local z, r, result; result := rec(); result.comment := "L2(223) as 224 x 224 monomial matrices over Z(z111)\n"; # Change the value of r to any number between 1 and 55 # to get the complete set of inequivalent faithful irreducible 224-dimensional # representations of L2(223) r := 1; z := E(111)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(224) ]; result.centralizeralgebra := [ IdentityMat(224) ]; result.generators := [ DiagonalMat([z^25,z^3,z^15,z^32,z^39,z^101,z^46,z^86,z^104,z^46,z^18, z^12,z^72,z^20,z^50,z^102,z^76,z^36,z^11,z^31,z^48,z^24,z^37,z^75, z^51,z^19,z^43,z^33,z^14,z^34,z^4,z,z^73,z^11,z^88,z^57,z^51,z^52, z^74,1,z^68,z^109,z^79,z^2,z^3,z^78,z^27,z^48,z^37,z^84,z^90,z^40, z^71,z^55,z^28,z^105,z^85,z^69,z^41,z^89,z^13,z^91,z^110,z^67,z^109, z^89,z^10,z^85,z^36,z^63,z^78,z^97,z^19,z^45,z^60,z^28,z^77,z^70, z^22,z^32,z^10,z^60,z^95,z^93,z^58,z^87,z^45,z^87,z^49,z^26,z^24, z^29,z^59,z^92,z^42,z^80,z^82,1,z^90,z^108,z^6,z^92,z^12,z^35,z^107, z^93,z^5,z^98,z^77,z^101,z^29,z^54,z,z^81,z^21,z^71,z^76,z^103,z^49, z^30,z^100,z^43,z^91,z^83,z^65,z^52,z^56,z^70,z^84,z^72,z^39,z^26, z^25,z^47,z^103,z^56,z^96,z^99,z^4,z^7,z^107,z^98,z^53,z^64,z^35, z^13,z^17,z^74,z^64,z^16,z^81,z^41,z^66,z^82,z^15,z^7,z^62,z^105, z^30,z^23,z^69,z^110,z^66,z^20,z^96,z^59,z^61,z^9,z^22,z^80,z^108, z^34,z^42,z^68,z^24,z^67,z^40,z^31,z^104,z^75,z^16,z^2,z^53,z^50, z^86,z^9,z^54,z^97,z^55,z^8,z^14,z^88,z^44,z^99,z^106,z^61,z^44, z^18,z^57,z^102,z^38,z^47,z^100,z^95,z^5,z^33,z^21,z^65,z^73,z^83, z^79,z^62,z^58,z^17,z^63,z^6,z^94,z^94,z^106,z^27,z^38,z^23,z^8, z^87]) * PermutationMat( ( 1, 8)( 2,100)( 3,165)( 4, 43)( 5, 13)( 6, 67)( 7,208)( 9,156) ( 10,125)( 11,106)( 12,138)( 14,123)( 15,167)( 16,168)( 17,145)( 18,180) ( 19,121)( 20, 96)( 21, 70)( 22, 88)( 23,148)( 24, 69)( 25, 82)( 26, 94) ( 27,174)( 28, 46)( 29, 72)( 30,109)( 31,105)( 32, 63)( 33,201)( 34,203) ( 35,160)( 36,187)( 37, 75)( 38,166)( 39, 49)( 40, 98)( 41,122)( 42, 44) ( 45,171)( 47,129)( 48,215)( 50,220)( 51,115)( 52, 53)( 54,136)( 55,124) ( 56,216)( 57, 90)( 58,173)( 59,128)( 60,169)( 61,142)( 62,164)( 64,193) ( 65,182)( 66, 79)( 68,132)( 71,206)( 73,102)( 74,153)( 76,210)( 77,172) ( 78,152)( 80,211)( 81,110)( 83,181)( 84,198)( 85,143)( 86, 91)( 87,163) ( 89,157)( 92, 97)( 93,126)( 95,161)( 