local z, r, result; result := rec(); result.comment := "2.L2(139) as 140 x 140 monomial matrices over Z(z138)\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 2.L2(139) r := 1; z := E(138)^(2*r-1); result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(140) ]; result.centralizeralgebra := [ IdentityMat(140) ]; result.generators := [ DiagonalMat([z^100,z^68,z^74,z^23,z^123,z^45,z^110,z^79,z^92,z,z^55, z^91,z^65,z^80,z^5,z^125,-1,z^11,z^40,z^17,z^102,z^32,z^30,z^83, z^93,z^4,z^71,z^22,z^103,z^130,z^84,z^127,z^105,z^46,z^7,z^48,z^76, z^41,z^132,z^96,z^44,z^63,z^86,z^89,z^94,z^126,z^135,z^21,z^16,z^60, z^99,z^59,z^14,z^18,z^131,z^121,z^88,z^82,z^78,z^54,z^34,z^85,z^120, z^28,z^62,z^33,z^129,z^29,z^87,z^108,z^64,z^109,z^81,z^137,z^47, z^117,z^67,z^56,z^2,z^3,z^72,z^124,z^8,z^116,z^35,z^90,z^107,z^43, z^27,z^52,z^15,z^98,z^50,z^36,z^66,1,z^77,z^114,z^26,z^19,z^97,z^111, z^6,z^136,z^104,z^122,z^95,z^106,z^118,z^75,z^10,z^12,z^133,z^112, z^49,z^115,z^53,z^61,z^101,z^58,z^31,z^128,z^119,z^42,z^113,z^37, z^57,z^73,z^70,z^134,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^80,z^124,z^25,z^123,z^78,z^82,z^57,z^47,z^14,z^8, z^4,z^118,z^98,z^11,z^46,z^92,z^126,z^97,z^55,z^93,z^13,z^34,z^128, z^35,z^7,z^63,z^111,z^43,z^131,z^120,z^66,z^67,z^136,z^50,z^72,z^42, z^99,z^16,z^33,z^107,z^91,z^116,z^79,z^24,z^114,z^100,z^130,z^64, z^3,z^40,z^90,z^83,z^23,z^37,z^70,z^62,z^30,z^48,z^21,z^32,z^44, z,z^74,z^76,z^59,z^38,z^113,z^41,z^117,z^125,z^27,z^41,z^95,z^54, z^45,z^106,z^39,z^101,z^121,z^137,z^134,z^60,z^102,z^89,z^77,z^103, z^84,z^115,z^122,z^88,z^73,z^132,1,z^87,z^49,z^109,z^36,z^5,z^18, z^65,z^119,z^17,z^129,z^6,-1,z^51,z^133,z^75,z^104,z^81,z^28,z^96, z^94,z^9,z^19,z^68,z^135,z^86,z^29,z^56,z^10,z^53,z^31,z^110,z^71, z^112,z^2,z^105,z^58,z^22,z^108,z^127,z^12,z^15,z^20,z^52,z^61,z^85, 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;