pgr21:=function()
local z,g,sg,p;
z:=FreeGroup("a","b");
g:=z/[z.1^3,z.2^2,z.1*z.2*z.1*z.2*z.1*z.2*z.1*z.2*z.1*z.2*z.1^2*z.2*z.1^2*z.2*z.1^2*z.2*z.1^2*z.2*z.1^2*z.2];
sg:=Subgroup(g,[g.1]);
p:=Image(ActionHomomorphism(g,RightTransversal(g,sg),OnRight));
return p;
end;
G21:=pgr21(); gap> Size(G21); 720 gap> N21:=NormalSubgroups(G21);; gap> NTSize(N21); Groesse des 1. Normalteilers: 1 Groesse des 2. Normalteilers: 2 Groesse des 3. Normalteilers: 3 Groesse des 4. Normalteilers: 4 Groesse des 5. Normalteilers: 6 Groesse des 6. Normalteilers: 12 Groesse des 7. Normalteilers: 120 Groesse des 8. Normalteilers: 240 Groesse des 9. Normalteilers: 360 Groesse des 10. Normalteilers: 720 gap> Centre(G21); <permutation group of size 12 with 2 generators> gap> Size(Centre(G21)); 12 gap> IsSolvable(G21); false gap> CompositionSeries(G21); [ <permutation group of size 720 with 3 generators>, <permutation group of size 360 with 7 generators>, <permutation group of size 6 with 2 generators>, <permutation group of size 3 with 1 generators>, Group(()) ]
gap> ct21:=CharacterTable(G21); CharacterTable( <permutation group of size 720 with 2 generators> ) gap> Display(ct21); CT1 2 4 4 4 4 4 4 4 4 4 4 4 4 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 5 1 1 1 1 1 1 1 1 1 1 1 1 . . . . . . . 1a 3a 3b 2a 6a 6b 12a 12b 4a 12c 12d 4b 12e 12f 12g 12h 12i 12j 3c 2P 1a 3b 3a 1a 3b 3a 6b 6a 2a 6b 6a 2a 6d 6c 6e 6d 6c 6e 3c 3P 1a 1a 1a 2a 2a 2a 4b 4b 4b 4a 4a 4a 4a 4a 4a 4b 4b 4b 1a 5P 1a 3b 3a 2a 6b 6a 12b 12a 4a 12d 12c 4b 12g 12f 12e 12j 12i 12h 3c 7P 1a 3a 3b 2a 6a 6b 12c 12d 4b 12a 12b 4a 12h 12i 12j 12e 12f 12g 3c 11P 1a 3b 3a 2a 6b 6a 12d 12c 4b 12b 12a 4a 12j 12i 12h 12g 12f 12e 3c 13P 1a 3a 3b 2a 6a 6b 12a 12b 4a 12c 12d 4b 12e 12f 12g 12h 12i 12j 3c 17P 1a 3b 3a 2a 6b 6a 12b 12a 4a 12d 12c 4b 12g 12f 12e 12j 12i 12h 3c 19P 1a 3a 3b 2a 6a 6b 12c 12d 4b 12a 12b 4a 12h 12i 12j 12e 12f 12g 3c 23P 1a 3b 3a 2a 6b 6a 12d 12c 4b 12b 12a 4a 12j 12i 12h 12g 12f 12e 3c 29P 1a 3b 3a 2a 6b 6a 12b 12a 4a 12d 12c 4b 12g 12f 12e 12j 12i 12h 3c 31P 1a 3a 3b 2a 6a 6b 12c 12d 4b 12a 12b 4a 12h 12i 12j 12e 12f 12g 3c 37P 1a 3a 3b 2a 6a 6b 12a 12b 4a 12c 12d 4b 12e 12f 12g 12h 12i 12j 3c 41P 1a 3b 3a 2a 6b 6a 12b 12a 4a 12d 12c 4b 12g 12f 12e 12j 12i 12h 3c 43P 1a 3a 3b 2a 6a 6b 12c 12d 4b 12a 12b 4a 12h 12i 12j 12e 12f 12g 3c 47P 