Polytope of Type {20,12,4} with group SmallGroup(1920,238871)

Overview

Group: SmallGroup(1920,238871)
Rank: 4
Schläfli Type: {20,12,4}
Vertices, edges, …: 20, 120, 24, 4
Order of s₀s₁s₂s₃: 60
Order of s₀s₁s₂s₃s₂s₁: 2
Also known as: if this polytope has a name.

Special Properties

Universal
Non-Orientable
Flat

Quotients maximal quotients in bold

2-fold

4-fold

{10,6,4}*480b

5-fold

{4,12,4}*384b

10-fold

20-fold

{2,6,4}*96c

40-fold

{2,3,4}*48

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP)

s0 := (  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156)(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)(172,176)(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)(192,196)(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)(212,216)(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)(232,236)(241,301)(242,302)(243,303)(244,304)(245,317)(246,318)(247,319)(248,320)(249,313)(250,314)(251,315)(252,316)(253,309)(254,310)(255,311)(256,312)(257,305)(258,306)(259,307)(260,308)(261,321)(262,322)(263,323)(264,324)(265,337)(266,338)(267,339)(268,340)(269,333)(270,334)(271,335)(272,336)(273,329)(274,330)(275,331)(276,332)(277,325)(278,326)(279,327)(280,328)(281,341)(282,342)(283,343)(284,344)(285,357)(286,358)(287,359)(288,360)(289,353)(290,354)(291,355)(292,356)(293,349)(294,350)(295,351)(296,352)(297,345)(298,346)(299,347)(300,348)(361,421)(362,422)(363,423)(364,424)(365,437)(366,438)(367,439)(368,440)(369,433)(370,434)(371,435)(372,436)(373,429)(374,430)(375,431)(376,432)(377,425)(378,426)(379,427)(380,428)(381,441)(382,442)(383,443)(384,444)(385,457)(386,458)(387,459)(388,460)(389,453)(390,454)(391,455)(392,456)(393,449)(394,450)(395,451)(396,452)(397,445)(398,446)(399,447)(400,448)(401,461)(402,462)(403,463)(404,464)(405,477)(406,478)(407,479)(408,480)(409,473)(410,474)(411,475)(412,476)(413,469)(414,470)(415,471)(416,472)(417,465)(418,466)(419,467)(420,468);;
s1 := (  1,245)(  2,246)(  3,248)(  4,247)(  5,241)(  6,242)(  7,244)(  8,243)(  9,257)( 10,258)( 11,260)( 12,259)( 13,253)( 14,254)( 15,256)( 16,255)( 17,249)( 18,250)( 19,252)( 20,251)( 21,285)( 22,286)( 23,288)( 24,287)( 25,281)( 26,282)( 27,284)( 28,283)( 29,297)( 30,298)( 31,300)( 32,299)( 33,293)( 34,294)( 35,296)( 36,295)( 37,289)( 38,290)( 39,292)( 40,291)( 41,265)( 42,266)( 43,268)( 44,267)( 45,261)( 46,262)( 47,264)( 48,263)( 49,277)( 50,278)( 51,280)( 52,279)( 53,273)( 54,274)( 55,276)( 56,275)( 57,269)( 58,270)( 59,272)( 60,271)( 61,305)( 62,306)( 63,308)( 64,307)( 65,301)( 66,302)( 67,304)( 68,303)( 69,317)( 70,318)( 71,320)( 72,319)( 73,313)( 74,314)( 75,316)( 76,315)( 77,309)( 78,310)( 79,312)( 80,311)( 81,345)( 82,346)( 83,348)( 84,347)( 85,341)( 86,342)( 87,344)( 88,343)( 89,357)( 90,358)( 91,360)( 92,359)( 93,353)( 94,354)( 95,356)( 96,355)( 97,349)( 98,350)( 