| Quellcodebibliothek Statistik Leitseite products/Sources/formale Sprachen/GAP/pkg/rcwa/data/3ctsgroups9/ (Algebra von RWTH Aachen Version 4.15.1©) Datei vom 22.8.2025 mit Größe 8 MB |
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Quelle mods.g Sprache: unbekannt |
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## #W mods.g GAP4 Package `RCWA' Stefan Kohl ## ## List of moduli of the groups generated by 3 class transpositions ## which interchange residue classes with moduli <= 9. ## Unbound entries stand for 0. ## return [,,[,[]],[,[],[]],[,[],[],[]],[,[],[],[],[]], [,[],[],[],[],[]],[,[],[],[],[],[,,6],[]], [,[],[],[],[,,,8],[],[,,,8],[]], [,[],[],[],[],[],[,8,,8],[],[,,,8,,,8]], [,[],[],[],[],[],[],[],[],[]], [,[],[],[],[,24],[],[,48],[,,,,,36],[],[,48,,,,,,,48],[]], [,[],[],[],[],[],[],[,,54],[],[],[],[]], [,[],[],[],[,12],[,,18],[,,,24],[,,18,,,18],[,,,24,,,24], [,,,24,,,24,,24],[6],[,24,,,,36,48,36],[,,54,,,,1152]], [,[],[],[],[,48],[],[,192],[,,36],[,,,,192,,192],[], [,,,,,,,36],[,48,,,,,192,36],[,,108,,,,2304,108],[]], [,[],[],[],[,108,,216],[,,162],[,72,,216],[,,54], [,,,,648,,216],[,,,216,,,216,,1944],[,,,,,,,54],[,72,,,,324,144,108], [,,54,,144,,1152,162],[],[]], [,[],[],[],[,,,192],[],[,,,192],[,,36],[],[,,,192,,,192], [],[,,,,48,,,36,,192],[],[,,36,,,,192,,,,,6], [,,36,,48,,192,36,,,,6],[,,108,,,,576,108,,,,18]], [,[],[],[],[],[],[,,,216],[,,54,,,162],[,,,648,864], [,,,216,,,216,,648],[],[],[,,,,144,,,54], [,,54,,,162,72,162,,648,,,9],[,1296,108,,,,576,108,,,,,18], [,324,54,648,36,162,72,54,648,648,,,9],[]], [,[],[],[],[],[,,36],[,,,192],[],[],[,48,,96],[,,,,48], [,24,,,24,36,48,,,48],[,,108,,,,1152],[],[,,36,,48,,,,,,6,6,18], [],[12,,36,,,,192,,,,,6,,,6],[,648,108,,,324,144,,,,,,18,,18]], [,[],[],[],[,432],[],[],[,,54],[],[],[,,,,,,,54], [,72,,,,,,108],[,,54,,,,,54],[],[],[,,54,,144,,,,,,9,18,9], [,,108,,,,,108,,,,18,,,,18],[,1296,162,,,,,54,,,,,9,,,9],[]], [,[],[],[],[],[],[],[,,54],[],[],[],[], [,,54,,144,,,54],[,,54,,,,1152,,,,,,9],[,,,,,,2304,108,,,,,18], [,,,,,,1152,162,,,,,9],[],[,,,,144,,,54,,,,,9,9,18,9], [,,108,,,,1152,,,,,,18,,18,,,18],[,,54,,144,,,54,,,,,9,,,9,,9]], [,[],[],[],[,,,864],[,,162],[],[,,54],[,,,648,,,216], [,,,216,,,216],[,,,,,,,54],[,72,,,,324,144,108],[,,54,,,,1152],[], [],[54,36,54,216,36,162,72,54,216,216,9,18,9], [,,108,,,,576,,,,,18,,,,18],[,,54,648,36,162,72,54,648,648,,,9,,,9], [],[,144,54,,144,,,54,,,9,18,9,,,9,18,9], [,,,,,,1152,,,,,,9,,,9,,9,,9]], [,[],[],[],[],[],[],[],[],[,,,,,,16],[12,,,,96],[],[], [12,,,