local z, r, result; result := rec(); result.comment := "2.L2(149) as 150 x 150 monomial matrices over Z(z148)\n"; # Change the value of r to any number between 1 and 37 # to get the complete set of inequivalent faithful irreducible 150-dimensional # representations of 2.L2(149) r := 1; z := E(148)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(150) ]; result.centralizeralgebra := [ IdentityMat(150) ]; result.generators := [ DiagonalMat([z^84,z^19,z^51,z^106,z^15,z^38,z^101,z^40,z^27,z^5,z, z^57,z^134,z^50,z^69,z^98,z^95,z^136,z^37,z^79,z^64,z^68,z^22,z^23, z^97,z^141,z^44,z^125,z^59,z^81,z^41,z^112,z^61,z^130,z^146,z^83, z^145,z^128,z^58,z^108,z^36,z^75,z^52,z^117,z^35,z^131,z^86,z^11, z^9,z^54,z^49,z^63,z^20,z^118,z^76,z^78,z^48,z^28,z^111,z^33,z^124, z^127,1,z^12,z^72,z^8,z^132,-1,z^18,z^133,z^53,z^77,z^65,z^99,z^104, z^140,z^2,z^109,z^80,z^100,z^46,z^14,z^135,z^107,z^116,z^6,z^110, z^42,z^89,z^119,z^66,z^47,z^39,z^114,z^120,z^30,z^21,z^67,z^29,z^62, z^87,z^73,z^55,z^70,z^105,z^45,z^93,z^147,z^85,z^104,z^10,z^71,z^16, z^115,z^26,z^138,z^122,z^139,z^4,z^126,z^92,z^129,z^82,z^90,z^31, z^24,z^96,z^103,z^121,z^25,z^142,z^94,z^13,z^56,z^17,z^7,z^34,z^60, z^91,z^144,z^123,z^3,z^43,z^32,z^143,z^137,z^102,z^113,z^88,z^118 ]) * PermutationMat( ( 1,116)( 2,103)( 3, 24)( 4, 85)( 5, 29)( 6, 41)( 7,129)( 8,137) ( 9, 92)( 10, 15)( 11,102)( 12,135)( 13,149)( 14,126)( 16, 61)( 17, 62) ( 18, 47)( 20,145)( 21,111)( 22, 86)( 23, 43)( 25, 28)( 26, 30)( 27, 96) ( 31, 60)( 32, 87)( 33,133)( 34,121)( 35, 55)( 36,118)( 37, 72)( 38,132) ( 39,113)( 40, 94)( 42,108)( 44,105)( 45, 93)( 46,139)( 48, 52)( 49, 73) ( 50, 53)( 51,130)( 54, 75)( 56,140)( 57,115)( 58, 81)( 63, 68)( 64,100) ( 65, 77)( 66, 91)( 67,124)( 69,134)( 70, 89)( 71, 97)( 74,141)( 76,123) ( 78,148)( 79,131)( 80,117)( 82,138)( 83,101)( 84,114)( 88,144)( 90,128) ( 95,147)( 98,136)( 99,106)(104,119)(107,122)(109,146)(110,150)(112,142) (120,127)(125,143), 150) , DiagonalMat([z^3,z^132,z^18,z^23,z^59,z^69,z^28,z^147,z^19,z^113,z^81, z^54,z^26,z^35,z^73,z^29,z^109,z^8,z^38,z^133,z^114,z^106,z^33,z^39, z^97,z^88,z^134,z^96,z^129,z^6,z^140,z^122,z^137,z^24,z^112,z^12, z^66,z^4,z^108,z^77,z^138,z^83,z^34,z^93,z^57,z^41,z^58,z^71,z^45, z^11,z^48,z,z^9,z^98,z^91,z^15,z^22,z^40,z^92,z^61,z^13,z^80,z^123, z^84,-1,z^101,z^127,z^10,z^63,z^42,z^70,z^110,z^99,z^62,z^56,z^21, z^32,z^7,z^86,z^118,z^25,z^82,z^105,z^20,z^107,z^94,z^72,z^68,z^124, z^53,z^117,z^136,z^17,z^14,z^55,z^104,z^146,z^131,z^135,z^89,z^90, z^16,z^60,z^111,z^44,z^126,1,z^108,z^31,z^128,z^49,z^65,z^2,z^64, z^47,z^125,z^27,z^103,z^142,z^119,z^36,z^102,z^50,z^5,z^78,z^76, z^121,z^116,z^130,z^87,z^37,z^143,z^145,z^115,z^95,z^30,z^100,z^43, z^46,z^67,z^79,z^139,z^75,z^51,z^141,z^85,z^52,z^120,z^144,z^114 ]) * PermutationMat( ( 1, 51, 25)( 2, 6,135)( 3,108, 57)( 4, 66, 34)( 5, 72, 67)( 7,113, 80) ( 8, 92, 61)( 9, 37, 69)( 10,125, 83)( 11, 35,118)( 12, 17, 20)( 13, 91,124) ( 14,138, 71)( 15,143,107)( 16, 74, 45)( 18, 85, 23)( 19,100, 76)( 21, 53, 81) ( 22,145,111)( 24, 86, 56)( 26, 62,110)( 27, 47, 96)( 28, 64,128)( 29,146, 82) ( 30,112, 40)( 31,134, 46)( 32,132,109)( 33,130, 87)( 36, 52, 99)( 38, 54,139) ( 39,150, 65)( 41, 98,117)( 42,119, 48)( 43, 63,142)( 44,104, 59)( 49,121,140) ( 50,126, 60)( 55, 79,120)( 58,129,106)( 68,127, 93)( 70, 73, 78)( 75,131, 95) ( 77,114,147)( 84, 88,103)( 89,115,116)( 90,141,102)( 94,105,101)( 97,148,136) (122,123,149)(133,144,137), 150)]; return result;