99,207)(101,158)(103,194)(104,117) (107,195)(108,146)(111,154)(112,199)(113,162)(114,159)(116,177)(118,223) (119,212)(120,151)(127,189)(130,131)(133,185)(134,144)(135,190)(137,155) (139,141)(140,179)(147,218)(149,202)(150,204)(170,178)(175,224)(176,197) (183,213)(184,196)(186,200)(188,191)(192,222)(205,219)(209,221)(214,217), 224) , DiagonalMat([z^7,z^91,z^71,z^103,z^67,z^18,z^45,z^60,z^79,z,z^27,z^42, z^10,z^59,z^52,z^4,z^14,z^103,z^42,z^77,z^75,z^40,z^69,z^27,z^69, z^31,z^8,z^6,z^11,z^41,z^74,z^24,z^62,z^64,z^93,z^72,z^90,z^99,z^74, z^105,z^17,z^89,z^75,z^98,z^80,z^59,z^83,z^11,z^36,z^94,z^63,z^3, z^53,z^58,z^85,z^31,z^12,z^82,z^25,z^73,z^65,z^47,z^34,z^38,z^52, z^66,z^54,z^21,z^8,z^7,z^29,z^85,z^38,z^78,z^81,z^97,z^100,z^89, z^80,z^35,z^46,z^17,z^106,z^110,z^56,z^46,z^109,z^63,z^23,z^48,z^64, z^108,z^100,z^44,z^87,z^12,z^5,z^51,z^92,z^48,z^2,z^78,z^41,z^43, z^102,z^4,z^62,z^90,z^16,z^24,z^50,z^105,z^49,z^22,z^13,z^86,z^57, z^109,z^95,z^35,z^32,z^68,z^102,z^36,z^79,z^37,z^101,z^107,z^70, z^26,z^81,z^88,z^43,z^26,1,z^39,z^84,z^20,z^29,z^82,z^77,z^98,z^15, z^3,z^47,z^55,z^65,z^61,z^44,z^40,z^110,z^45,z^99,z^76,z^76,z^88, z^9,z^20,z^5,z^101,z^96,z^108,z^14,z^21,z^83,z^28,z^68,z^86,z^28, 1,z^105,z^54,z^2,z^32,z^84,z^58,z^18,z^104,z^13,z^30,z^6,z^19,z^57, z^33,z,z^25,z^15,z^107,z^16,z^97,z^94,z^55,z^104,z^70,z^39,z^33, z^34,z^56,z^93,z^50,z^91,z^61,z^95,z^96,z^60,z^9,z^30,z^19,z^66, z^72,z^22,z^53,z^37,z^10,z^87,z^67,z^51,z^23,z^71,z^106,z^73,z^92, z^49,z^6]) * PermutationMat( ( 1, 53,217)( 2,160,180)( 3,200,127)( 4,124, 47)( 5,163,207)( 6, 80, 54) ( 7,173, 34)( 8,145,106)( 9, 95,198)( 10,175,130)( 11, 84, 72)( 12, 25,135) ( 13,148,150)( 14,142, 61)( 15, 17,152)( 16,125,166)( 18, 45,136)( 19,167,185) ( 20,157, 59)( 21,108,183)( 22, 64,196)( 23,151,104)( 24,114,107)( 26, 69, 36) ( 27,169, 43)( 28,123, 52)( 29,120,147)( 30,140,153)( 31,177,208)( 32, 33,186) ( 35,212,155)( 37, 67, 74)( 38,187,162)( 40,149,221)( 41,161,118)( 42,137,113) ( 44, 55,195)( 46,209, 76)( 48,203, 97)( 49,172,164)( 50, 79,100)( 51,141, 58) ( 56, 82, 88)( 57,144,204)( 60,219,102)( 62, 87, 66)( 63,168,105)( 65, 86,115) ( 68,184,117)( 70,156,189)( 71,197, 90)( 73,216,181)( 75,190, 94)( 77, 83,109) ( 78,103, 99)( 81,154, 93)( 85,159,111)( 89,178,119)( 91, 98,128)( 92,206,171) ( 96,139,129)(101,143,191)(110,121,192)(112,224,170)(116,223,215)(122,218,138) (131,214,158)(132,133,201)(134,179,210)(146,202,220)(165,174,188)(176,193,205) (182,194,211)(199,213,222), 224)]; return result;