,,,,,,,12],[],[108,,,,216,2916,432,,,432,324], [24,,,,96,,384,,,384,,,,48],[108,,,,,,,,,6912,,,,,,108], [24,,,,48,432,96,,,384,48,,,,,,24],[], [,,,,2592,,6912,,,,,,,,,108,,108,1296],[108,,,,,,,,,,,,,,,108,1296,324,,,324] ],[,[],[],[],[],[],[],[,,,,,12],[],[],[],[],[], [,,,,,36,,36],[,,,,,,,72],[,,,,,324,,108],[,,,,,,,72,,,,,,72,72,216], [,,,,,,,108,,,,,,108,216,108],[,,,,,72,,,,,,,,,72,,72,216], [,,,,,,,108,,,,,,,,108,216],[,,,,,,,216,,,,,,216,432,648,,,432,216], [,,,,,324,,108,,,,,,,,108,216,108,,108,648],[]], [,[],[],[],[,8],[],[,16],[],[,,,,16,,16],[,16,,,,,16,,16], [],[,48,,,48,432,96,,96,96],[],[,24,,,24,,96,,48,,,48], [,96,,,96,,384,,384,,,96],[,72,,,216,11664,144,,1728,1296,,144], [,,,,192,,384,,,384,,96,,96,192,288], [,648,,,648,,1296,,1296,,,,,648,2592,648], [,48,,,96,432,96,,,96,,48,,,96,,96,1296], [,144,,,864,,,,,,,144,,,,,576,2592], [,,,,10368,,82944,,,,,,,864,864,432,,1296,432,432], [,72,,,,,,,432,432,,144,,,,72,288,648,,144,1296],[],[]], [,[],[],[],[,8,,16],[,,12],[,16,,16],[,,12,,,12], [,,,16,16,,16],[,16,,16,,,16,,16],[12,,,,,,,36], [,48,,,,72,96,72,192,96],[,,108,,,,,108], [12,24,36,48,24,36,48,36,48,48,12,24,108],[],[],[], [,1944,324,3888,648,972,432,324,3888,3888,,,108], [,48,72,,,72,,,,96,24,24,216,,,,,216],[,,108,,,,,108,,,,216,108,,,,,324], [,,108,,,,,108,,,,,108,108,,,,108,216,108], [,648,324,3888,648,972,432,324,3888,3888,324,216,324,,,,,,,108,324], [4,,,,8,,16,,,16,12,,,12,,,,972,,,,972], [,,,,,12,,12,,,,,,36,,,,324,72,108,,324], [,8,,,8,,16,,16,16,,48,,24,,,,648,48,432,2592,216]], [,[],[],[],[,16,,32],[,,24],[,32,,32],[,,24,,,24], [,,,32,32,,32],[,32,,32,,,32,,32],[96,,,,384,,,72], [,96,,,96,144,192,144,192,192],[,,216,,5184,,,216],[], [,768,144,,,,,144,3072,,192,48,576],[],[96,,288,768,192,,,288,,768,,96] ,[,1296,216,864,432,648,288,216,2592,864,,,72,,144], [96,,144,192,192,144,192,,,192,48,48,144,,48,,96,144], [,,216,,5184,,,216,,,864,432,216,,,,2592,216], [,,,,,,9216,216,,,,,288,,576,,,72,144,864], [,1296,1944,7776,1296,5832,2592,1944,7776,7776,648,1296,648,,,,2592,648,, 648,648],[8,,,,16,,32,,,32,48,,,,,,96,216,96,,864,648], [,,,,,24,,24,,,,,,,144,,288,216,144,216,864,648], [,16,,,16,,32,,32,32,,48,,,192,,192,648,,1296,,648],[]], [,[],[],[],[],[],[],[,,36],[,,,16],[],[12,,,,,,,108], [,,,,,,,216],[,,324,,,,,324],[12,,108,,,,,,,,12,24,36], [,96,216,,,,,,384,,24,24,72],[,72,324,432,,,,,432,,36,72,36], [,,,384,,,,216,,,,24,,24,24,72],[,,,,,,,324,,,,,36,36,72,36], [,96,216,,,,,,,,24,24,72,,24,,24,72], [,144,324,,,,,324,,,36,72,36,,,36,72,36], [,,324,,,,,324,,,,,36,36,72,36,,36,72,36], [,,324,,,,,324,,,36,72,36,,,36,72,36,,36,36], [4,,,,,,,,,,12,,,12,,108,24,,,,108],[], [,8,,,,,,,16,,,,,96,96,72,96,,96,144,648], [4,8,,16,,,,,16,,12,48,,12,,,,108,24,,108,108,4,,8], [,16,,32,,,,,32,,48,48,144,,96,,,72,96,,72,648,8,,8]], [,[],[],[],[],[],[],[,,12],[],[],[],[,,,,,,,72],[], [,,36,,,,,,,,,72],[],[,,324,,,,,,,,,648],[,,216,,,,,216,,,,72,,72,,648], [,,,,,,,324,,,,,,324,,324],[,,72,,,,,,,,,72,,,,,72,648],[],[], [,,324,,,,,,,,,648,,,,324,648,324],[], [,,,,,,,12,,,,,,36,,324,72,,72,,,324],[], [,,12,,,,,12,,,,72,,36,,,,972,72,,,972,,12], [,,24,,,,,24,,,,144,,,,,,648,144,,,1944,,24],[]], [,[],[],[],[,8,,16],[],[],[,,72],[,,,16,16], [,16,,16,,,,,16],[96,,,,96,,,432],[,48,,,48,,,432,384,96], [,,648,,288,,,648],[,24,,96,24,,,,,48,,48], [,96,1728,,96,,,864,384,,192,,1728], [,216,2592,432,72,,,,1296,432,,432,144], [96,,864,384,96,,,,,384,,48,,96,96], [,1944,,432,72,,,648,1728,432,,,144,216,,72], [96,96,432,192,48,,,,,192,48,48,432,,96,,48], [,864,648,,288,,,648,,,1296,,72,,,144], [,,,,288,,,2592,,,,,288,864,,288,,288,,288], [,,648,1728,72,,,3888,432,432,1296,864,144,,,72,864,72,,144,288], [8,,,,8,,,,,16,48,,,96,,216,48,,48,,2592],[], [,8,,,8,,,,16,16,,48,,24,96,216,96,648,96,432,2592], [,8,,16,8,,,,16,16,48,48,864,24,,,,216,48,,864,648,8,,8], [8,16,72,32,16,,,,32,32,48,48,216,,192,,96,216,48,216,864,648,8,,8], [],[]],[,[],[],[],[],[,,12],[],[],[],[],[], [,,,,,72],[,,108],[,,36,,,,,,,,,72],[,,72,,,,,,,,72,72,216], [,,108,,,,,,,,,216],[,,72,,,,,,,,,72,,72,72,216], [,,108,,,324,,,,,,,108,324,216,108],[],[], [,,108,,,,,,,,,,108,,216,,,108], [,,108,,,,,,,,216,216,648,,,108,216,108,,,648],[], [,,,,,12,,,,,,,,36,72,108,72,108,,,216,108],[], [,,12,,,12,,,,,36,72,108,36,,,,324,,,108,324,,12], [,,24,,,24,,,,,72,144,216,,144,,288,216,,,216,648,,24],[], [,,12,,,,,,,,,72,,36,,,72,324,,,,,,12,,12,24],[]], [,[],[],[],[,8,,16],[],[,16,,16],[],[],[,16,,16,,,16],[], [,48,,,,432,96,,,96],[,,,,864,,2304],[,24,,48,24,,,,,96,,48,144],[], [,,,,216,,432,,,1296,432,432,864],[,,,384,96,,384,,,384,,,,48,,432], [,1944,,432,,,,,,432,,,144,72,,216], [,48,,96,48,432,96,,,96,48,48,144,,,,48,144],[], [,,,,864,,2304,,,,,,144,144,,432,,144,144], [,648,,1296,648,,1296,,,,,1296,2592,,,648,1296,648,,,1296],[],[], [,8,,,8,72,16,,,16,,48,,24,,,96,648,48,,216,648], [,8,,16,8,,16,,,16,,48,1296,24,,,,648,48,,,648,,,8], [,,,32,16,72,32,,,32,48,48,144,,,,96,72,48,,72,648,,,8], [,8,,16,,,,,,,,96,144,,,648,48,,,,72,,,,8,8,8],[], [,8,,16,8,,,,,16,,,432,24,,216,48,,48,,864