Polytope of Type {2,15,6,4} with group SmallGroup(1920,240232)

s0 := (1,2);;
s1 := (  4,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 22)( 11, 15)( 12, 17)( 13, 16)( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)( 29, 60)( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)( 37, 52)( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)( 68, 81)( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)( 84,105)( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)( 92,117)( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)(100,109)(101,108)(102,110)(124,125)(127,139)(128,141)(129,140)(130,142)(131,135)(132,137)(133,136)(134,138)(143,163)(144,165)(145,164)(146,166)(147,179)(148,181)(149,180)(150,182)(151,175)(152,177)(153,176)(154,178)(155,171)(156,173)(157,172)(158,174)(159,167)(160,169)(161,168)(162,170)(184,185)(187,199)(188,201)(189,200)(190,202)(191,195)(192,197)(193,196)(194,198)(203,223)(204,225)(205,224)(206,226)(207,239)(208,241)(209,240)(210,242)(211,235)(212,237)(213,236)(214,238)(215,231)(216,233)(217,232)(218,234)(219,227)(220,229)(221,228)(222,230);;
s2 := (  3, 27)(  4, 28)(  5, 30)(  6, 29)(  7, 23)(  8, 24)(  9, 26)( 10, 25)( 11, 39)( 12, 40)( 13, 42)( 14, 41)( 15, 35)( 16, 36)( 17, 38)( 18, 37)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 43, 47)( 44, 48)( 45, 50)( 46, 49)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 57, 58)( 63, 87)( 64, 88)( 65, 90)( 66, 89)( 67, 83)( 68, 84)( 69, 86)( 70, 85)( 71, 99)( 72,100)( 73,102)( 74,101)( 75, 95)( 76, 96)( 77, 98)( 78, 97)( 79, 91)( 80, 92)( 81, 94)( 82, 93)(103,107)(104,108)(105,110)(106,109)(111,119)(112,120)(113,122)(114,121)(117,118)(123,147)(124,148)(125,150)(126,149)(127,143)(128,144)(129,146)(130,145)(131,159)(132,160)(133,162)(134,161)(135,155)(136,156)(137,158)(138,157)(139,151)(140,152)(141,154)(142,153)(163,167)(164,168)(165,170)(166,169)(171,179)(172,180)(173,182)(174,181)(177,178)(183,207)(184,208)(185,210)(186,209)(187,203)(188,204)(189,206)(190,205)(191,219)(192,220)(193,222)(194,221)(195,215)(196,216)(197,218)(198,217)(199,211)(200,212)(201,214)(202,213)(223,227)(224,228)(225,230)(226,229)(231,239)(232,240)(233,242)(234,241)(237,238);;
s3 := (  3,  6)(  7, 10)( 11, 14)( 15, 18)( 19, 22)( 23, 46)( 24, 44)( 25, 45)( 26, 43)( 27, 50)( 28, 48)( 29, 49)( 30, 47)( 31, 54)( 32, 52)( 33, 53)( 34, 51)( 35, 58)( 36, 56)( 37, 57)( 38, 55)( 39, 62)( 40, 60)( 41, 61)( 42, 59)( 63, 66)( 67, 70)( 71, 74)( 75, 78)( 79, 82)( 83,106)( 84,104)( 85,105)( 86,103)( 87,110)( 88,108)( 89,109)( 90,107)( 91,114)( 92,112)( 93,113)( 94,111)( 95,118)( 96,116)( 97,117)( 98,115)( 99,122)(100,120)(101,121)(102,119)(123,186)(124,184)(125,185)(126,183)(127,190)(128,188)(129,189)(130,187)(131,194)(132,192)(133,193)(134,191)(135,198)(136,196)(137,197)(138,195)(139,202)(140,200)(141,201)(142,199)(143,226)(144,224)(145,225)(146,223)(147,230)(148,228)(149,229)(150,227)(151,234)(152,232)(153,233)(154,231)(155,238)(156,236)(157,237)(158,235)(159,242)(160,240)(161,241)(162,239)(163,206)(164,204)(165,205)(166,203)(167,210)(168,208)(169,209)(170,207)(171,214)(172,212)(173,213)(174,211)(175,218)(176,216)(177,217)(178,215)(179,222)(180,220)(181,221)(182,219);;
s4 := (  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240)(121,241)(122,242);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP)

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s4*s3*s2*s3*s4*s3, s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma)

