local z, r, result; result := rec(); result.comment := "L2(197) as 198 x 198 monomial matrices over Z(z98)\n"; # Change the value of r to any number between 1 and 48 # to get the complete set of inequivalent faithful irreducible 198-dimensional # representations of L2(197) r := 1; z := E(98)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(198) ]; result.centralizeralgebra := [ IdentityMat(198) ]; result.generators := [ DiagonalMat([z^37,z^75,z^66,z^41,z^70,z^14,z^62,z^33,z^23,z^20,z^91, z^40,z^48,z^88,z^34,z^74,z^96,z^18,z^81,z^75,z^33,z^92,z^71,z^77, z^6,z^16,-1,z^39,z^38,z^36,z^46,z^8,z^15,z^69,z^88,z^51,z^8,z^4, z^25,z^97,z^65,z^90,z^54,z^38,z^18,z^37,z^52,z^87,z^61,z^92,z^19, z^95,1,z^42,z^78,z^58,z^3,z^93,z^32,z^21,z^22,z^22,z^31,z^95,z^84, z^56,-1,z^69,z^9,z^50,z^55,z^89,z^68,z^45,z^4,z^57,z^16,z^7,z^57, z^83,z^85,z^94,z^24,z^73,z^30,1,z^24,z^32,z^19,z^64,z^10,z^68,z^34, z^61,z,z^94,z^2,z^85,z^17,z^5,z^44,z^27,z^58,z^6,z^80,z^66,z^96, z^30,z^59,z^77,z^14,z^9,z^45,z^79,z^41,z^90,z^10,z^13,z^86,z,z^29, z^26,z^3,z^83,z^11,z^89,z^47,z^35,z^87,z^12,z^55,z^39,z^53,z^35, z^67,z^79,z^27,z^28,z^78,z^70,z^48,z^53,z^36,z^52,z^46,z^67,z^74, z^23,z^21,z^72,z^59,z^26,z^43,z^28,z^43,z^97,z^73,z^20,z^31,z^72, z^91,z^64,z^81,z^5,z^7,z^76,z^62,z^86,z^82,z^63,z^13,z^50,z^15,z^76, z^80,z^44,z^25,z^93,z^60,z^29,z^42,z^65,z^18,z^84,z^2,z^60,z^71, z^40,z^54,z^47,z^51,z^12,z^82,z^17,z^56,z^11,z^63,z^80]) * PermutationMat( ( 1, 49)( 2, 9)( 3, 59)( 4, 79)( 5,154)( 6,184)( 7,143)( 8, 41) ( 10, 55)( 11, 78)( 12, 56)( 13,172)( 14,117)( 15, 90)( 16, 83)( 17, 97) ( 18,175)( 19,194)( 20,148)( 21,182)( 22, 25)( 23,137)( 24,149)( 26,169) ( 28,109)( 29,179)( 30,167)( 31,144)( 32,116)( 33,124)( 34,180)( 35, 91) ( 36,190)( 37, 42)( 38, 82)( 39, 84)( 40, 95)( 43,176)( 44,186)( 45,198) ( 46, 94)( 47,145)( 48,196)( 50,104)( 51,114)( 52, 57)( 53, 86)( 54,195) ( 58,100)( 60,110)( 61,166)( 62,174)( 63,146)( 64,123)( 65,111)( 66,181) ( 68,121)( 69, 72)( 70,141)( 71,153)( 73,108)( 74,142)( 75, 96)( 76,115) ( 77,193)( 80,173)( 81,118)( 85, 92)( 87,147)( 88,106)( 89,136)( 93,162) ( 98,171)( 99,163)(101,189)(102,187)(103,188)(105,183)(107,185)(112,126) (113,133)(119,192)(120,156)(122,160)(125,129)(127,191)(128,197)(130,168) (131,155)(132,151)(134,170)(135,159)(138,140)(139,158)(150,152)(157,177) (161,165)(164,178), 198) , DiagonalMat([z^38,z^27,z^4,z^84,z^12,z^90,z^48,z^36,z^88,z^13,z^56, z^40,z^54,z^36,z^68,z^80,z^28,z^29,z^79,z^71,-1,z^54,z^37,z^53,z^47, z^68,z^75,z^24,z^22,z^73,z^60,z^27,z^44,z^29,z^44,1,z^74,z^21,z^32, z^73,z^92,z^65,z^82,z^6,z^8,z^77,z^63,z^87,z^83,z^64,z^14,z^51,z^16, z^77,z^81,z^45,z^26,z^94,z^61,z^30,z^43,z^66,z^19,z^85,z^3,z^61, z^72,z^41,z^55,z^48,z^52,z^13,z^83,z^18,z^57,z^12,z^64,z^76,z^67, z^42,z^71,z^15,z^63,z^34,z^24,z^21,z^92,z^41,-1,z^89,z^35,z^75,z^97, z^19,z^82,z^76,z^34,z^93,z^72,z^78,z^7,z^17,z^50,z^40,z^39,z^37, z^47,z^9,z^16,z^70,z^89,z^52,z^9,z^5,z^26,1,z^66,z^91,z^55,z^39, z^39,z^38,z^53,z^88,z^62,z^93,z^20,z^96,z,z^43,z^79,z^59,z^4,z^94, z^33,z^22,z^23,z^23,z^32,z^96,z^85,z^57,z^50,z^70,z^10,z^51,z^56, z^90,z^69,z^46,z^5,z^58,z^17,z^8,z^58,z^84,z^86,z^95,z^25,z^74,z^31, z,z^25,z^33,z^20,z^65,z^11,z^69,z^35,z^62,z^2,z^95,z^3,z^86,z^18, z^6,z^45,z^28,z^59,z^7,z^81,z^67,z^97,z^31,z^60,z^78,z^15,z^10,z^46, z^80,z^42,z^91,z^11,z^14,z^87,z^2,z^30,z^59]) * PermutationMat( ( 1,141, 30)( 2, 71, 94)( 3, 28,110)( 4,143,170)( 5, 77,136)( 6,197, 96) ( 7,194, 8)( 9, 53, 87)( 10,147, 34)( 11,180, 91)( 12,131, 54)( 13, 57,175) ( 14,138,120)( 15,172,164)( 16, 76, 44)( 17,160,134)( 18,154, 66)( 19,150, 81) ( 20,123, 67)( 21, 40, 37)( 22,186, 50)( 23, 75,133)( 24, 70,158)( 25,188, 88) ( 26, 45, 29)( 27,125,132)( 31,163, 72)( 32,115, 56)( 33, 97,165)( 35,190, 99) ( 36,121,198)( 38, 63,152)( 39,130,137)( 41,174, 74)( 42,104,192)( 43,129,187) ( 46,195,139)( 47,181,112)( 48,196,108)( 49,128,102)( 51, 98, 90)( 52,142,124) ( 55,171, 82)( 58, 68, 59)( 60,166, 65)( 61,126,185)( 62, 92,119)( 64,168,191) ( 69,122,151)( 73, 93,109)( 78, 84,157)( 79,146,100)( 80, 83,118)( 85,159, 89) ( 86,117,167)( 95,145,176)(101,155,135)(103,177,173)(105,178,184)(106,148,149) (107,161,127)(111,140,193)(113,114,156)(116,183,162)(144,179,182)(153,169,189), 198)]; return result;