local z, r, result; result := rec(); result.comment := "L2(227) as 228 x 228 monomial matrices over Z(z113)\n"; # Change the value of r to any number between 1 and 56 # to get the complete set of inequivalent faithful irreducible 228-dimensional # representations of L2(227) r := 1; z := E(113)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(228) ]; result.centralizeralgebra := [ IdentityMat(228) ]; result.generators := [ DiagonalMat([z^79,z^28,z^98,z^9,z^64,z^91,z^88,z^29,z^6,z^74,z^59, z^46,z^50,z^42,z^82,z^70,z^39,z^76,z^93,z^27,z^83,z^103,z^20,z^23, z^75,z^5,z^63,z^43,z^49,z^111,z^29,z^3,z^13,z^10,z^97,z^103,z^70, z^34,z^78,z^33,z^68,z^100,z^93,z^5,z^7,z^109,z^21,z^102,z^39,z^32, z^51,z^105,z^61,z^8,z^4,z^86,z^65,z^8,z^73,z^55,z^17,z^47,z^58,z^17, z^24,z^19,z^31,z^45,z^89,z^111,z^56,z^58,z^30,z^87,z^62,z^104,z^82, z^35,z^69,z^32,z^18,z^54,z^40,z^69,z^77,z^38,z^18,z^57,z^110,z^6, z^92,z^112,z^48,z^16,z^94,z^75,z^108,z^95,z^23,z^37,z^54,z^24,z^94, z^99,z^2,z^11,z^12,z^12,z,z^64,z^4,z^28,z^92,z^63,z^86,z^13,z^11, z^84,z^26,z^48,z^56,z^72,z^21,z^95,z^15,z^66,z^61,z^96,z^20,z^52, z^67,z^14,z^2,z^9,z^60,z^107,z^15,z^99,z^27,z^112,z^88,z^44,z^90, z^44,z^62,z^65,1,z^26,z^41,z^35,z^80,z^110,z^79,z^33,z^38,z^22,z^108, z^59,z^55,z^36,z^81,z^34,z^77,z^100,z^14,z^85,1,z^91,z^43,z^104, z^96,z^107,z^46,z^30,z^110,z^72,z^36,z^40,z^101,z^67,z^105,z^42, z^25,z^16,z^106,z^50,z^89,z^90,z^49,z^25,z^53,z^101,z^76,z^22,z^71, z^81,z^80,z^78,z^68,z^51,z^45,z^87,z^3,z^98,z^83,z^41,z^53,z^19, z^37,z^71,z^102,z^52,z^31,z^57,z^47,z^106,z^66,z^85,z^10,z,z^84, z^97,z^60,z^73,z^109,z^74,z^7,z^3]) * PermutationMat( ( 1, 38)( 2,166)( 3,125)( 4, 76)( 5,189)( 6,194)( 7,183)( 8,221) ( 9,136)( 10, 17)( 11, 82)( 12,131)( 13, 27)( 14,210)( 15,213)( 16,169) ( 18,100)( 19,129)( 20, 56)( 21,174)( 22, 34)( 23, 43)( 24,188)( 25, 86) ( 26,157)( 28, 37)( 29,110)( 30,105)( 31,118)( 32, 89)( 33,164)( 35, 94) ( 36,219)( 39,150)( 40,151)( 41, 68)( 42,116)( 44, 97)( 45,216)( 46,111) ( 47, 91)( 48,106)( 49,226)( 50,196)( 51, 75)( 52, 58)( 53,212)( 54,181) ( 55,225)( 57,120)( 59,178)( 60, 63)( 61,171)( 62,126)( 64,128)( 65,187) ( 66,103)( 67, 77)( 69,102)( 70,133)( 71,214)( 72,159)( 73,205)( 74,148) ( 78,198)( 79,144)( 80,161)( 81, 98)( 83,224)( 84,142)( 85,160)( 87,124) ( 88,121)( 90,172)( 92,109)( 93,146)( 95,208)( 96,155)( 