local z, r, result; result := rec(); result.comment := "L2(139) as 140 x 140 monomial matrices over Z(z69)\n"; # Change the value of r to any number between 1 and 34 # to get the complete set of inequivalent faithful irreducible 140-dimensional # representations of L2(139) r := 1; z := E(69)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(140) ]; result.centralizeralgebra := [ IdentityMat(140) ]; result.generators := [ DiagonalMat([z^31,z^68,z^5,z^23,z^54,z^45,z^41,z^10,z^23,z,z^55,z^22, z^65,z^11,z^5,z^56,1,z^11,z^40,z^17,z^33,z^32,z^30,z^14,z^24,z^4, z^2,z^22,z^34,z^61,z^15,z^58,z^36,z^46,z^7,z^48,z^7,z^41,z^63,z^27, z^44,z^63,z^17,z^20,z^25,z^57,z^66,z^21,z^16,z^60,z^30,z^59,z^14, z^18,z^62,z^52,z^19,z^13,z^9,z^54,z^34,z^16,z^51,z^28,z^62,z^33, z^60,z^29,z^18,z^39,z^64,z^40,z^12,z^68,z^47,z^48,z^67,z^56,z^2, z^3,z^3,z^55,z^8,z^47,z^35,z^21,z^38,z^43,z^27,z^52,z^15,z^29,z^50, z^36,z^66,1,z^8,z^45,z^26,z^19,z^28,z^42,z^6,z^67,z^35,z^53,z^26, z^37,z^49,z^6,z^10,z^12,z^64,z^43,z^49,z^46,z^53,z^61,z^32,z^58, z^31,z^59,z^50,z^42,z^44,z^37,z^57,z^4,z,z^65,z^38,z^25,z^13,z^39, z^20,z^51,z^58,z^24,z^9,z^11]) * PermutationMat( ( 1, 87)( 2, 10)( 3,113)( 4, 34)( 5, 31)( 6,138)( 7,101)( 8,122) ( 9,116)( 11, 53)( 12, 84)( 13, 26)( 14, 32)( 15, 71)( 16, 58)( 17, 96) ( 18,137)( 19, 68)( 20, 90)( 21, 33)( 22,126)( 23,134)( 24, 82)( 25, 98) ( 27,104)( 28, 75)( 29,105)( 30, 97)( 35, 65)( 36, 48)( 37, 55)( 38, 64) ( 39,110)( 40,102)( 41,132)( 42,103)( 43, 56)( 44,109)( 45,125)( 46, 73) ( 47, 81)( 49,117)( 50,139)( 51, 70)( 52,111)( 54,136)( 57,123)( 59, 67) ( 60, 91)( 61, 85)( 62,106)( 63, 69)( 66, 94)( 72, 92)( 74,129)( 76, 86) ( 77, 79)( 78,133)( 80, 95)( 83,118)( 88, 99)( 89,124)( 93,100)(107,114) (108,119)(112,127)(115,135)(120,140)(121,131)(128,130), 140) , DiagonalMat([z^26,z^11,z^55,z^25,z^54,z^9,z^13,z^57,z^47,z^14,z^8, z^4,z^49,z^29,z^11,z^46,z^23,z^57,z^28,z^55,z^24,z^13,z^34,z^59, z^35,z^7,z^63,z^42,z^43,z^62,z^51,z^66,z^67,z^67,z^50,z^3,z^42,z^30, z^16,z^33,z^38,z^22,z^47,z^10,z^24,z^45,z^31,z^61,z^64,z^3,z^40, z^21,z^14,z^23,z^37,z,z^62,z^30,z^48,z^21,z^32,z^44,z,z^5,z^7,z^59, z^38,z^44,z^41,z^48,z^56,z^27,z^41,z^26,z^54,z^45,z^37,z^39,z^32, z^52,z^68,z^65,z^60,z^33,z^20,z^8,z^34,z^15,z^46,z^53,z^19,z^4,z^63, 1,z^18,z^49,z^40,z^36,z^5,z^18,z^65,z^50,z^17,z^60,z^6,1,z^51,z^64, z^6,z^35,z^12,z^28,z^27,z^25,z^9,z^19,z^68,z^66,z^17,z^29,z^56,z^10, z^53,z^31,z^41,z^2,z^43,z^2,z^36,z^58,z^22,z^39,z^58,z^12,z^15,z^20, z^52,z^61,z^16,z^28]) * PermutationMat( ( 1, 98, 65)( 2, 26,107)( 3, 76, 41)( 4,119, 72)( 5,103, 34)( 6, 78, 60) ( 7, 31, 64)( 8,109,105)( 9, 53, 11)( 10,124, 21)( 12, 47, 23)( 13,123,129) ( 14, 45, 39)( 15, 75, 92)( 18, 79, 96)( 19,132,126)( 20, 42, 48)( 22,118, 24) ( 25, 66, 62)( 27,111, 93)( 28,137, 68)( 29, 99, 52)( 30,130, 95)( 32,131, 35) ( 33, 58, 69)( 36, 91, 43)( 37,116, 86)( 38, 83, 70)( 40,139,136)( 44, 87,114) ( 46, 51, 90)( 49,100,121)( 50, 71,122)( 54, 77,115)( 55,134, 85)( 56, 94,117) ( 57, 84,127)( 59,108, 74)( 61, 89,104)( 63,112, 97)( 67, 82,110)( 73,140,106) ( 80,135,128)( 81,120,125)( 88,133,101)(102,113,138), 140)]; return result;