local z, r, result; result := rec(); result.comment := "L2(167) as 168 x 168 monomial matrices over Z(z83)\n"; # Change the value of r to any number between 1 and 41 # to get the complete set of inequivalent faithful irreducible 168-dimensional # representations of L2(167) r := 1; z := E(83)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(168) ]; result.centralizeralgebra := [ IdentityMat(168) ]; result.generators := [ DiagonalMat([z^79,z^68,z^21,z^29,z^39,z^28,z^19,z^65,z^76,z^30,z^20, z^27,z^59,z^13,z^40,z^39,z^4,z^61,z^41,z^18,z^11,z^53,z^73,z^43, z^71,z^5,z^38,z^23,z^49,z^75,z^62,z^3,z^71,z^7,z^55,z^41,z^12,z^19, z^40,z^28,z^69,z^44,z^48,z^45,z^68,z^51,z^15,z^36,z^25,z^20,z^11, z^13,z^77,z^23,z^80,z^78,z^12,z^17,z^35,z^66,z^56,z^32,z^81,z^34, z^77,z^64,z^21,z^24,z^37,z,z^32,z^47,z^63,z^7,z^37,z^14,z^10,z^53, z^58,z^59,z^52,z^67,z^14,z^58,z^78,z^33,1,z,z^82,z^31,z^75,z^54, z^9,z^61,z^45,z^51,z^49,z^43,z^82,z^2,z^24,z^76,z^48,z^31,z^15,z^66, z^18,z^4,1,z^42,z^54,z^10,z^56,z^6,z^29,z^38,z^6,z^70,z^64,z^46, z^47,z^72,z^42,z^60,z^57,z^65,z^69,z^79,z^57,z^9,z^25,z,z^3,z^81, z^22,z^63,z^74,z^52,z^44,z^72,z^2,z^36,z^16,z^30,z^5,z^17,z^73,z^46, z^60,z^26,z^8,z^62,z^8,z^70,z^27,z^33,z^55,z^74,z^16,z^50,z^50,z^22, z^67,z^34,z^26,z^35,z^80,z^82]) * PermutationMat( ( 1, 17)( 2,105)( 3, 31)( 4, 92)( 5, 42)( 6, 35)( 7, 66)( 8,107) ( 9, 34)( 10, 78)( 11,136)( 12,113)( 13,101)( 14,118)( 15, 24)( 16,139) ( 18,162)( 19,110)( 20,126)( 21,140)( 22,144)( 23,112)( 25, 37)( 26, 56) ( 27, 95)( 28,124)( 29, 64)( 30,151)( 32, 55)( 33, 57)( 36,123)( 38,119) ( 39, 98)( 40,157)( 41, 76)( 43, 59)( 44,116)( 45, 47)( 46, 62)( 48, 72) ( 49, 79)( 50, 73)( 51,122)( 52,154)( 53,117)( 54,149)( 58, 60)( 61,155) ( 63,100)( 65,114)( 67,152)( 68, 80)( 69,148)( 70, 99)( 71, 96)( 74,102) ( 75,120)( 77,147)( 81, 90)( 82,159)( 83,127)( 84,131)( 85,145)( 86,161) ( 87,109)( 88,168)( 89,132)( 91,153)( 93,158)( 94,135)( 97,164)(103,166) (104,138)(106,146)(108,128)(111,115)(121,142)(125,165)(129,150)(130,137) (133,167)(134,141)(143,163)(156,160), 168) , DiagonalMat([z^78,z^24,z^19,z^10,z^12,z^76,z^22,z^79,z^77,z^11,z^16, z^34,z^65,z^55,z^31,z^80,z^33,z^76,z^63,z^20,z^23,z^36,1,z^31,z^46, z^62,z^6,z^36,z^13,z^9,z^52,z^57,z^58,z^51,z^66,z^13,z^57,z^77,z^32, z^82,z^49,z^81,z^30,z^74,z^53,z^8,z^60,z^44,z^50,z^48,z^42,z^81, z,z^23,z^75,z^47,z^30,z^14,z^65,z^17,z^3,z^82,z^41,z^53,z^9,z^55, z^5,z^28,z^37,z^5,z^69,z^63,z^45,z^46,z^71,z^41,z^59,z^56,z^64,z^68, z^78,z^56,z^8,z^24,1,z^2,z^80,z^21,z^62,z^73,z^51,z^43,z^71,z,z^35, z^15,z^29,z^4,z^16,z^72,z^45,z^59,z^25,z^7,z^61,z^7,z^69,z^26,z^32, z^54,z^73,z^15,z^49,z^49,z^21,z^66,z^33,z^25,z^34,z^79,z^67,z^20, z^28,z^38,z^27,z^18,z^64,z^75,z^29,z^19,z^26,z^58,z^12,z^39,z^38, z^3,z^60,z^40,z^17,z^10,z^52,z^72,z^42,z^70,z^4,z^37,z^22,z^48,z^74, z^61,z^2,z^70,z^6,z^54,z^40,z^11,z^18,z^39,z^27,z^68,z^43,z^47,z^44, z^67,z^50,z^14,z^35,z^34]) * PermutationMat( ( 1,158,114)( 2, 64, 27)( 3,162, 60)( 4, 56,131)( 5, 83, 72)( 6,135, 31) ( 7, 25, 96)( 8, 26,103)( 9, 93,126)( 10, 61,107)( 11,167,109)( 12, 48, 67) ( 13,133,153)( 14,144, 76)( 15, 80,121)( 16, 40,145)( 17, 54,159)( 18, 78,119) ( 19,123, 55)( 20, 46, 66)( 21,132,151)( 22, 90, 32)( 23, 92,138)( 24, 73,106) ( 28,127,116)( 29, 68,143)( 30,139, 37)( 33,115, 98)( 34, 62,117)( 35,149,108) ( 36, 59, 70)( 38, 43,102)( 39, 49, 53)( 41,168, 85)( 42,118, 47)( 44, 89, 57) ( 45, 88, 65)( 50,164, 91)( 51,130,147)( 52, 69,148)( 58, 87,100)( 63,105, 79) ( 71, 77,124)( 74, 86, 95)( 75,122,128)( 81,157,152)( 82,137,165)( 84,166,101) ( 94,136,120)( 97,156,161)( 99,112,141)(104,113,125)(110,155,142)(111,154,134) (129,140,163)(146,150,160), 168)]; return result;