local z, r, result; result := rec(); result.comment := "L2(191) as 192 x 192 monomial matrices over Z(z95)\n"; # Change the value of r to any number between 1 and 47 # to get the complete set of inequivalent faithful irreducible 192-dimensional # representations of L2(191) r := 1; z := E(95)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(192) ]; result.centralizeralgebra := [ IdentityMat(192) ]; result.generators := [ DiagonalMat([z^36,z^73,z^4,z^8,z^53,z^24,z^27,z^84,z^91,z^52,z^19, z^86,z^67,z^22,z^91,z^75,z^51,z^87,z^18,z^57,z^26,z^60,z^42,z^63, z^48,z^13,z^25,z,z^30,z^16,z^34,z^5,z^47,z^55,z^44,z^2,z^24,z^63, z^37,z^35,z^15,z^93,z^61,z^25,z^52,z^74,z^66,z^80,z^77,z^41,z^79, z^58,z^17,z^29,z^31,z^10,z^56,z^31,1,z^70,z^20,z^81,z^49,z^57,z^9, z^3,z^44,z^11,z^30,z^76,z^64,z^23,z^66,z^32,z^28,z^23,z^16,z^60, z^69,z^39,z^17,z^22,z^35,z^93,z^81,z^65,z^75,z^58,z^48,z^4,z^46, z^64,z^45,z^2,z^45,z^54,z^70,z^59,z^74,z^85,z^26,z^12,z^6,z^27,z^56, z^46,z,z^7,z^11,z^14,z^47,z^3,z^43,z^54,z^7,z^82,z^19,z^72,z^77, z^29,z^20,z^51,z^84,z^38,z^62,z^92,z^21,z^69,z^89,z^86,z^73,z^18, z^38,z^94,z^34,z^36,z^21,z^28,z^5,z^72,z^12,z^43,z^59,z^78,z^79, z^9,z^64,z^41,z^82,z^92,z^83,z^40,z^68,z^49,z^62,z^32,z^55,z^42, z^76,z^90,z^68,z^85,z^50,z^80,z^40,z^13,z^71,z^94,z^14,z^39,z^83, z^6,z^33,z^65,z^8,1,z^37,z^33,z^61,z^15,z^10,z^78,z^71,z^53,z^90, z^89,z^87,z^88,z^88,z^50,z^67,z^31]) * PermutationMat( ( 1, 98)( 2, 82)( 3, 15)( 4, 18)( 5,158)( 6,167)( 7,153)( 8,109) ( 9, 90)( 10,142)( 11,159)( 12, 65)( 13,138)( 14,131)( 16,121)( 17, 35) ( 19, 49)( 20,133)( 21,128)( 22, 83)( 23,184)( 24, 74)( 25, 33)( 26,149) ( 27, 97)( 28,134)( 29, 86)( 30, 51)( 31,179)( 32,185)( 34,152)( 36, 84) ( 37,183)( 38,156)( 39, 88)( 40, 78)( 41,164)( 42, 94)( 43,135)( 44, 60) ( 45,113)( 46,137)( 47, 54)( 48,180)( 50,114)( 52,177)( 53,144)( 55,147) ( 56,162)( 57,170)( 58, 71)( 59,176)( 61, 87)( 62,169)( 63, 91)( 64,124) ( 66,126)( 67,122)( 68,123)( 69,174)( 70,117)( 72,118)( 73,120)( 75,191) ( 76,140)( 77,145)( 79,101)( 80,105)( 81,182)( 85,110)( 89,111)( 92,192) ( 93,163)( 95,190)( 96,148)( 99,127)(100,181)(102,151)(103,129)(104,161) (106,154)(107,168)(108,188)(112,150)(115,189)(116,166)(119,132)(125,178) (130,146)(136,143)(139,160)(141,171)(155,173)(157,165)(172,186)(175,187), 192) , DiagonalMat([z^36,z^73,z^4,z^8,z^53,z^24,z^27,z^84,z^91,z^52,z^19, z^86,z^67,z^22,z^91,z^75,z^51,z^87,z^18,z^57,z^26,z^60,z^42,z^63, z^48,z^13,z^25,z,z^30,z^16,z^34,z^5,z^47,z^55,z^44,z^2,z^24,z^63, z^37,z^35,z^15,z^93,z^61,z^25,z^52,z^74,z^66,z^80,z^77,z^41,z^79, z^58,z^17,z^29,z^31,z^10,z^56,z^31,1,z^70,z^20,z^81,z^49,z^57,z^9, z^3,z^44,z^11,z^30,z^76,z^64,z^23,z^66,z^32,z^28,z^23,z^16,z^60, z^69,z^39,z^17,z^22,z^35,z^93,z^81,z^65,z^75,z^58,z^48,z^4,z^46, z^64,z^45,z^2,z^45,z^54,z^70,z^59,z^74,z^85,z^26,z^12,z^6,z^27,z^56, z^46,z,z^7,z^11,z^14,z^47,z^3,z^43,z^54,z^7,z^82,z^19,z^72,z^77, z^29,z^20,z^51,z^84,z^38,z^62,z^92,z^21,z^69,z^89,z^86,z^73,z^18, z^38,z^94,z^34,z^36,z^21,z^28,z^5,z^72,z^12,z^43,z^59,z^78,z^79, z^9,z^64,z^41,z^82,z^92,z^83,z^40,z^68,z^49,z^62,z^32,z^55,z^42, z^76,z^90,z^68,z^85,z^50,z^80,z^40,z^13,z^71,z^94,z^14,z^39,z^83, z^6,z^33,z^65,z^8,1,z^37,z^33,z^61,z^15,z^10,z^78,z^71,z^53,z^90, z^89,z^87,z^88,z^88,z^50,z^67,z^31]) * PermutationMat( ( 1,178, 21)( 2, 90, 19)( 3, 55, 22)( 4, 63,133)( 5,113,168)( 6, 91, 44) ( 7, 50,104)( 8, 98, 33)( 9, 40, 71)( 10, 23, 28)( 11, 80, 39)( 12,134,181) ( 13,152,171)( 14,119, 15)( 16, 83,164)( 17, 76,137)( 18, 27,144)( 20,189, 95) ( 24,101,103)( 25, 77, 58)( 26,121,125)( 29,123,159)( 30, 73,166)( 31,105,139) ( 32,177,184)( 34, 82,132)( 35,176,122)( 36,179, 74)( 37,100, 85)( 38,135, 42) ( 41,190, 69)( 43,185,170)( 45,148, 94)( 46,138,188)( 47,172, 72)( 48, 86, 93) ( 49,131,165)( 51,111,147)( 52, 57, 70)( 53, 62,126)( 54,145,149)( 56,167,169) ( 59, 92,192)( 60,175, 81)( 61,180, 78)( 64,106,187)( 65,151, 66)( 67, 99,118) ( 68, 89,136)( 75,102,157)( 79,155,143)( 84,114,142)( 87,116,173)( 88,160,158) ( 96,161,153)( 97,154,183)(107,146,162)(108,124,163)(109,174,117)(110,182,112) (115,191,127)(120,140,129)(128,156,186)(130,150,141), 192)]; return result;