local z, r, result; result := rec(); result.comment := "L2(107) as 108 x 108 monomial matrices over Z(z53)\n"; # Change the value of r to any number between 1 and 26 # to get the complete set of inequivalent faithful irreducible 108-dimensional # representations of L2(107) r := 1; z := E(53)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(108) ]; result.centralizeralgebra := [ IdentityMat(108) ]; result.generators := [ DiagonalMat([z^34,z^22,z^13,z^39,z^9,z^49,z^4,z^8,z^29,z^26,z^14,z, z^31,z^23,z^2,z^45,z^16,z^12,z^27,z^47,z^19,z^35,z^51,z^34,z^17, z^44,z^23,z^7,z^10,z^38,z^47,z^14,z^21,z^43,z^2,z^13,z^15,z^46,z^41, z^32,z^44,z^20,z^46,z,z^39,z^27,z^28,z^38,z^3,z^22,z^24,z^30,z^48, z^37,z^42,z^45,z^31,z^5,z^50,z^51,z^51,z^4,z^37,z^19,z^41,z^16,z^20, z^36,z^18,z^32,1,z^9,z^3,z^42,z^18,z^33,z^17,z^40,1,z^5,z^48,z^26, z^11,z^28,z^11,z^6,z^30,z^7,z^24,z^43,z^36,z^35,z^33,z^40,z^12,z^25, z^21,z^15,z^25,z^6,z^52,z^49,z^29,z^10,z^52,z^50,z^8,z^2]) * PermutationMat( ( 1, 64)( 2, 13)( 3, 94)( 4, 32)( 5, 41)( 6, 7)( 8, 16)( 9, 51) ( 10, 19)( 11, 45)( 12,101)( 14, 87)( 15, 61)( 17, 54)( 18, 65)( 20,100) ( 21, 24)( 22, 69)( 23,108)( 25, 91)( 26, 72)( 27, 52)( 28, 38)( 29, 34) ( 30, 37)( 31, 86)( 33, 70)( 35, 60)( 36, 78)( 39, 95)( 40, 97)( 42, 76) ( 43, 88)( 44,105)( 46, 82)( 47, 96)( 48, 98)( 49, 59)( 50, 57)( 53, 58) ( 55, 83)( 56,107)( 62,102)( 63, 66)( 67, 93)( 68, 77)( 71, 79)( 73,106) ( 74, 85)( 75, 92)( 80, 81)( 84, 99)( 89,103)( 90,104), 108) , DiagonalMat([z^36,z^33,z^7,z^52,1,1,z^6,z^39,z^21,z^43,z^18,z^22,z^38, z^20,z^34,z^2,z^11,z^5,z^44,z^20,z^35,z^19,z^42,z^2,z^7,z^50,z^28, z^13,z^30,z^13,z^8,z^32,z^9,z^26,z^45,z^38,z^37,z^35,z^42,z^14,z^27, z^23,z^17,z^27,z^8,z,z^51,z^31,z^12,z,z^52,z^10,z^24,z^15,z^41,z^11, z^51,z^6,z^10,z^31,z^28,z^16,z^3,z^33,z^25,z^4,z^47,z^18,z^14,z^29, z^49,z^21,z^37,z^51,z^36,z^19,z^46,z^25,z^9,z^12,z^40,z^49,z^16, z^23,z^45,z^4,z^15,z^17,z^48,z^43,z^34,z^46,z^22,z^48,z^3,z^41,z^29, z^30,z^40,z^5,z^24,z^26,z^32,z^50,z^39,z^44,z^47,z^2]) * PermutationMat( ( 1, 83, 46)( 2,103, 55)( 3, 29, 62)( 4, 50, 6)( 5, 74,108)( 7, 97, 68) ( 8, 84,106)( 9, 14, 80)( 10, 38, 61)( 11, 59, 78)( 12, 91, 26)( 13, 41, 96) ( 15,100, 69)( 16, 58, 85)( 17, 33, 64)( 18, 34, 93)( 19, 23, 20)( 21, 53, 67) ( 22, 48, 95)( 24, 75, 87)( 25, 66, 39)( 27, 70, 82)( 28, 32, 31)( 30, 90,104) ( 35, 72, 99)( 36, 88, 57)( 37, 42, 77)( 40, 79, 98)( 43, 51, 73)( 44, 89, 60) ( 45,107, 47)( 49,102, 54)( 52, 81, 63)( 56, 71, 92)( 65, 86,101)( 76,105, 94), 108)]; return result;