,648,,,8,8,8],[]], [,[],[],[],[,16,,32],[,,24],[,32,,32],[,,24,,,24], [,,,32,32,,32],[,32,,32,,,32,,32],[,,,,,,,72], [,96,,,96,144,192,144,192,192],[,,216,,576,,4608,216], [,192,288,384,192,288,384,288,384,384,96,96,864], [,,144,,384,,1536,144,,,,48], [,,864,3456,576,2592,1152,864,10368,,864,288,288], [192,,288,,192,,768,288,,3072,,96], [,1296,216,2592,144,648,288,216,864,2592,,,72,,,288], [192,384,144,192,192,144,192,,,192,48,48,144,,48,,96,144], [,,216,,576,,,216,,,,144,72,,,288,,72], [,,864,,,,18432,216,,,,,144,864,,288,,72,144], [,432,216,864,144,648,288,216,2592,864,216,144,72,,,288,,72,,72,72], [8,,,,16,,32,,,32,,,,96,,864,96,648,96,,,216], [,,,,,24,,24,,,,,,288,144,864,288,216,144,216,864,216], [,16,,,16,72,32,,32,32,,48,,96,192,864,192,648,48,432,,216],[], [8,16,24,32,16,24,32,24,32,32,24,48,216,,48,,96,216,48,216,216,,8,24, 8],[,16,,32,,,,,32,,,48,288,96,48,288,96,72,48,288,72,72,8,,8,,8], [,,24,,,,,24,,,,144,,288,,2592,,648,144,,,648,,24,,,24], [8,16,,32,16,,,72,32,32,48,48,72,96,96,288,96,72,48,72,288,72,8,,8,,8 ],[,,24,,,24,,,,,72,144,216,288,144,864,288,216,,,216,216,,24,,,24,,24] ,[,,,32,16,,32,,,32,48,48,432,96,,2592,,216,48,,,648,,,8,,8,8,,8]], [,[],[],[],[,8,,16],[],[,16,,16],[,,72],[,,,16,16,,16],[], [],[,48,,,,,,432,96],[,,648,,,,6912,1944],[,24,,,24,,48,,96,,,48,864] ,[,96,,,,,384,1728,384,,,96,864],[,72,,1296,,,144,2592,432,,,144,1296], [192,,,384,,,384,1728,,,,,,96,192], [,,,,648,,1296,648,1296,,,,1296,648,2592,648], [192,48,432,,,,96,,,,,48,432,,,,96,1296], [,144,648,,,,,648,,,,144,216,,,144,576,1296],[], [,72,1944,432,648,,144,,1728,,,144,432,,,72,288,648], [8,,,,8,,16,,,,,,,,,,96,,96],[], [,8,,,8,,16,,16,,,48,,24,96,72,96,,48,144,,72], [,8,,16,8,,16,,16,,,48,2592,24,,,,648,48,864,,216,8,,8], [8,16,,32,,,32,72,32,,,48,216,,192,,,648,48,216,,648,8,,8],[],[], [8,8,72,16,8,,,72,16,,,,216,24,96,216,96,648,,216,,216,8,,8,8,8],[], [,8,,16,8,,16,,,,,48,1296,24,,216,96,648,,,,,,,8,8,8,,,8], [8,16,72,32,,,32,,32,,,96,216,96,192,,192,648,48,216,,216,8,,8,,8,,,8,, 8]],[,[],[],[],[],[],[],[],[,,,,,,640],[,,,,,,640], [30,,,,,,,810],[],[],[30,,,,,,,,,,15],[,,,,,,122880,3240,,,120],[], [,,,,,,30720,6480,,30720,,,,60,120],[,,,,,196830,17280,,,,,,,405], [,,,,,,3840,,,,60,,,,60,,,540],[,,,,,,,2430,,,135,,,,,,,405], [,,,,,,,21870,,,,,,135,540,,,135,1620,405], [7290,,,,,590490,17280,7290,,,,,,,,,3240,135,,135,135], [20,,,,,4860,320,,,1280,60,,,60,,,480,,,,14580,4860],[],[], [20,,,,,1620,,1620,,1280,60,,,60,,,,4860,240,1620,1620,14580,20], [,,,,,,1280,,2560,2560,,,,