99,352)(100,351)(101,325)(102,326)(103,328)(104,327)(105,321)(106,322)(107,324)(108,323)(109,337)(110,338)(111,340)(112,339)(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)(120,331)(121,365)(122,366)(123,368)(124,367)(125,361)(126,362)(127,364)(128,363)(129,377)(130,378)(131,380)(132,379)(133,373)(134,374)(135,376)(136,375)(137,369)(138,370)(139,372)(140,371)(141,405)(142,406)(143,408)(144,407)(145,401)(146,402)(147,404)(148,403)(149,417)(150,418)(151,420)(152,419)(153,413)(154,414)(155,416)(156,415)(157,409)(158,410)(159,412)(160,411)(161,385)(162,386)(163,388)(164,387)(165,381)(166,382)(167,384)(168,383)(169,397)(170,398)(171,400)(172,399)(173,393)(174,394)(175,396)(176,395)(177,389)(178,390)(179,392)(180,391)(181,425)(182,426)(183,428)(184,427)(185,421)(186,422)(187,424)(188,423)(189,437)(190,438)(191,440)(192,439)(193,433)(194,434)(195,436)(196,435)(197,429)(198,430)(199,432)(200,431)(201,465)(202,466)(203,468)(204,467)(205,461)(206,462)(207,464)(208,463)(209,477)(210,478)(211,480)(212,479)(213,473)(214,474)(215,476)(216,475)(217,469)(218,470)(219,472)(220,471)(221,445)(222,446)(223,448)(224,447)(225,441)(226,442)(227,444)(228,443)(229,457)(230,458)(231,460)(232,459)(233,453)(234,454)(235,456)(236,455)(237,449)(238,450)(239,452)(240,451);;
s2 := (  1, 21)(  2, 24)(  3, 23)(  4, 22)(  5, 25)(  6, 28)(  7, 27)(  8, 26)(  9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)(226,228)(230,232)(234,236)(238,240)(241,381)(242,384)(243,383)(244,382)(245,385)(246,388)(247,387)(248,386)(249,389)(250,392)(251,391)(252,390)(253,393)(254,396)(255,395)(256,394)(257,397)(258,400)(259,399)(260,398)(261,361)(262,364)(263,363)(264,362)(265,365)(266,368)(267,367)(268,366)(269,369)(270,372)(271,371)(272,370)(273,373)(274,376)(275,375)(276,374)(277,377)(278,380)(279,379)(280,378)(281,401)(282,404)(283,403)(284,402)(285,405)(286,408)(287,407)(288,406)(289,409)(290,412)(291,411)(292,410)(293,413)(294,416)(295,415)(296,414)(297,417)(298,420)(299,419)(300,418)(301,441)(302,444)(303,443)(304,442)(305,445)(306,448)(307,447)(308,446)(309,449)(310,452)(311,451)(312,450)(313,453)(314,456)(315,455)(316,454)(317,457)(318,460)(319,459)(320,458)(321,421)(322,424)(323,423)(324,422)(325,425)(326,428)(327,427)(328,426)(329,429)(330,432)(331,431)(332,430)(333,433)(334,436)(335,435)(336,434)(337,437)(338,440)(339,439)(340,438)(341,461)(342,464)(343,463)(344,462)(345,465)(346,468)(347,467)(348,466)(349,469)(350,472)(351,471)(352,470)(353,473)(354,476)(355,475)(356,474)(357,477)(358,480)(359,479)(360,478);;
s3 := (  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);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3, s3*s2*s1*s3*s2*s3*s2*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(480)!