local z, r, result; result := rec(); result.comment := "2.L2(53) as 54 x 54 monomial matrices over Z(z52)\n"; # Change the value of r to any number between 1 and 13 # to get the complete set of inequivalent faithful irreducible 54-dimensional # representations of 2.L2(53) r := 1; z := E(52)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(54) ]; result.centralizeralgebra := [ IdentityMat(54) ]; result.generators := [ DiagonalMat([z^17,-1,z^29,z^31,z^10,z^47,z^12,z^21,z^32,z^39,z^20, z^28,z^49,z^25,z^19,z^44,z^42,z^48,z^37,z^4,z^51,z^11,z^38,z^24, z,z^16,1,z^22,z^35,z^7,z^46,z^50,z^30,z^40,z^33,z^34,z^8,z^13,z^36, z^14,z^5,z^23,z^15,z^3,z^45,z^27,z^41,z^9,z^6,z^2,z^18,z^37,z^43, z^41]) * PermutationMat( ( 1,48)( 2,27)( 3,13)( 4, 6)( 5,26)( 7,40)( 8,41)( 9,31)(11,49)(12,32)(14,25) (15,30)(16,36)(17,39)(18,33)(19,47)(20,28)(21,46)(22,43)(23,34)(24,50)(29,53) (35,45)(37,51)(42,44)(52,54), 54) , DiagonalMat([z^20,-1,z^18,z^6,z^48,z^30,z^44,z^12,z^9,z^5,z^21,z^22, z^46,z^29,z^32,z^34,z^13,z^50,z^15,z^24,z^35,z^42,z^23,z^31,1,z^28, z^22,z^47,z^45,z^51,z^40,z^7,z^2,z^14,z^41,z^27,z^4,z^19,z^3,z^25, z^38,z^10,z^49,z,z^33,z^43,z^36,z^37,z^11,z^16,z^39,z^17,z^8,z^4 ]) * PermutationMat( ( 1,47, 5)( 2,12,54)( 3, 8,27)( 4,32,51)( 6,31,16)( 7,10,39)( 9,22,44) (11,18,45)(13,17,29)(14,41,48)(15,37,50)(19,34,23)(20,49,52)(21,35,26) (24,38,33)(25,40,36)(28,53,43)(30,42,46), 54)]; return result;