,1920,,960,3240,480,6480,6480,38880,80], [20,,,,,,,,1280,,60,,,60,480,,480,1620,480,1620,1620,4860,20,,,20,80], [,,,,,,,1080,,,,,,38880,,,4320,,2160,,,174960,,,,2160,17280],[], [,,,,,,,,,,6480,,,38880,25920,,12960,174960,,,58320,116640,,,,,,,2160], [,,,,,,320,,,1280,960,,,,,,1920,,960,,38880,349920,,,,160,80,80], [160,,,,,,,,,,,,,480,960,,1920,1080,1920,,6480,4320,80,,,,40,80,,,,80], [160,,,,,,320,38880,1280,,,,,480,3840,,1920,,480,2160,,38880,80,,,80,80,,,,, 80,80]], [,[],[],[],[,20,,160],[,,30],[,,,40],[,,30,,,30],[,,,40,,,40], [,,,40,,,40,,40],[30,,,,,,,270],[],[,,2430,,466560,,276480,2430], [30,60,90,120,60,90,120,90,120,120,15],[],[], [,,,,960,,,,,7680,,,,120],[],[,,,480,240,1080,,,,,,,3240,,,,60], [,,2430,,,,,2430,,,405,,135],[,,,,,,,2430,,,,,135,135,,,,,,135], [,4860,2430,9720,4860,2430,9720,810,9720,,135,,135,,,,,,,135,135], [20,,,,,,1280,,,320,60,,,60,,,240,,,,1620,14580], [,,,,,120,,120,,,,,,180,,,720,,8640,,77760,1620], [,40,,,40,466560,160,,80,160,,,,120,,,3840,,480,77760,155520,3240], [20,40,60,80,40,60,80,60,80,80,60,,14580,60,,,,,240,14580,4860,,20,60,40 ],[],[20,160,,1280,,,,,1280,,60,,,60,,,240,,480,,,4860,20,,160,20], [,,120,,,,,120,,,,,,180,,,6480,,4320,,,4860,,60,,60], [,40,12960,160,40,,,12960,160,80,,,12960,120,,,960,,480,,8640,3240,,,40,40] ,[,,,,,120,,,,,1080,,9720,180,,,720,,,,,4860,,60,,60,,,60], [,40,,80,40,466560,160,,,,,,51840,120,,,960,,480,,,9720,,,40,40,,80,,40], [],[,40,,,40,,80,,,,,,233280,120,,,,,480,,,1080,160,,40,40,,,,40,,40], [10,,,,,270,,,640,,15,,,15,,,120,,,,1215,405,20,,,20,,20,,,2160]], [,[],[],[],[],[],[],[],[],[,160,,640,,,,,640],[30,,,,,,,810], [,,,,,,,1620],[,,,,,,,2430],[30,,,,,,,,,1920,15,30,45], [,,,,,,,,,,30,30,90],[,,,,,,,,,,45,90,45], [480,,,983040,,,,1620,,,,30,,30,30,90],[,,,,,,,2430,,,,,45,45,90,45], [480,1920,,,,,,,,15360,30,30,90,,30,,30,90], [,5760,,,,,,2430,,,45,90,45,,,45,90,45], [,,,,,,,2430,,,,,45,45,90,45,,45,90,45], [,,,,,,,2430,,,45,90,45,,,45,90,45,,45,45], [20,,,,,,,,,320,60,,,60,,,480,1620,480,,540,1620], [,,,,,,,,,,,,,6480,12960,19440,,19440,12960,19440,,19440], [,80,,,,,,,1280,320,,,,960,960,1440,,58320,480,2880,77760], [20,80,,,,,,,,1280,60,240,1620,60,,,,1620,480,1620,1620,540,20,,80], [,320,,5120,,,,2160,5120,5120,240,480,720,,3840,,,,960,,720,29160,80,17280, 80],[20,80,,1280,,,,,1280,,60,120,180,60,120,180,120,180,120,180,180, 180,20,,80,20,80],[],[], [,,,,,,,,,,6480,12960,19440,,,,12960,19440,,,19440,,,,,2160,8640], [,80,,1280,,,,,,640,960,1920,5760,,,,,,960,,1440,,,,80,80,80,80], [,,,2560,,,,,,1280,480,480,1440,,480,1440,480,720,480,1440,1440,360,,,80,, 