99,143)(101,158) (104,165)(107,192)(108,179)(112,218)(113,123)(114,186)(115,139)(117,211) (119,202)(122,149)(127,130)(132,138)(134,170)(135,191)(137,204)(140,220) (141,190)(145,200)(147,167)(152,228)(153,162)(154,197)(156,168)(163,177) (173,180)(175,203)(176,206)(182,195)(184,222)(185,227)(193,209)(199,201) (207,223)(215,217), 228) , DiagonalMat([z^102,z^48,z^76,z^11,z^99,z^45,z^94,z^104,z^103,z^101, z^91,z^74,z^68,z^110,z^26,z^8,z^106,z^64,z^76,z^42,z^60,z^94,z^12, z^75,z^54,z^80,z^70,z^16,z^89,z^108,z^33,z^24,z^107,z^7,z^83,z^96, z^19,z^97,z^30,z^51,z^8,z^32,z^87,z,z^111,z^52,z^29,z^97,z^82,z^69, z^73,z^65,z^105,z^93,z^62,z^99,z^3,z^50,z^106,z^13,z^43,z^46,z^98, z^28,z^86,z^66,z^72,z^21,z^52,z^26,z^36,z^33,z^7,z^13,z^93,z^57, z^101,z^56,z^91,z^10,z^3,z^28,z^30,z^19,z^44,z^12,z^62,z^55,z^74, z^15,z^84,z^31,z^27,z^109,z^88,z^31,z^96,z^78,z^40,z^70,z^81,z^40, z^47,z^42,z^54,z^68,z^112,z^21,z^79,z^81,z^53,z^110,z^85,z^14,z^105, z^58,z^92,z^55,z^41,z^77,z^63,z^92,z^100,z^61,z^41,z^80,z^20,z^29, z^2,z^22,z^71,z^39,z^4,z^98,z^18,z^5,z^46,z^60,z^77,z^47,z^4,z^9, z^25,z^34,z^35,z^35,z^24,z^87,z^27,z^51,z^2,z^86,z^109,z^36,z^34, z^107,z^49,z^71,z^79,z^95,z^44,z^5,z^38,z^89,z^84,z^6,z^43,z^75, z^90,z^37,z^25,z^32,z^83,z^17,z^38,z^9,z^50,z^22,z^111,z^67,1,z^67, z^85,z^88,z^23,z^49,z^64,z^58,z^103,z^49,z^102,z^56,z^61,z^45,z^18, z^82,z^78,z^59,z^104,z^57,z^100,z^10,z^37,z^108,z^23,z,z^66,z^14, z^6,z^17,z^69,z^53,z^20,z^95,z^59,z^63,z^11,z^90,z^15,z^65,z^48, z^39,z^16,z^73,z^112,1,z^72,z^64]) * PermutationMat( ( 1,142,151)( 2, 69, 60)( 3, 73, 39)( 4, 66,154)( 5,127,156)( 6,189,197) ( 7, 71, 97)( 8,217, 45)( 9, 35, 99)( 10, 48, 64)( 11, 51, 87)( 12, 30, 85) ( 13,145,202)( 14,147,117)( 15,188,128)( 16, 88,177)( 17, 36, 32)( 18, 90,155) ( 19, 55, 95)( 20, 78,219)( 21, 76, 94)( 22,193,158)( 23,108, 26)( 24,119,112) ( 25,168, 38)( 27,146, 41)( 28, 86,113)( 29,210, 34)( 31,149,111)( 33,103, 67) ( 37,104, 46)( 40,102,178)( 42, 58, 96)( 43,201,132)( 44,226,225)( 47,159,162) ( 49,169,105)( 50,137,179)( 52,123,124)( 53,216,116)( 54,208,209)( 56,153,195) ( 57,227,163)( 59,170,173)( 61,115, 98)( 62,107,106)( 63,200,131)( 65,186, 79) ( 68,164, 81)( 70, 89, 74)( 72,122, 77)( 75,221,183)( 80,224, 83)( 82,220,213) ( 84,174,139)( 91,204,144)( 92,215,185)( 93,130,187)(100,135,143)(101,176,205) (109,134,157)(110,196,121)(114,160,133)(118,148,165)(120,140,191)(125,207,166) (126,138,152)(129,182,161)(136,222,211)(141,192,212)(150,203,171)(167,184,214) (172,218,199)(175,198,223)(180,194,206)(181,190,228), 228)]; return result;