(100,442)(101,321)(102,324)(103,323)(104,322)(105,337)(106,340)(107,339)(108,338)(109,333)(110,336)(111,335)(112,334)(113,329)(114,332)(115,331)(116,330)(117,325)(118,328)(119,327)(120,326)(121,301)(122,304)(123,303)(124,302)(125,317)(126,320)(127,319)(128,318)(129,313)(130,316)(131,315)(132,314)(133,309)(134,312)(135,311)(136,310)(137,305)(138,308)(139,307)(140,306)(141,397)(142,400)(143,399)(144,398)(145,393)(146,396)(147,395)(148,394)(149,389)(150,392)(151,391)(152,390)(153,385)(154,388)(155,387)(156,386)(157,381)(158,384)(159,383)(160,382)(161,377)(162,380)(163,379)(164,378)(165,373)(166,376)(167,375)(168,374)(169,369)(170,372)(171,371)(172,370)(173,365)(174,368)(175,367)(176,366)(177,361)(178,364)(179,363)(180,362)(181,357)(182,360)(183,359)(184,358)(185,353)(186,356)(187,355)(188,354)(189,349)(190,352)(191,351)(192,350)(193,345)(194,348)(195,347)(196,346)(197,341)(198,344)(199,343)(200,342)(201,521)(202,524)(203,523)(204,522)(205,537)(206,540)(207,539)(208,538)(209,533)(210,536)(211,535)(212,534)(213,529)(214,532)(215,531)(216,530)(217,525)(218,528)(219,527)(220,526)(221,501)(222,504)(223,503)(224,502)(225,517)(226,520)(227,519)(228,518)(229,513)(230,516)(231,515)(232,514)(233,509)(234,512)(235,511)(236,510)(237,505)(238,508)(239,507)(240,506)(241,597)(242,600)(243,599)(244,598)(245,593)(246,596)(247,595)(248,594)(249,589)(250,592)(251,591)(252,590)(253,585)(254,588)(255,587)(256,586)(257,581)(258,584)(259,583)(260,582)(261,577)(262,580)(263,579)(264,578)(265,573)(266,576)(267,575)(268,574)(269,569)(270,572)(271,571)(272,570)(273,565)(274,568)(275,567)(276,566)(277,561)(278,564)(279,563)(280,562)(281,557)(282,560)(283,559)(284,558)(285,553)(286,556)(287,555)(288,554)(289,549)(290,552)(291,551)(292,550)(293,545)(294,548)(295,547)(296,546)(297,541)(298,544)(299,543)(300,542);
s2 := Sym(600)!(  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);
poly := sub<Sym(600)|s0,s1,s2>;

Finitely Presented Group Representation (Magma)

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