local z, r, result; result := rec(); result.comment := "2.L2(199) as 200 x 200 monomial matrices over Z(z198)\n"; # Change the value of r to any number between 1 and 49 # to get the complete set of inequivalent faithful irreducible 200-dimensional # representations of 2.L2(199) r := 1; z := E(198)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(200) ]; result.centralizeralgebra := [ IdentityMat(200) ]; result.generators := [ DiagonalMat([z^63,z^129,z^182,z^140,z^73,z^61,z^183,z^110,z^153,z^75, z^22,z^189,z^23,z^86,z^197,z^170,z^69,z^96,z^180,z^71,z^130,z^15, z^142,z^154,z^35,z^37,z^18,z^141,z^164,z^21,z^160,z^92,z^26,z^172, z^188,z^193,z^144,z^118,z^135,z^54,z^98,z^191,1,z^152,z^187,z^95, z^88,z^5,z^33,z^127,z^79,z^59,z^12,z^83,z^6,z^166,z^36,z^13,z^3, z^158,z^136,z^66,z^41,z^45,z^84,z^29,z^131,z^68,z^104,z^137,z^133, z^103,z^111,z^14,z^48,z^32,z^169,z^70,z^126,z^190,z^108,z^19,z^50, z^155,z^49,z^17,z^105,z^186,z^121,z^64,z^162,z^24,z^39,z^4,z^100, z^91,z^120,z^123,z^89,z^52,z^114,z^11,z^65,z^25,z^20,z^44,z^113, z^134,z^176,z^185,z^9,z^138,z^175,z^53,z^179,z^27,z^46,z^93,z^196, z^167,z^51,z^57,z^148,z^112,z^157,z^149,z^55,z^10,z^90,z^72,z^97, z^145,z^139,z^122,z^173,z^40,z^107,z^165,z^109,z^85,z^159,z^177, z^174,z^94,z^81,z^151,z^67,z^7,z^115,z^30,z^2,z^102,z^128,z^16,z^150, z^117,z^147,z,z^78,z^34,z^106,z^181,z^192,z^60,z^101,z^47,z^195, z^87,z^76,z^77,z^38,z^58,z^43,z^116,z^28,z^168,z^31,z^178,-1,z^184, z^143,z^156,z^152,z^56,z^42,z^82,z^194,z^74,z^124,z^62,z^119,z^8, z^132,z^146,z^125,z^163,z^161,z^171,z^80,z^145]) * PermutationMat( ( 1, 57)( 2,176)( 3,149)( 4,125)( 5, 33)( 6,171)( 7,101)( 8, 45) ( 9, 37)( 10, 92)( 11,170)( 12, 81)( 13,169)( 14, 58)( 15, 95)( 16, 50) ( 17,150)( 18, 59)( 19,156)( 20,175)( 21,120)( 22, 65)( 23, 84)( 24,181) ( 25, 90)( 26,190)( 27,145)( 28,182)( 29, 71)( 30,159)( 31, 70)( 32,148) ( 34,195)( 35,139)( 36, 69)( 38,115)( 39, 91)( 40, 64)( 41,158)( 42,161) ( 43,179)( 44,132)( 46, 94)( 47,102)( 48,144)( 49, 62)( 51,105)( 52,136) ( 53,168)( 54,154)( 55,118)( 56, 67)( 60,133)( 61,197)( 63,172)( 66, 78) ( 68,177)( 72,187)( 73, 88)( 74,140)( 75,121)( 76,147)( 77,153)( 79,198) ( 80,137)( 82,199)( 83, 85)( 86,186)( 87,163)( 89,109)( 93,164)( 96,192) ( 97,142)( 98,143)( 99,128)(100,166)(103,160)(104,188)(106,127)(107,180) (108,196)(110,124)(111,129)(112,141)(113,134)(114,117)(116,130)(119,165) (122,185)(123,126)(131,151)(135,189)(138,193)(146,194)(152,167)(155,157) (162,174)(173,184)(178,191)(183,200), 200) , DiagonalMat([z^156,z^127,z,z^76,z^87,z^153,z^194,z^140,z^90,z^180, z^169,z^170,z^131,z^151,z^136,z^11,z^121,z^63,z^124,z^73,z^192,z^79, z^38,z^51,z^19,z^149,z^135,z^175,z^89,z^167,z^19,z^155,z^14,z^101, z^27,z^41,z^20,z^58,z^56,z^66,z^173,z^24,z^77,z^35,z^166,z^154,z^78, z^5,z^48,z^168,z^115,z^84,z^116,z^179,z^92,z^65,z^162,z^189,z^75, z^164,z^25,z^108,z^37,z^49,z^128,z^130,z^111,z^36,z^59,z^114,z^55, z^185,z^119,z^67,z^83,z^88,z^39,z^13,z^30,z^147,z^191,z^86,z^93, z^47,z^82,z^188,z^181,z^98,z^126,z^22,z^172,z^152,z^105,z^176,-1, z^61,z^129,z^106,z^96,z^53,z^31,z^159,z^134,z^138,z^177,z^122,z^26, z^161,z^197,z^32,z^28,z^196,z^6,z^107,z^141,z^125,z^64,z^163,z^21, z^85,z^3,z^112,z^143,z^50,z^142,z^110,1,z^81,z^16,z^157,z^57,z^117, z^132,z^97,z^193,z^184,z^15,z^18,z^182,z^145,z^9,z^104,z^158,z^118, z^113,z^137,z^8,z^29,z^71,z^80,z^102,z^33,z^70,z^146,z^74,z^120, z^139,z^186,z^91,z^62,z^144,z^150,z^43,z^7,z^52,z^44,z^148,z^103, z^183,z^165,z^190,z^40,z^34,z^17,z^68,z^133,z^2,z^60,z^4,z^178,z^54, z^72,z^69,z^187,z^174,z^46,z^160,z^100,z^10,z^123,z^95,z^195,z^23, z^109,z^45,z^12,z^42,z^94,z^171,z^80]) * PermutationMat( ( 1,148, 78)( 2, 69,196)( 3,120,122)( 4,153,165)( 5,155, 63)( 6,199,182) ( 7,111,185)( 8, 20,169)( 9, 92, 46)( 10, 56, 14)( 11,197, 72)( 12,179, 42) ( 13, 93,187)( 15, 24, 16)( 17,119, 39)( 18,168,110)( 19, 67,108)( 21, 98, 88) ( 22, 79, 29)( 23, 83, 74)( 25,200, 95)( 26,107,193)( 27, 45,191)( 28, 91, 64) ( 30, 49, 87)( 31, 34, 47)( 32,103,114)( 33,102, 61)( 35,195, 89)( 36,135, 57) ( 37, 96,132)( 38,137,116)( 41, 77,136)( 43,125,105)( 44,173, 97)( 48,130, 68) ( 50, 73,194)( 51, 53,170)( 52,190, 58)( 54,156,134)( 55,113,188)( 59, 70,141) ( 60,118,183)( 62,166,186)( 65,106,154)( 66,147,178)( 71,140,112)( 75,152, 85) ( 76,198,129)( 80,160,184)( 81,164,127)( 82,145,109)( 84,176,138)( 86,124,143) ( 90,150, 99)( 94,151,144)(100,123,177)(101,174,162)(104,171,175)(115,181,121) (117,163,159)(126,139,142)(128,146,180)(131,192,161)(149,158,157)(167,189,172), 200)]; return result;