40,80,,,,80],[,160,,1280,,,,,,,,960,6480,1920,3840,1440,30720,4199040, 960,1440,,1440,80,,160,80,80,,,,,,80], [10,,,,,,,,640,640,15,,,15,60,,60,135,60,,,135,20,,,20,160,20,,,2160,,,80], [10,,,640,,,,270,,640,15,,135,15,,,,,60,135,,,20,2160,160,20,,20,,,,80,,,5 ]],[,[],[],[],[,20,,40],[,,30],[,40,,40],[,,30,,,30], [,,,40,40,,40],[,40,,40,,,40,,40],[30],[,240,,,,,480,1080,960,480], [,,,,,,1105920,2430],[30,60,90,120,60,90,120,90,120,120,15,,135],[], [,,810,,,2430,1080,2430,,29160,,3240,135],[],[], [,240,1080,3840,,1080,,,,480,60,,540],[,,2430,,,,,2430,,,135,,405,,,135], [,,2430,,,,276480,,,,,,135,135],[], [20,,,,40,180,80,,,80,60,,,60,,,,,,,4860], [,,,,,120,,120,,,,,,180,,1620,,,4320,29160], [,40,,,40,360,80,,,80,,480,,120,,29160,,,480,,9720], [20,40,60,80,40,60,80,60,80,80,60,240,4860,60,,,,,240,,,,20,60,40], [40,,120,160,320,120,160,120,160,160,240,480,9720,,,,,,480,87480,3240,,40, 120,40],[20,40,180,80,,,,180,80,,60,,1620,60,,,,,480,1620,,,20,,40,20, 40],[,,120,,,,,,,,,4320,,180,,4860,,,,,,,,60,,60,120], [40,40,360,80,40,,,360,80,320,,480,9720,120,,,,,,3240,,,40,,40,40,40], [,,120,,,120,,,,,,4320,9720,180,,4860,,,,,,,,60,,60,120,,60], [,40,,320,40,360,80,,,80,1920,480,,120,,9720,,,480,,9720,,,,40,40,40,40,, 40],[40,,120,160,,120,160,120,160,160,240,480,9720,,,933120,,,480,3240, 29160,,40,120,40,,40,40,120,40,120,40], [40,40,360,80,40,,,360,80,,,480,9720,120,,9720,,,480,3240,,,40,,40,40,40,, ,40,,40,40],[10,,,,,,640,270,,640,15,,,15,,,,,60,135,135,,20,,,20,40, 20,2160,,,80,40],[10,20,30,40,20,30,40,30,40,40,15,,405,15,,,,,,,,, 20,60,40,20,,20,60,40,60,40,,40,5], [10,80,,640,,,,,640,,15,60,135,15,,135,,,,135,135,,20,2160,80,20,40,20,,, 2160,80,40,80,5,5]], [,[],[],[],[],[],[],[,,,,,18],[,,,,96,,96],[], [6,,,,48,,,18],[],[],[6,,,,,18,96,18,,,6],[,,,,,,768,36,,,12], [54,,,,,162,288,54,,,18],[12,,,,96,,,36,,,,,,12,12,36], [54,,,,,,,162,,,,,,54,108,54],[12,,,,48,36,192,,,,12,,,,12,,12,108], [,,,,,,,54,,,18,,,,,18,36,54],[], [54,,,,,162,288,54,,,18,,,,,18,36,54,,18], [12,,,,48,108,192,,,,12,,,12,,108,24,108,24,,,108],[],[], [12,,,,48,36,,36,,,12,,,12,,,,324,24,108,,108,12], [24,,,,96,72,384,72,,,24,,,,48,,96,216,48,216,,648,24], [12,,,,,,,108,192,,12,,,12,24,36,,,24,36,,36,12,,,12,48], [,,,,,,,36,,,,,,36,,324,72,,72,,,324,,,,36,72], [24,,,,48,,,216,192,,48,,,,192,,96,,48,216,,216,24,,,48,24], [,,,,,36,,,,,36,,,36,72,108,72,324,,,,108,,,,36,72,,36], 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2026-03-28