local z, r, result; result := rec(); result.comment := "L2(157) as 158 x 158 monomial matrices over Z(z78)\n"; # Change the value of r to any number between 1 and 38 # to get the complete set of inequivalent faithful irreducible 158-dimensional # representations of L2(157) r := 1; z := E(78)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(158) ]; result.centralizeralgebra := [ IdentityMat(158) ]; result.generators := [ DiagonalMat([z^17,z^51,z^66,z^60,z^48,z^57,z^47,z^58,z^63,z^47,z^77, z,z^48,z^62,z^19,z^23,z^15,z^56,z^22,z^73,z^2,z^76,z^23,z^55,z,z^40, z^61,z^3,z^11,z^45,z^63,z^43,z^29,z^31,z^20,z^61,z^65,z^70,z^9,z^74, z^19,z^50,z^38,z^64,z^44,z^77,z^52,z^3,z^72,z^21,z^59,z^46,z^10, z^16,z^22,z^71,z^27,z^67,z^50,z^12,z^75,z^57,z^58,z^74,z^21,z^30, z^7,z^27,z^13,z^67,z^51,z^18,z^16,z^44,z^62,-1,z^49,1,z^46,z^36, z^36,z^8,z^29,z^32,z^28,z^6,z^33,z^32,z^41,z^72,z^42,z^31,z^53,z^34, z^5,z^6,z^38,z^53,z^76,z^11,z^68,z^12,z^2,z^54,z^37,z^35,z^52,z^66, z^25,z^41,1,z^43,z^71,z^64,z^57,z^14,z^26,z^65,z^37,z^45,z^15,-1, z^5,z^24,z^75,z^8,z^54,z^30,z^42,z^24,z^18,z^13,z^49,z^59,z^56,z^69, z^10,z^69,z^34,z^25,z^4,z^60,z^20,z^73,z^40,z^14,z^17,z^9,z^35,z^68, z^26,z^33,z^28,z^70,z^55,z^7,z^4,z^21]) * PermutationMat( ( 1, 36)( 2, 57)( 3, 60)( 4, 72)( 5, 66)( 6,158)( 7, 34)( 8, 35) ( 9,121)( 10, 92)( 11, 25)( 12, 46)( 13,128)( 14, 73)( 15, 51)( 16,155) ( 17, 31)( 18, 19)( 20, 95)( 21, 99)( 22,103)( 23, 24)( 26, 43)( 27,147) ( 28,125)( 29, 70)( 30,152)( 32,106)( 33, 77)( 37,132)( 38,126)( 39,138) ( 40,141)( 41,134)( 42, 85)( 44,116)( 45,139)( 47,151)( 48, 61)( 49, 86) ( 50, 62)( 52, 84)( 53,101)( 54, 75)( 55,135)( 56, 67)( 58,100)( 59,153) ( 63,143)( 64,157)( 65,115)( 68, 71)( 69,118)( 74, 94)( 78,111)( 79, 88) ( 80,129)( 81, 91)( 82,154)( 83,133)( 87,120)( 89,105)( 90, 96)( 93,109) ( 97,145)( 98,140)(102,108)(104,124)(107,117)(110,119)(112,149)(113,156) (114,146)(123,144)(127,130)(131,142)(136,148)(137,150), 158) , DiagonalMat([z,z^37,z^18,z^67,z^68,z^22,z^37,z^60,z^73,z^52,z^74,z^64, z^38,z^21,z^19,z^36,z^50,z^9,z^25,z^62,z^27,z^55,z^48,z^41,z^76, z^10,z^49,z^21,z^29,z^77,z^23,z^67,z^8,z^59,z^70,z^38,z^14,z^26, z^8,z^2,z^75,z^33,z^43,z^40,z^53,z^72,z^53,z^18,z^9,z^66,z^44,z^4, z^57,z^24,z^76,z,z^71,z^19,z^52,z^10,z^17,z^12,z^54,-1,z^69,z^66, z^35,z^50,z^44,z^32,z^8,z^31,z^42,z^47,z^31,z^61,z^63,z^32,z^46, z^3,z^7,z^77,z^40,z^6,z^57,z^64,z^60,z^7,-1,z^63,z^24,z^45,z^65, z^73,z^29,z^47,z^27,z^13,z^15,z^4,z^45,z^49,z^54,z^71,z^58,z^3,z^34, z^22,z^48,z^28,z^61,z^36,z^65,z^56,z^5,z^43,z^30,z^72,1,z^6,z^55, z^11,z^51,z^34,z^74,z^59,z^41,z^42,z^58,z^5,z^14,z^69,z^11,z^75, z^51,z^35,z^2,1,z^28,z^46,z^23,z^33,z^62,z^30,z^20,z^20,z^70,z^13, z^16,z^12,z^68,z^17,z^16,z^25,z^56,z^26,z^15,z^70]) * PermutationMat( ( 1,144, 96)( 2, 14,145)( 3, 9, 93)( 4, 82,150)( 5, 21, 76)( 6, 86, 35) ( 7, 25,116)( 8, 98,115)( 10, 17,103)( 11,107, 23)( 12, 68, 73)( 13, 74,104) ( 15,143,134)( 16,110, 37)( 18,137, 32)( 19, 79, 88)( 20, 60, 84)( 22,105, 43) ( 24,129, 53)( 26, 61,123)( 27, 78, 41)( 28, 69,148)( 29,106,140)( 30, 75,109) ( 31, 67,146)( 33, 92,154)( 34, 52, 99)( 36,108, 48)( 38, 54,139)( 39,131,155) ( 40,127,136)( 42, 49,112)( 44, 81, 72)( 45, 57, 70)( 46,111,141)( 47,142,147) ( 50, 56,122)( 51,100,117)( 55, 65,133)( 58, 77,125)( 62, 64, 97)( 63, 94, 95) ( 66,135, 89)( 71,158,119)( 80,149,126)( 83, 87,114)( 85,113,124)( 90,138,157) ( 91,102,130)(101,128,132)(118,151,153)(120,121,152), 158)]; return result;