1a 3b 3a 2a 6b 6a 12d 12c 4b 12b 12a 4a 12j 12i 12h 12g 12f 12e 3c 53P 1a 3b 3a 2a 6b 6a 12b 12a 4a 12d 12c 4b 12g 12f 12e 12j 12i 12h 3c 59P 1a 3b 3a 2a 6b 6a 12d 12c 4b 12b 12a 4a 12j 12i 12h 12g 12f 12e 3c X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 X.3 1 A /A 1 A /A A /A 1 A /A 1 /A 1 A /A 1 A 1 X.4 1 A /A 1 A /A -A -/A -1 -A -/A -1 -/A -1 -A -/A -1 -A 1 X.5 1 /A A 1 /A A /A A 1 /A A 1 A 1 /A A 1 /A 1 X.6 1 /A A 1 /A A -/A -A -1 -/A -A -1 -A -1 -/A -A -1 -/A 1 X.7 2 B /B -2 -B -/B G -/G H -G /G -H M N -/M -M -N /M -1 X.8 2 B /B -2 -B -/B -G /G -H G -/G H -M -N /M M N -/M -1 X.9 2 /B B -2 -/B -B -/G G H /G -G -H -/M N M /M -N -M -1 X.10 2 /B B -2 -/B -B /G -G -H -/G G H /M -N -M -/M N M -1 X.11 2 2 2 -2 -2 -2 H H H -H -H -H N N N -N -N -N -1 X.12 2 2 2 -2 -2 -2 -H -H -H H H H -N -N -N N N N -1 X.13 2 B /B -2 -B -/B G -/G H -G /G -H M N -/M -M -N /M -1 X.14 2 B /B -2 -B -/B -G /G -H G -/G H -M -N /M M N -/M -1 X.15 2 /B B -2 -/B -B -/G G H /G -G -H -/M N M /M -N -M -1 X.16 2 /B B -2 -/B -B /G -G -H -/G G H /M -N -M -/M N M -1 X.17 2 2 2 -2 -2 -2 H H H -H -H -H N N N -N -N -N -1 X.18 2 2 2 -2 -2 -2 -H -H -H H H H -N -N -N N N N -1 X.19 3 3 3 3 3 3 3 3 3 3 3 3 . . . . . . . X.20 3 3 3 3 3 3 -3 -3 -3 -3 -3 -3 . . . . . . . X.21 3 C /C 3 C /C C /C 3 C /C 3 . . . . . . . X.22 3 C /C 3 C /C -C -/C -3 -C -/C -3 . . . . . . . X.23 3 /C C 3 /C C /C C 3 /C C 3 . . . . . . . X.24 3 /C C 3 /C C -/C -C -3 -/C -C -3 . . . . . . . X.25 3 3 3 3 3 3 3 3 3 3 3 3 . . . . . . . X.26 3 3 3 3 3 3 -3 -3 -3 -3 -3 -3 . . . . . . . X.27 3 C /C 3 C /C C /C 3 C /C 3 . . . . . . . X.28 3 C /C 3 C /C -C -/C -3 -C -/C -3 . . . . . . . X.29 3 /C C 3 /C C /C C 3 /C C 3 . . . . . . . X.30 3 /C C 3 /C C -/C -C -3 -/C -C -3 . . . . . . . X.31 4 4 4 4 4 4 4 4 4 4 4 4 1 1 1 1 1 1 1 X.32 4 4 4 4 4 4 -4 -4 -4 -4 -4 -4 -1 -1 -1 -1 -1 -1 1 X.33 4 D /D 4 D /D D /D 4 D /D 4 /A 1 A /A 1 A 1 X.34 4 D /D 4 D /D -D -/D -4 -D -/D -4 -/A -1 -A -/A -1 -A 1 X.35 4 /D D 4 /D D /D D 4 /D D 4 A 1 /A A 1 /A 1 X.36 4 /D D 4 /D D -/D -D -4 -/D -D -4 -A -1 -/A -A -1 -/A 1 X.37 4 D /D -4 -D -/D I -/I J -I /I -J -M -N /M M N -/M 1 X.38 4 D /D -4 -D -/D -I /I -J I -/I J M N -/M -M -N /M 1 X.39 4 /D D -4 -/D -D -/I I J /I -I -J /M -N -M -/M N M 1 X.40 4 /D D -4 -/D -D /I -I -J -/I I J -/M N M /M -N -M 1 X.41 4 4 4 -4 -4 -4 J J J -J -J -J -N -N -N N N N 1 X.42 4 4 4 -4 -4 -4 -J -J -J J J J N N N -N -N -N 1 X.43 5 5 5 5 5 5 5 5 5 5 5 5 -1 -1 -1 -1 -1 -1 -1 X.44 5 5 5 5 5 5 -5 -5 -5 -5 -5 -5 1 1 1 1 1 1 -1 X.45 5 E /E 5 E /E E /E 5 E /E 5 -/A -1 -A -/A -1 -A -1 X.46 5 E /E 5 E /E -E -/E -5 -E -/E -5 /A 1 A /A 1 A -1 X.47 5 /E E 5 /E E /E E 5 /E E 5 -A -1 -/A -A -1 -/A -1 X.48 5 /E E 5 /E E -/E -E -5 -/E -E -5 A 1 /A A 1 /A -1 X.49 6 F /F -6 -F -/F K -/K L -K /K -L . . . . . . . X.50 6 F /F -6 -F -/F -K /K -L K -/K L . . . . . . . X.51 6 /F F -6 -/F -F -/K K L /K -K -L . . . . . . . X.52 6 /F F -6 -/F -F /K -K -L -/K K L . . . . . . . X.53 6 6 6 -6 -6 -6 L L L -L -L -L . . . . . . . X.54 6 6 6 -6 -6 -6 -L -L -L L L L . . . . . . . 2 2 2 2 2 2 3 3 3 3 3 3 2 2 2 2 2 2 2 3 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 5 . . . . . . . . . . . 1 1 1 1 1 1 1 3d 3e 6c 6d 6e 2b 6f 6g 12k 12l 4c 60a 20a 60b 60c 20b 60d 5a 2P 3e 3d 3c 3e 3d 1a 3b 3a 6b 6a 2a 30c 10b 30d 30c 10b 30d 5b 3P 1a 1a 2a 2a 2a 2b 2b 2b 4c 4c 4c 20d 20d 20d 20c 20c 20c 5b 5P 3e 3d 6c 6e 6d 2b 6g 6f 12l 12k 4c 12c 4b 12d 12a 4a 12b 1a 7P 3d 3e 6c 6d 6e 2b 6f 6g 12k 12l 4c 60g 20d 60h 60e 20c 60f 5b 11P 3e 3d 6c 6e 6d 2b 6g 6f 12l 12k 4c 60d 20b 60c 60b 20a 60a 5a 13P 3d 3e 6c 6d 6e 2b 6f 6g 12k 12l 4c 60e 20c 60f 60g 20d 60h 5b 17P 3e 3d 6c 6e 6d 2b 6g 6f 12l 12k 4c 60f 20c 60e 60h 20d 60g 5b 19P 3d 3e 6c 6d 6e 2b 6f 6g 12k 12l 4c 60c 20b 60d 60a 20a 60b 5a 23P 3e 3d 6c 6e 6d 2b 6g 6f 12l 12k 4c 60h 20d 60g 60f 20c 60e 5b 29P 3e 3d 6c 6e 6d 2b 6g 6f 12l 12k 4c 60b 20a 60a 60d 20b 60c 5a 31P 3d 3e 6c 6d 6e 2b 6f 6g 12k 12l 4c 60c 20b 60d 60a 20a 60b 5a 37P 3d 3e 6c 6d 6e 2b 6f 6g 12k 12l 4c 60e 20c 60f 60g 20d 60h 5b 41P 3e 3d 6c 6e 6d 2b 6g 6f 12l 12k 4c 60b 20a 60a 60d 20b 60c 5a 43P 3d 3e 6c 6d 6e 2b 6f 6g 12k 12l 4c 60g 20d 60h 60e 20c 60f 5b 47P 3e 3d 6c 6e 6d 2b 6g 6f 12l 12k 4c 60h 20d 60g 60f 20c 60e 5b 53P 3e 3d 6c 6e 6d 2b 6g 6f 12l 12k 4c 60f 20c 60e 60h 20d 60g 5b 59P 3e 3d 6c 6e 6d 2b 6g 6f 12l 12k 4c 60d 20b 60c 60b 20a 60a 5a X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 1 1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 X.3 A /A 1 A /A 1 A /A A /A 1 /A 1 A /A 1 A 1 X.4 A /A 1 A /A -1 -A -/A A /A 1 -/A -1 -A -/A -1 -A 1 X.5 /A A 1 /A A 1 /A A /A A 1 A 1 /A A 1 /A 1 X.6 /A A 1 /A A -1 -/A -A /A A 1 -A -1 -/A -A -1 -/A 1 X.7 -A -/A 1 A /A . . . . . . O P -/O -O -P /O -S X.8 -A -/A 1 A /A . . . . . . -O -P /O O P -/O -S X.9 -/A -A 1 /A A . . . . . . -/O P O /O -P -O -S X.10 -/A -A 1 /A A . . . . . . /O -P -O -/O P O -S X.11 -1 -1 1 1 1 . . . . . . P P P -P -P -P -S X.12 -1 -1 1 1 1 . . . . . . -P -P -P P P P -S X.13 -A -/A 1 A /A . . . . . . Q R -/Q -Q -R /Q -*S X.14 -A -/A 1 A /A . . . . . . -Q -R /Q Q R -/Q -*S X.15 -/A -A 1 /A A . . . . . . -/Q R Q /Q -R -Q -*S X.16 -/A -A 1 /A A . . . . . . /Q -R -Q -/Q R Q -*S X.17 -1 -1 1 1 1 . . . . . . R R R -R -R -R -*S X.18 -1 -1 1 1 1 . . . . . . -R -R -R R R R -*S X.19 . . . . . -1 -1 -1 -1 -1 -1 S S S S S S S X.20 . . . . . 1 1 1 -1 -1 -1 -S -S -S -S -S -S S X.21 . . . . . -1 -A -/A -A -/A -1 T S /T T S /T S X.22 . . . . . 1 A /A -A -/A -1 -T -S -/T -T -S -/T S X.23 . . . . . -1 -/A -A -/A -A -1 /T S T /T S T S X.24 . . . . . 1 /A A -/A -A -1 -/T -S -T -/T -S -T S X.25 . . . . . -1 -1 -1 -1 -1 -1 *S *S *S *S *S *S *S X.26 . . . . . 1 1 1 -1 -1 -1 -*S -*S -*S -*S -*S -*S *S X.27 . . . . . -1 -A -/A -A -/A -1 U *S /U U *S /U *S X.28 . . . . . 1 A /A -A -/A -1 -U -*S -/U -U -*S -/U *S X.29 . . . . . -1 -/A -A -/A -A -1 /U *S U /U *S U *S X.30 . . . . . 1 /A A -/A -A -1 -/U -*S -U -/U -*S -U *S X.31 1 1 1 1 1 . . . . . . -1 -1 -1 -1 -1 -1 -1 X.32 1 1 1 1 1 . . . . . . 1 1 1 1 1 1 -1 X.33 A /A 1 A /A . . . . . . -/A -1 -A -/A -1 -A -1 X.34 A /A 1 A /A . . . . . . /A 1 A /A 1 A -1 X.35 /A A 1 /A A . . . . . . -A -1 -/A -A -1 -/A -1 X.36 /A A 1 /A A . . . . . . A 1 /A A 1 /A -1 X.37 A /A -1 -A -/A . . . . . . M N -/M -M -N /M -1 X.38 A /A -1 -A -/A . . . . . . -M -N /M M N -/M -1 X.39 /A A -1 -/A -A . . . . . . -/M N M /M -N -M -1 X.40 /A A -1 -/A -A . . . . . . /M -N -M -/M N M -1 X.41 1 1 -1 -1 -1 . . . . . . N N N -N -N -N -1 X.42 1 1 -1 -1 -1 . . . . . . -N -N -N N N N -1 X.43 -1 -1 -1 -1 -1 1 1 1 1 1 1 . . . . . . . X.44 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 . . . . . . . X.45 -A -/A -1 -A -/A 1 A /A A /A 1 . . . . . . . X.46 -A -/A -1 -A -/A -1 -A -/A A /A 1 . . . . . . . X.47 -/A -A -1 -/A -A 1 /A A /A A 1 . . . . . . . X.48 -/A -A -1 -/A -A -1 -/A -A /A A 1 . . . . . . . X.49 . . . . . . . . . . . -M -N /M M N -/M 1 X.50 . . . . . . . . . . . M N -/M -M -N /M 1 X.51 . . . . . . . . . . . /M -N -M -/M N M 1 X.52 . . . . . . . . . . . -/M N M /M -N -M 1 X.53 . . . . . . . . . . . -N -N -N N N N 1 X.54 . . . . . . . . . . . N N N -N -N -N 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15a 15b 10a 30a 30b 30c 30d 10b 15c 15d 5b 60e 20c 60f 60g 20d 60h 2P 15d 15c 5b 15d 15c 15b 15a 5a 15b 15a 5a 30a 10a 30b 30a 10a 30b 3P 5b 5b 10b 10b 10b 10a 10a 10a 5a 5a 5a 20b 20b 20b 20a 20a 20a 5P 3b 3a 2a 6b 6a 6b 6a 2a 3b 3a 1a 12c 4b 12d 12a 4a 12b 7P 15c 15d 10b 30c 30d 30a 30b 10a 15a 15b 5a 60c 20b 60d 60a 20a 60b 11P 15b 15a 10a 30b 30a 30d 30c 10b 15d 15c 5b 60h 20d 60g 60f 20c 60e 13P 15c 15d 10b 30c 30d 30a 30b 10a 15a 15b 5a 60a 20a 60b 60c 20b 60d 17P 15d 15c 10b 30d 30c 30b 30a 10a 15b 15a 5a 60b 20a 60a 60d 20b 60c 19P 15a 15b 10a 30a 30b 30c 30d 10b 15c 15d 5b 60g 20d 60h 60e 20c 60f 23P 15d 15c 10b 30d 30c 30b 30a 10a 15b 15a 5a 60d 20b 60c 60b 20a 60a 29P 15b 15a 10a 30b 30a 30d 30c 10b 15d 15c 5b 60f 20c 60e 60h 20d 60g 31P 15a 15b 10a 30a 30b 30c 30d 10b 15c 15d 5b 60g 20d 60h 60e 20c 60f 37P 15c 15d 10b 30c 30d 30a 30b 10a 15a 15b 5a 60a 20a 60b 60c 20b 60d 41P 15b 15a 10a 30b 30a 30d 30c 10b 15d 15c 5b 60f 20c 60e 60h 20d 60g 43P 15c 15d 10b 30c 30d 30a 30b 10a 15a 15b 5a 60c 20b 60d 60a 20a 60b 47P 15d 15c 10b 30d 30c 30b 30a 10a 15b 15a 5a 60d 20b 60c 60b 20a 60a 53P 15d 15c 10b 30d 30c 30b 30a 10a 15b 15a 5a 60b 20a 60a 60d 20b 60c 59P 15b 15a 10a 30b 30a 30d 30c 10b 15d 15c 5b 60h 20d 60g 60f 20c 60e X.1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 X.3 A /A 1 A /A A /A 1 A /A 1 /A 1 A /A 1 A X.4 A /A 1 A /A A /A 1 A /A 1 -/A -1 -A -/A -1 -A X.5 /A A 1 /A A /A A 1 /A A 1 A 1 /A A 1 /A X.6 /A A 1 /A A /A A 1 /A A 1 -A -1 -/A -A -1 -/A X.7 -/T -T S /T T /U U *S -/U -U -*S Q R -/Q -Q -R /Q X.8 -/T -T S /T T /U U *S -/U -U -*S -Q -R /Q Q R -/Q X.9 -T -/T S T /T U /U *S -U -/U -*S -/Q R Q /Q -R -Q X.10 -T -/T S T /T U /U *S -U -/U -*S /Q -R -Q -/Q R Q X.11 -S -S S S S *S *S *S -*S -*S -*S R R R -R -R -R X.12 -S -S S S S *S *S *S -*S -*S -*S -R -R -R R R R X.13 -/U -U *S /U U /T T S -/T -T -S O P -/O -O -P /O X.14 -/U -U *S /U U /T T S -/T -T -S -O -P /O O P -/O X.15 -U -/U *S U /U T /T S -T -/T -S -/O P O /O -P -O X.16 -U -/U *S U /U T /T S -T -/T -S /O -P -O -/O P O X.17 -*S -*S *S *S *S S S S -S -S -S P P P -P -P -P X.18 -*S -*S *S *S *S S S S -S -S -S -P -P -P P P P X.19 S S S S S *S *S *S *S *S *S *S *S *S *S *S *S X.20 S S S S S *S *S *S *S *S *S -*S -*S -*S -*S -*S -*S X.21 /T T S /T T /U U *S /U U *S U *S /U U *S /U X.22 /T T S /T T /U U *S /U U *S -U -*S -/U -U -*S -/U X.23 T /T S T /T U /U *S U /U *S /U *S U /U *S U X.24 T /T S T /T U /U *S U /U *S -/U -*S -U -/U -*S -U X.25 *S *S *S *S *S S S S S S S S S S S S S X.26 *S *S *S *S *S S S S S S S -S -S -S -S -S -S X.27 /U U *S /U U /T T S /T T S T S /T T S /T X.28 /U U *S /U U /T T S /T T S -T -S -/T -T -S -/T X.29 U /U *S U /U T /T S T /T S /T S T /T S T X.30 U /U *S U /U T /T S T /T S -/T -S -T -/T -S -T X.31 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 X.32 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 1 1 X.33 -A -/A -1 -A -/A -A -/A -1 -A -/A -1 -/A -1 -A -/A -1 -A X.34 -A -/A -1 -A -/A -A -/A -1 -A -/A -1 /A 1 A /A 1 A X.35 -/A -A -1 -/A -A -/A -A -1 -/A -A -1 -A -1 -/A -A -1 -/A X.36 -/A -A -1 -/A -A -/A -A -1 -/A -A -1 A 1 /A A 1 /A X.37 -A -/A 1 A /A A /A 1 -A -/A -1 M N -/M -M -N /M X.38 -A -/A 1 A /A A /A 1 -A -/A -1 -M -N /M M N -/M X.39 -/A -A 1 /A A /A A 1 -/A -A -1 -/M N M /M -N -M X.40 -/A -A 1 /A A /A A 1 -/A -A -1 /M -N -M -/M N M X.41 -1 -1 1 1 1 1 1 1 -1 -1 -1 N N N -N -N -N X.42 -1 -1 1 1 1 1 1 1 -1 -1 -1 -N -N -N N N N X.43 . . . . . . . . . . . . . . . . . X.44 . . . . . . . . . . . . . . . . . X.45 . . . . . . . . . . . . . . . . . X.46 . . . . . . . . . . . . . . . . . X.47 . . . . . . . . . . . . . . . . . X.48 . . . . . . . . . . . . . . . . . X.49 A /A -1 -A -/A -A -/A -1 A /A 1 -M -N /M M N -/M X.50 A /A -1 -A -/A -A -/A -1 A /A 1 M N -/M -M -N /M X.51 /A A -1 -/A -A -/A -A -1 /A A 1 /M -N -M -/M N M X.52 /A A -1 -/A -A -/A -A -1 /A A 1 -/M N M /M -N -M X.53 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -N -N -N N N N X.54 1 1 -1 -1 -1 -1 -1 -1 1 1 1 N N N -N -N -N A = E(3)^2 = (-1-ER(-3))/2 = -1-b3 B = 2*E(3)^2 = -1-ER(-3) = -1-i3 C = 3*E(3)^2 = (-3-3*ER(-3))/2 = -3-3b3 D = 4*E(3)^2 = -2-2*ER(-3) = -2-2i3 E = 5*E(3)^2 = (-5-5*ER(-3))/2 = -5-5b3 F = 6*E(3)^2 = -3-3*ER(-3) = -3-3i3 G = 2*E(12)^11 H = 2*E(4) = 2*ER(-1) = 2i I = 4*E(12)^11 J = 4*E(4) = 4*ER(-1) = 4i K = 6*E(12)^11 L = 6*E(4) = 6*ER(-1) = 6i M = E(12)^7 N = E(4) = ER(-1) = i O = -E(60)^23-E(60)^47 P = -E(20)-E(20)^9 Q = -E(60)^11-E(60)^59 R = -E(20)^13-E(20)^17 S = -E(5)-E(5)^4 = (1-ER(5))/2 = -b5 T = -E(15)^2-E(15)^8 U = -E(15)^11-E(15)^14 gap> quit;