local z, r, result; result := rec(); result.comment := "2.L2(233) as 234 x 234 monomial matrices over Z(z232)\n"; # Change the value of r to any number between 1 and 58 # to get the complete set of inequivalent faithful irreducible 234-dimensional # representations of 2.L2(233) r := 1; z := E(232)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(234) ]; result.centralizeralgebra := [ IdentityMat(234) ]; result.generators := [ DiagonalMat([z^220,z^36,z^133,z^26,-1,z^179,z^170,z^197,z^213,z^65, z^173,z^140,z^178,z^19,z^73,z^46,z^92,z^9,z^81,z^125,1,z^221,z^104, z^171,z,z^141,z^2,z^200,z^15,z^145,z^159,z^75,z^45,z^210,z^129,z^187, z^211,z^168,z^131,z^132,z^83,z^136,z^61,z^175,z^18,z^151,z^50,z^68, z^119,z^24,z^218,z^122,z^43,z^48,z^166,z^216,z^4,z^183,z^20,z^79, z^44,z^28,z^67,z^89,z^217,z^77,z^148,z^76,z^215,z^86,z^63,z^23,z^38, z^72,z^12,z^174,z^226,z^205,z^154,z^35,z^29,z^107,z^202,z^7,z^101, z^49,z^30,z^130,z^228,z^152,z^37,z^111,z^57,z^105,z^103,z^139,z^181, z^156,z^97,z^177,z^11,z^40,z^123,z^108,z^209,z^161,z^194,z^100,z^191, z^128,z^60,z^176,z^186,z^78,z^33,z^192,z^42,z^227,z^21,z^198,z^124, z^85,z^117,z^8,z^155,z^138,z^110,z^118,z^54,z^195,z^69,z^203,z^98, z^80,z^169,z^91,z^25,z^56,z^219,z^230,z^84,z^90,z^109,z^229,z^167, z^34,z^121,z^99,z^208,z^52,z^112,z^157,z^126,z^207,z^199,z^142,z^206, z^182,z^96,z^70,z^189,z^153,z^47,z^87,z^222,z^172,z^114,z^224,z^144, z^146,z^150,z^193,z^31,z^27,z^82,z^53,z^94,z^223,z^3,z^225,z^6,z^149, z^63,z^32,z^120,z^106,z^115,z^102,z^204,z^162,z^190,z^134,z^137, z^66,z^22,z^17,z^14,z^93,z^214,z^39,z^88,z^184,z^143,z^16,z^51,z^163, z^188,z^41,z^64,z^231,z^55,z^62,z^212,z^10,z^196,z^135,z^58,z^180, z^201,z^113,z^13,z^74,z^185,z^165,z^158,z^71,z^59,z^127,z^95,z^160, z^5,z^147,z^164,z^53]) * PermutationMat( ( 1,110)( 2,134)( 3, 69)( 4,142)( 5, 21)( 6,135)( 7, 13)( 8, 46) ( 9,216)( 10,205)( 11, 44)( 12,149)( 14, 99)( 15, 53)( 16,160)( 17, 50) ( 18, 82)( 19, 80)( 20,178)( 22,228)( 23, 75)( 24,100)( 25,187)( 26,154) ( 27,167)( 28, 67)( 29, 85)( 30,132)( 31,161)( 32,208)( 33,226)( 34,126) ( 35,139)( 36,106)( 37,193)( 38,218)( 39, 65)( 40, 56)( 41,115)( 42,213) ( 43,211)( 45,133)( 47,194)( 48, 54)( 49,144)( 51, 88)( 52, 77)( 55,158) ( 57,151)( 58,224)( 59,159)( 60, 91)( 61, 74)( 62,201)( 63, 86)( 64,174) ( 66,200)( 68,102)( 70, 87)( 71,176)( 72,198)( 73,114)( 78,203)( 79,107) ( 81,164)( 83,170)( 84,143)( 89,185)( 90,215)( 92,231)( 93,227)( 94,101) ( 95,221)( 96,105)( 97,145)( 