(  5, 17)(  6, 18)(  7, 19)(  8, 20)(  9, 13)( 10, 14)( 11, 15)( 12, 16)( 25, 37)( 26, 38)( 27, 39)( 28, 40)( 29, 33)( 30, 34)( 31, 35)( 32, 36)( 45, 57)( 46, 58)( 47, 59)( 48, 60)( 49, 53)( 50, 54)( 51, 55)( 52, 56)( 65, 77)( 66, 78)( 67, 79)( 68, 80)( 69, 73)( 70, 74)( 71, 75)( 72, 76)( 85, 97)( 86, 98)( 87, 99)( 88,100)( 89, 93)( 90, 94)( 91, 95)( 92, 96)(105,117)(106,118)(107,119)(108,120)(109,113)(110,114)(111,115)(112,116)(125,137)(126,138)(127,139)(128,140)(129,133)(130,134)(131,135)(132,136)(145,157)(146,158)(147,159)(148,160)(149,153)(150,154)(151,155)(152,156)(165,177)(166,178)(167,179)(168,180)(169,173)(170,174)(171,175)(172,176)(185,197)(186,198)(187,199)(188,200)(189,193)(190,194)(191,195)(192,196)(205,217)(206,218)(207,219)(208,220)(209,213)(210,214)(211,215)(212,216)(225,237)(226,238)(227,239)(228,240)(229,233)(230,234)(231,235)(232,236)(241,301)(242,302)(243,303)(244,304)(245,317)(246,318)(247,319)(248,320)(249,313)(250,314)(251,315)(252,316)(253,309)(254,310)(255,311)(256,312)(257,305)(258,306)(259,307)(260,308)(261,321)(262,322)(263,323)(264,324)(265,337)(266,338)(267,339)(268,340)(269,333)(270,334)(271,335)(272,336)(273,329)(274,330)(275,331)(276,332)(277,325)(278,326)(279,327)(280,328)(281,341)(282,342)(283,343)(284,344)(285,357)(286,358)(287,359)(288,360)(289,353)(290,354)(291,355)(292,356)(293,349)(294,350)(295,351)(296,352)(297,345)(298,346)(299,347)(300,348)(361,421)(362,422)(363,423)(364,424)(365,437)(366,438)(367,439)(368,440)(369,433)(370,434)(371,435)(372,436)(373,429)(374,430)(375,431)(376,432)(377,425)(378,426)(379,427)(380,428)(381,441)(382,442)(383,443)(384,444)(385,457)(386,458)(387,459)(388,460)(389,453)(390,454)(391,455)(392,456)(393,449)(394,450)(395,451)(396,452)(397,445)(398,446)(399,447)(400,448)(401,461)(402,462)(403,463)(404,464)(405,477)(406,478)(407,479)(408,480)(409,473)(410,474)(411,475)(412,476)(413,469)(414,470)(415,471)(416,472)(417,465)(418,466)(419,467)(420,468);
s1 := Sym(480)!(  1,245)(  2,246)(  3,248)(  4,247)(  5,241)(  6,242)(  7,244)(  8,243)(  9,257)( 10,258)( 11,260)( 12,259)( 13,253)( 14,254)( 15,256)( 16,255)( 17,249)( 18,250)( 19,252)( 20,251)( 21,285)( 22,286)( 23,288)( 24,287)( 25,281)( 26,282)( 27,284)( 28,283)( 29,297)( 30,298)( 31,300)( 32,299)( 33,293)( 34,294)( 35,296)( 36,295)( 37,289)( 38,290)( 39,292)( 40,291)( 41,265)( 42,266)( 43,268)( 44,267)( 45,261)( 46,262)( 47,264)( 48,263)( 49,277)( 50,278)( 51,280)( 52,279)( 53,273)( 54,274)( 55,276)( 56,275)( 57,269)( 58,270)( 59,272)( 60,271)( 61,305)( 62,306)( 63,308)( 64,307)( 65,301)( 66,302)( 67,304)( 68,303)( 69,317)( 70,318)( 71,320)( 72,319)( 73,313)( 74,314)( 75,316)( 76,315)( 77,309)( 78,310)( 79,312)( 80,311)( 81,345)( 82,346)( 83,348)( 84,347)( 85,341)( 86,342)( 87,344)( 88,343)( 89,357)( 90,358)( 91,360)( 92,359)( 93,353)( 94,354)( 95,356)( 96,355)( 97,349)( 98,350)( 99,352)(100,351)(101,325)(102,326)(103,328)(104,327)(105,321)(106,322)(107,324)(108,323)(109,337)(110,338)(111,340)(112,339)(113,333)(114,334)(115,336)(116,335)(117,329)(118,330)(119,332)(120,331)(121,365)(122,366)(123,368)(124,367)(125,361)(126,362)(127,364)(128,363)(129,377)(130,378)(131,380)(132,379)(133,373)(134,374)(135,376)(136,375)(137,369)(138,370)(139,372)(140,371)(141,405)(142,406)(143,408)(144,407)(145,401)(146,402)(147,404)(148,403)(149,417)(150,418)(151,420)(152,419)(153,413)(154,414)(155,416)(156,415)(157,409)(158,410)(159,412)(160,411)(161,385)(162