local z, r, result; result := rec(); result.comment := "L2(151) as 152 x 152 monomial matrices over Z(z75)\n"; # Change the value of r to any number between 1 and 37 # to get the complete set of inequivalent faithful irreducible 152-dimensional # representations of L2(151) r := 1; z := E(75)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(152) ]; result.centralizeralgebra := [ IdentityMat(152) ]; result.generators := [ DiagonalMat([z^10,z^23,z^62,z^7,z^37,z^63,z^22,z^50,z^57,z^63,z^64, z^56,z^72,z^27,z^72,z^67,z^30,z^16,z^18,z^59,z^42,z^65,z^54,z^48, z^11,z^9,z^34,z^21,z^10,z^66,z^68,z^71,z^19,z^15,z^18,z^69,z^65, z^62,z^5,z^15,z^27,z,z^2,z^38,z^43,z^53,z^29,z^45,z^3,1,z^13,z^49, z^53,z^7,z^51,z^34,z^41,z^39,z^32,z^24,z^70,z^35,z^8,z^52,z^31,z^66, z^41,z^55,z^59,z^11,z^20,z^46,z^28,z^71,z^23,z^13,z^30,z^52,z^6, z^61,1,z^39,z,z^60,z^17,z^29,z^60,z^54,z^42,z^33,z^46,z^3,z^24,z^73, z^26,z^44,z^37,z^16,z^4,z^45,z^25,z^2,z^26,z^4,z^44,z^43,z^58,z^49, z^33,z^48,z^56,z^40,z^40,z^74,z^20,z^70,z^17,z^36,z^69,z^5,z^25, z^31,z^12,z^58,z^8,z^61,z^28,z^14,z^22,z^33,z^38,z^6,z^68,z^35,z^50, z^12,z^47,z^32,z^51,z^21,z^73,z^55,z^64,z^36,z^67,z^9,z^57,z^47, z^19,z^14,z^74,z^42]) * PermutationMat( ( 1, 37)( 2, 64)( 3, 76)( 4, 31)( 5, 44)( 6,123)( 7, 53)( 8,101) ( 9, 19)( 10,136)( 11, 25)( 12, 33)( 13, 92)( 14,110)( 15, 49)( 16,125) ( 17,100)( 18, 20)( 21,130)( 22, 29)( 23,140)( 24, 41)( 26, 30)( 27, 67) ( 28, 88)( 32,104)( 34, 84)( 35,147)( 36,132)( 38, 51)( 39, 61)( 40, 87) ( 42,114)( 43, 94)( 45,138)( 46,129)( 47, 72)( 48, 77)( 50, 81)( 52,103) ( 54,133)( 55, 60)( 56, 57)( 58,118)( 59,106)( 62,112)( 63,145)( 65, 96) ( 66,146)( 68, 71)( 69, 98)( 70,143)( 73,148)( 74, 99)( 75, 78)( 79,119) ( 80,150)( 82,144)( 83,151)( 85,107)( 86, 91)( 89, 90)( 93,139)( 95,108) ( 97,131)(102,141)(105,122)(109,152)(111,149)(113,134)(115,142)(116,120) (117,124)(121,135)(126,128)(127,137), 152) , DiagonalMat([z^7,z^64,z^6,z^54,z^44,z^16,z^11,z^71,z^20,z^59,z^4,z^34, z^60,z^19,z^47,z^54,z^60,z^61,z^53,z^69,z^24,z^69,z^64,z^27,z^13, z^15,z^56,z^39,z^62,z^51,z^45,z^8,z^6,z^31,z^18,z^7,z^63,z^65,z^68, z^16,z^12,z^15,z^66,z^62,z^59,z^2,z^12,z^24,z^73,z^74,z^35,z^40, z^50,z^26,z^42,1,z^72,z^10,z^46,z^50,z^4,z^48,z^31,z^38,z^36,z^29, z^21,z^67,z^32,z^5,z^49,z^28,z^63,z^38,z^52,z^56,z^8,z^17,z^43,z^25, z^68,z^20,z^10,z^27,z^49,z^3,z^58,z^72,z^36,z^73,z^57,z^14,z^26, z^57,z^51,z^39,z^30,z^43,1,z^21,z^70,z^23,z^41,z^34,z^13,z,z^42, z^22,z^74,z^23,z,z^41,z^40,z^55,z^46,z^29,z^45,z^53,z^37,z^37,z^71, z^17,z^67,z^14,z^33,z^66,z^2,z^22,z^28,z^9,z^55,z^5,z^58,z^25,z^11, z^19,z^30,z^35,z^3,z^65,z^32,z^47,z^9,z^44,z^29,z^48,z^18,z^70,z^52, z^61,z^33,z^46]) * PermutationMat( ( 1, 17, 77)( 2,144, 55)( 3, 83, 10)( 4, 5,149)( 6, 49, 18)( 7,101, 22) ( 8, 76,102)( 9, 88, 87)( 11, 97,103)( 12, 16, 29)( 13, 37, 24)( 14, 61, 75) ( 15, 38, 74)( 19, 60,142)( 20, 40,140)( 21, 66,108)( 23, 33, 70)( 25, 67,112) ( 26,146, 47)( 27, 44, 69)( 28, 35,147)( 30, 36,122)( 31, 57,125)( 32,126,111) ( 34,135,151)( 39, 68, 42)( 41, 79, 82)( 43,138, 71)( 45,124, 46)( 48,133, 81) ( 50,130,123)( 51, 54, 92)( 52,150, 85)( 56,116,152)( 58, 72,119)( 59, 95,118) ( 62,145, 90)( 63,100,110)( 64, 89,106)( 65, 94, 91)( 73,114,141)( 78,139,131) ( 84,127,115)( 86,137,107)( 93,113,143)( 96,120,109)( 98,105,136)( 99,132,148) (104,117,121)(128,129,134), 152)]; return result;