98,116)(103,180)(104,124)(108,204)(109,152) (111,138)(112,166)(113,190)(117,222)(118,147)(119,229)(120,171)(121,168) (122,173)(123,210)(125,172)(127,181)(128,140)(129,212)(130,162)(131,163) (136,137)(141,184)(146,175)(148,196)(150,209)(153,165)(155,182)(156,157) (169,189)(177,195)(179,220)(183,234)(186,214)(188,197)(191,225)(192,199) (202,233)(206,223)(207,230)(219,232), 234) , DiagonalMat([z^25,z^187,z^230,z^68,z^64,z^119,z^90,z^131,z^28,z^40, z^30,z^43,z^186,z^195,z^69,z^157,z^143,z^152,z^139,z^9,z^199,z^227, z^171,z^174,z^103,z^59,z^54,z^51,z^130,z^19,z^76,z^125,z^221,z^180, z^53,z^88,z^200,z^225,z^78,z^101,z^36,z^92,z^99,z^17,z^47,z,z^172, z^95,z^217,z^6,z^150,z^50,z^111,z^222,z^202,z^195,z^108,z^96,z^164, z^132,z^197,z^42,z^184,z^201,z^73,z^170,z^63,z^153,z^216,z^207,z^2, z^18,z^102,z^210,z^177,z^215,z^56,z^110,z^83,z^129,z^46,z^118,z^162, z^37,z^26,z^141,z^208,z^38,z^178,z^39,z^5,z^52,z^182,z^196,z^112, z^82,z^15,z^166,z^224,z^16,z^205,z^168,z^169,z^120,z^173,z^98,z^212, z^55,z^188,z^87,z^105,z^156,z^61,z^23,z^159,z^80,z^85,z^203,z^21, z^41,z^220,z^57,-1,z^81,z^65,z^104,z^126,z^22,z^114,z^185,z^113, z^20,z^123,z^100,z^60,z^75,z^109,z^49,z^211,z^31,z^10,z^191,z^72, z^66,z^144,z^7,z^44,z^138,z^86,z^67,z^167,z^33,z^189,z^74,z^148, z^94,z^142,z^140,z^176,z^218,z^193,z^134,z^214,z^48,z^77,z^160,z^145, z^14,z^198,z^231,z^137,z^228,z^165,z^97,z^213,z^223,z^115,z^70,z^229, z^79,z^32,z^58,z^3,z^161,z^122,z^154,z^45,z^192,z^175,z^147,z^155, z^91,1,z^106,z^8,z^135,z^117,z^206,z^128,z^62,z^93,z^24,z^35,z^121, z^127,z^146,z^34,z^204,z^71,z^158,z^136,z^13,z^89,z^149,z^194,z^163, z^12,z^4,z^179,z^11,z^219,z^133,z^107,z^226,z^190,z^84,z^124,z^27, z^209,z^151,z^29,z^181,z^183,z^153]) * PermutationMat( ( 1,146, 37)( 2,197,166)( 3,131,204)( 4,125, 43)( 5, 61,118)( 6, 71, 53) ( 7, 73, 10)( 8, 33, 95)( 9,170,101)( 11,165, 32)( 12,202,173)( 13,199, 51) ( 14,234,123)( 15,221,159)( 16,113,168)( 17,205,215)( 18,174, 76)( 19, 26,207) ( 20,178, 68)( 21,194,115)( 22,112,124)( 23,136,160)( 24,137,232)( 25, 62,110) ( 27,132,210)( 28,133,182)( 29,157,188)( 30, 75, 41)( 31, 91,230)( 34, 64, 79) ( 35,156,117)( 36, 48,138)( 38, 70,181)( 39, 67,192)( 40,104,220)( 42, 99,155) ( 44,196,116)( 45,198,139)( 46,208,228)( 47,144,224)( 49, 72,179)( 50, 98,135) ( 52, 66,217)( 54, 60, 78)( 55,223,191)( 56,120,172)( 57, 74,206)( 58,189,161) ( 59,222,151)( 63,229,209)( 65,127,152)( 69,129,162)( 77,212,216)( 80,167,225) ( 81, 96,126)( 82,100,106)( 83,176,180)( 84,218,142)( 85,130,119)( 86,103,186) ( 87,153,150)( 88,111,213)( 89,154,107)( 90,122,211)( 92,214,140)( 93,121,200) ( 94,108,175)( 97,183,163)(102,231,203)(105,201,169)(109,193,147)(114,164,184) (128,227,149)(134,141,185)(143,177,187)(145,233,171)(148,219,190)(158,226,195), 234)]; return result;