,386)(163,388)(164,387)(165,381)(166,382)(167,384)(168,383)(169,397)(170,398)(171,400)(172,399)(173,393)(174,394)(175,396)(176,395)(177,389)(178,390)(179,392)(180,391)(181,425)(182,426)(183,428)(184,427)(185,421)(186,422)(187,424)(188,423)(189,437)(190,438)(191,440)(192,439)(193,433)(194,434)(195,436)(196,435)(197,429)(198,430)(199,432)(200,431)(201,465)(202,466)(203,468)(204,467)(205,461)(206,462)(207,464)(208,463)(209,477)(210,478)(211,480)(212,479)(213,473)(214,474)(215,476)(216,475)(217,469)(218,470)(219,472)(220,471)(221,445)(222,446)(223,448)(224,447)(225,441)(226,442)(227,444)(228,443)(229,457)(230,458)(231,460)(232,459)(233,453)(234,454)(235,456)(236,455)(237,449)(238,450)(239,452)(240,451);
s2 := Sym(480)!(  1, 21)(  2, 24)(  3, 23)(  4, 22)(  5, 25)(  6, 28)(  7, 27)(  8, 26)(  9, 29)( 10, 32)( 11, 31)( 12, 30)( 13, 33)( 14, 36)( 15, 35)( 16, 34)( 17, 37)( 18, 40)( 19, 39)( 20, 38)( 42, 44)( 46, 48)( 50, 52)( 54, 56)( 58, 60)( 61, 81)( 62, 84)( 63, 83)( 64, 82)( 65, 85)( 66, 88)( 67, 87)( 68, 86)( 69, 89)( 70, 92)( 71, 91)( 72, 90)( 73, 93)( 74, 96)( 75, 95)( 76, 94)( 77, 97)( 78,100)( 79, 99)( 80, 98)(102,104)(106,108)(110,112)(114,116)(118,120)(121,141)(122,144)(123,143)(124,142)(125,145)(126,148)(127,147)(128,146)(129,149)(130,152)(131,151)(132,150)(133,153)(134,156)(135,155)(136,154)(137,157)(138,160)(139,159)(140,158)(162,164)(166,168)(170,172)(174,176)(178,180)(181,201)(182,204)(183,203)(184,202)(185,205)(186,208)(187,207)(188,206)(189,209)(190,212)(191,211)(192,210)(193,213)(194,216)(195,215)(196,214)(197,217)(198,220)(199,219)(200,218)(222,224)(226,228)(230,232)(234,236)(238,240)(241,381)(242,384)(243,383)(244,382)(245,385)(246,388)(247,387)(248,386)(249,389)(250,392)(251,391)(252,390)(253,393)(254,396)(255,395)(256,394)(257,397)(258,400)(259,399)(260,398)(261,361)(262,364)(263,363)(264,362)(265,365)(266,368)(267,367)(268,366)(269,369)(270,372)(271,371)(272,370)(273,373)(274,376)(275,375)(276,374)(277,377)(278,380)(279,379)(280,378)(281,401)(282,404)(283,403)(284,402)(285,405)(286,408)(287,407)(288,406)(289,409)(290,412)(291,411)(292,410)(293,413)(294,416)(295,415)(296,414)(297,417)(298,420)(299,419)(300,418)(301,441)(302,444)(303,443)(304,442)(305,445)(306,448)(307,447)(308,446)(309,449)(310,452)(311,451)(312,450)(313,453)(314,456)(315,455)(316,454)(317,457)(318,460)(319,459)(320,458)(321,421)(322,424)(323,423)(324,422)(325,425)(326,428)(327,427)(328,426)(329,429)(330,432)(331,431)(332,430)(333,433)(334,436)(335,435)(336,434)(337,437)(338,440)(339,439)(340,438)(341,461)(342,464)(343,463)(344,462)(345,465)(346,468)(347,467)(348,466)(349,469)(350,472)(351,471)(352,470)(353,473)(354,476)(355,475)(356,474)(357,477)(358,480)(359,479)(360,478);
s3 := Sym(480)!(  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);
poly := sub<Sym(480)|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, s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s3*s2*s3*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References