s0 := Sym(242)!(1,2);
s1 := Sym(242)!(  4,  5)(  7, 19)(  8, 21)(  9, 20)( 10, 22)( 11, 15)( 12, 17)( 13, 16)( 14, 18)( 23, 43)( 24, 45)( 25, 44)( 26, 46)( 27, 59)( 28, 61)( 29, 60)( 30, 62)( 31, 55)( 32, 57)( 33, 56)( 34, 58)( 35, 51)( 36, 53)( 37, 52)( 38, 54)( 39, 47)( 40, 49)( 41, 48)( 42, 50)( 64, 65)( 67, 79)( 68, 81)( 69, 80)( 70, 82)( 71, 75)( 72, 77)( 73, 76)( 74, 78)( 83,103)( 84,105)( 85,104)( 86,106)( 87,119)( 88,121)( 89,120)( 90,122)( 91,115)( 92,117)( 93,116)( 94,118)( 95,111)( 96,113)( 97,112)( 98,114)( 99,107)(100,109)(101,108)(102,110)(124,125)(127,139)(128,141)(129,140)(130,142)(131,135)(132,137)(133,136)(134,138)(143,163)(144,165)(145,164)(146,166)(147,179)(148,181)(149,180)(150,182)(151,175)(152,177)(153,176)(154,178)(155,171)(156,173)(157,172)(158,174)(159,167)(160,169)(161,168)(162,170)(184,185)(187,199)(188,201)(189,200)(190,202)(191,195)(192,197)(193,196)(194,198)(203,223)(204,225)(205,224)(206,226)(207,239)(208,241)(209,240)(210,242)(211,235)(212,237)(213,236)(214,238)(215,231)(216,233)(217,232)(218,234)(219,227)(220,229)(221,228)(222,230);
s2 := Sym(242)!(  3, 27)(  4, 28)(  5, 30)(  6, 29)(  7, 23)(  8, 24)(  9, 26)( 10, 25)( 11, 39)( 12, 40)( 13, 42)( 14, 41)( 15, 35)( 16, 36)( 17, 38)( 18, 37)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 43, 47)( 44, 48)( 45, 50)( 46, 49)( 51, 59)( 52, 60)( 53, 62)( 54, 61)( 57, 58)( 63, 87)( 64, 88)( 65, 90)( 66, 89)( 67, 83)( 68, 84)( 69, 86)( 70, 85)( 71, 99)( 72,100)( 73,102)( 74,101)( 75, 95)( 76, 96)( 77, 98)( 78, 97)( 79, 91)( 80, 92)( 81, 94)( 82, 93)(103,107)(104,108)(105,110)(106,109)(111,119)(112,120)(113,122)(114,121)(117,118)(123,147)(124,148)(125,150)(126,149)(127,143)(128,144)(129,146)(130,145)(131,159)(132,160)(133,162)(134,161)(135,155)(136,156)(137,158)(138,157)(139,151)(140,152)(141,154)(142,153)(163,167)(164,168)(165,170)(166,169)(171,179)(172,180)(173,182)(174,181)(177,178)(183,207)(184,208)(185,210)(186,209)(187,203)(188,204)(189,206)(190,205)(191,219)(192,220)(193,222)(194,221)(195,215)(196,216)(197,218)(198,217)(199,211)(200,212)(201,214)(202,213)(223,227)(224,228)(225,230)(226,229)(231,239)(232,240)(233,242)(234,241)(237,238);
s3 := Sym(242)!(  3,  6)(  7, 10)( 11, 14)( 15, 18)( 19, 22)( 23, 46)( 24, 44)( 25, 45)( 26, 43)( 27, 50)( 28, 48)( 29, 49)( 30, 47)( 31, 54)( 32, 52)( 33, 53)( 34, 51)( 35, 58)( 36, 56)( 37, 57)( 38, 55)( 39, 62)( 40, 60)( 41, 61)( 42, 59)( 63, 66)( 67, 70)( 71, 74)( 75, 78)( 79, 82)( 83,106)( 84,104)( 85,105)( 86,103)( 87,110)( 88,108)( 89,109)( 90,107)( 91,114)( 92,112)( 93,113)( 94,111)( 95,118)( 96,116)( 97,117)( 98,115)( 99,122)(100,120)(101,121)(102,119)(123,186)(124,184)(125,185)(126,183)(127,190)(128,188)(129,189)(130,187)(131,194)(132,192)(133,193)(134,191)(135,198)(136,196)(137,197)(138,195)(139,202)(140,200)(141,201)(142,199)(143,226)(144,224)(145,225)(146,223)(147,230)(148,228)(149,229)(150,227)(151,234)(152,232)(153,233)(154,231)(155,238)(156,236)(157,237)(158,235)(159,242)(160,240)(161,241)(162,239)(163,206)(164,204)(165,205)(166,203)(167,210)(168,208)(169,209)(170,207)(171,214)(172,212)(173,213)(174,211)(175,218)(176,216)(177,217)(178,215)(179,222)(180,220)(181,221)(182,219);
s4 := Sym(242)!(  3,123)(  4,124)(  5,125)(  6,126)(  7,127)(  8,128)(  9,129)( 10,130)( 11,131)( 12,132)( 13,133)( 14,134)( 15,135)( 16,136)( 17,137)( 18,138)( 19,139)( 20,140)( 21,141)( 22,142)( 23,143)( 24,144)( 25,145)( 26,146)( 27,147)( 28,148)( 29,149)( 30,150)( 31,151)( 32,152)( 33,153)( 34,154)( 35,155)( 36,156)( 37,157)( 38,158)( 39,159)( 40,160)( 41,161)( 42,162)( 43,163)( 44,164)( 45,165)( 46,166)( 47,167)( 48,168)( 49,169)( 50,170)( 51,171)( 52,172)( 53,173)( 54,174)( 55,175)( 56,176)( 57,177)( 58,178)( 59,179)( 60,180)( 61,181)( 62,182)( 63,183)( 64,184)( 65,185)( 66,186)( 67,187)( 68,188)( 69,189)( 70,190)( 71,191)( 72,192)( 73,193)( 74,194)( 75,195)( 76,196)( 77,197)( 78,198)( 79,199)( 80,200)( 81,201)( 82,202)( 83,203)( 84,204)( 85,205)( 86,206)( 87,207)( 88,208)( 89,209)( 90,210)( 91,211)( 92,212)( 93,213)( 94,214)( 95,215)( 96,216)( 97,217)( 98,218)( 99,219)(100,220)(101,221)(102,222)(103,223)(104,224)(105,225)(106,226)(107,227)(108,228)(109,229)(110,230)(111,231)(112,232)(113,233)(114,234)(115,235)(116,236)(117,237)(118,238)(119,239)(120,240)(121,241)(122,242);
poly := sub<Sym(242)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma)

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s4*s3*s2*s3*s4*s3, 
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s3*s2*s1*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s1*s3*s2*s1*s2*s1 >;

Overview

Special Properties

Related Polytopes

Quotients maximal quotients in bold

Covers minimal covers in bold

Representations