local z, r, result; result := rec(); result.comment := "L2(137) as 138 x 138 monomial matrices over Z(z68)\n"; # Change the value of r to any number between 1 and 33 # to get the complete set of inequivalent faithful irreducible 138-dimensional # representations of L2(137) r := 1; z := E(68)^r; result.symmetricforms := [ ]; result.antisymmetricforms := [ ]; result.hermitianforms := [ IdentityMat(138) ]; result.centralizeralgebra := [ IdentityMat(138) ]; result.generators := [ DiagonalMat([z^67,z^58,1,z^57,z^37,z^32,z^20,z^17,z^38,z^56,z^27,1, z^67,z^60,z^29,z^4,z^36,z^23,z^43,z^13,z^62,1,z^66,z^13,z^18,z^49, z^51,z^46,z^11,z^24,z,z^61,z^25,z^10,z^2,z^31,z^11,z^53,z^39,z^16, z^27,z^43,z^59,z^48,z^56,z^40,z^52,z^28,z^55,z^63,z^12,z^45,z^62, z^14,z^42,z^16,z^46,z^19,z^33,z^36,z^8,z^2,z^23,z^54,z^64,z^54,z^10, z^8,z^52,z^48,z^57,z^47,z^50,z^5,z^6,z^49,z^58,z^47,z^15,z^61,z^66, z^25,z^21,z^6,z^32,z,z^26,z^65,z^44,z^26,z^60,z^42,z^33,z^5,z^28, z^15,z^30,z^21,z^31,z^14,z^65,z^53,z^7,z^20,z^45,z^64,-1,z^41,z^55, z^22,z^29,z^51,z^37,z^3,z^7,z^4,z^40,-1,z^18,z^19,z^12,z^30,z^59, z^38,z^50,z^17,z^41,z^3,z^9,z^9,z^35,z^63,z^44,z^22,z^24,z^35,z^39, 1]) * PermutationMat( ( 1, 86)( 2, 34)( 3,138)( 4, 29)( 5, 36)( 6, 17)( 7, 70)( 8, 27) ( 9,122)( 10, 51)( 11,127)( 12, 22)( 13, 31)( 14, 68)( 15, 39)( 16,106) ( 18, 52)( 19, 82)( 20, 49)( 21, 75)( 23, 35)( 24,109)( 25,125)( 26,120) ( 28,134)( 30, 89)( 32,115)( 33, 42)( 37, 71)( 38, 79)( 40, 69)( 41,108) ( 43,130)( 44,104)( 45,121)( 46, 95)( 47, 56)( 48,117)( 50, 74)( 53, 84) ( 54, 66)( 55, 87)( 57,110)( 58, 76)( 59,136)( 60, 85)( 61, 91)( 62, 81) ( 63,105)( 64,100)( 65,116)( 67, 77)( 72, 83)( 73,119)( 78, 98)( 80,103) ( 88,114)( 90, 92)( 93,131)( 94,132)( 96,102)( 97,124)( 99,113)(101,128) (111,137)(112,126)(123,129)(133,135), 138) , DiagonalMat([z^45,z^23,z^22,z^21,z^20,z^19,z^18,z^17,z^16,z^15,z^14, z^13,z^12,z^11,z^10,z^9,z^8,z^7,z^6,z^5,z^4,z^3,z^2,z,1,z^67,z^66, z^65,z^64,z^63,z^62,z^61,z^60,z^59,z^58,z^57,z^56,z^55,z^54,z^53, z^52,z^51,z^50,z^49,z^48,z^47,z^46,z^45,z^44,z^43,z^42,z^41,z^40, z^39,z^38,z^37,z^36,z^35,-1,z^33,z^32,z^31,z^30,z^29,z^28,z^27,z^26, z^25,z^24,z^23,z^22,z^21,z^20,z^19,z^18,z^17,z^16,z^15,z^14,z^13, z^12,z^11,z^10,z^9,z^8,z^7,z^6,z^5,z^4,z^3,z^2,z,1,z^67,z^66,z^65, z^64,z^63,z^62,z^61,z^60,z^59,z^58,z^57,z^56,z^55,z^54,z^53,z^52, z^51,z^50,z^49,z^48,z^47,z^46,z^45,z^44,z^43,z^42,z^41,z^40,z^39, z^38,z^37,z^36,z^35,-1,z^33,z^32,z^31,z^30,z^29,z^28,z^27,z^26,z^25, z^24,z^23]) * PermutationMat( ( 1,138, 93)( 2, 87,122)( 3, 59, 13)( 4,118, 89)( 5, 32, 38)( 6,134, 71) ( 7,116, 88)( 8, 27, 40)( 9, 66,136)( 10, 23, 42)( 11,128, 72)( 12, 18, 45) ( 14,135, 62)( 15, 94,102)( 16, 31, 28)( 17, 77,117)( 19, 34, 22)( 20,111, 80) ( 21, 86,104)( 24,113, 74)( 25,103, 83)( 26,112, 73)( 29, 82,100)( 30,106, 75) ( 33, 69,109)( 35, 84, 92)( 36,124, 51)( 37,127, 47)( 39,114, 58)( 41, 50,120) ( 43, 98, 70)( 44,115, 52)( 46, 97, 68)( 48, 64, 99)( 49,108, 54)( 53,101, 57) ( 55, 65, 91)( 56, 76, 79)( 60, 61, 90)( 63, 67, 81)( 78,137,132)( 85,133,129) ( 95,121,131)( 96,125,126)(105,119,123)(107,110,130), 138)]; return result;