Script started on Fri 18 Apr 2008 10:16:45 AM CEST ]0;carlo@ka37: ~/work/sagestuffcarlo@ka37:~/work/sagestuff$ sage ---------------------------------------------------------------------- | SAGE Version 2.11, Release Date: 2008-03-30 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- sage: attach 'carlo.sage' T1 = [0 1] [1 0] row, column, symbol relabelling: r0 = x0 r1 = x1 c0 = x0 c1 = x1 s0 = x0 s1 = x1 Cayley table: [x0 x1] [x1 x0] ... of Multiplicative Abelian Group isomorphic to C2 T1 = [ 0 1 -1] [ 2 0 -1] [ 1 2 -1] row, column, symbol relabelling: r0 = x0 r1 = x2 r2 = x1 c0 = x0 c2 = x2 s0 = x0 s1 = x1 s2 = x2 Cayley table: [x0 x1 x2] [x1 x2 x0] [x2 x0 x1] ... of Multiplicative Abelian Group isomorphic to C3 T1 = [ 0 1 2] [ 1 -1 0] [-1 2 1] row, column, symbol relabelling: r0 = x0 r1 = x3 r2 = x1 c0 = x0 c2 = x2 c2 = x2 s0 = x0 s1 = x3 s2 = x2 Cayley table: [x0 x1 x2 x3] [x1 x0 x3 x2] [x2 x3 x1 x0] [x3 x2 x0 x1] ... of Multiplicative Abelian Group isomorphic to C4 T1 = [ 0 1 -1 -1] [ 2 0 -1 -1] [ 3 2 -1 -1] [ 1 3 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x3 r2 = x1 r3 = x2 c0 = x0 c3 = x2 s0 = x0 s1 = x2 s2 = x3 s3 = x1 Cayley table: [x0 x1 x2 x3] [x1 x0 x3 x2] [x2 x3 x1 x0] [x3 x2 x0 x1] ... of Multiplicative Abelian Group isomorphic to C4 T1 = [ 0 1 2 -1] [ 3 -1 0 -1] [ 1 2 3 -1] [-1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x4 r2 = x3 c0 = x0 c3 = x2 c3 = x2 s0 = x0 s1 = x3 s2 = x1 s3 = x4 Cayley table: [x0 x1 x2 x3 x4] [x1 x2 x3 x4 x0] [x2 x3 x4 x0 x1] [x3 x4 x0 x1 x2] [x4 x0 x1 x2 x3] ... of Multiplicative Abelian Group isomorphic to C5 T1 = [ 0 1 2 3] [ 1 -1 -1 0] [-1 2 3 1] [-1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x5 r2 = x2 c0 = x0 c3 = x3 c3 = x3 c3 = x3 s0 = x0 s1 = x5 s2 = x4 s3 = x3 Cayley table: [x0 x1 x2 x3 x4 x5] [x1 x2 x0 x4 x5 x3] [x2 x0 x1 x5 x3 x4] [x3 x4 x5 x1 x2 x0] [x4 x5 x3 x2 x0 x1] [x5 x3 x4 x0 x1 x2] ... of Multiplicative Abelian Group isomorphic to C6 T1 = [ 0 1 2 -1] [ 3 -1 0 2] [ 1 2 -1 3] [-1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x6 r2 = x4 c0 = x0 c3 = x2 c3 = x2 c3 = x2 s0 = x0 s1 = x4 s2 = x1 s3 = x6 Cayley table: [x0 x1 x2 x3 x4 x5 x6] [x1 x2 x3 x4 x5 x6 x0] [x2 x3 x4 x5 x6 x0 x1] [x3 x4 x5 x6 x0 x1 x2] [x4 x5 x6 x0 x1 x2 x3] [x5 x6 x0 x1 x2 x3 x4] [x6 x0 x1 x2 x3 x4 x5] ... of Multiplicative Abelian Group isomorphic to C7 T1 = [ 0 1 -1 -1 -1] [ 2 0 -1 -1 -1] [ 3 2 -1 -1 -1] [ 4 3 -1 -1 -1] [ 1 4 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x4 r2 = x3 r3 = x2 r4 = x1 c0 = x0 c4 = x2 s0 = x0 s1 = x1 s2 = x4 s3 = x3 s4 = x2 Cayley table: [x0 x1 x2 x3 x4] [x1 x2 x3 x4 x0] [x2 x3 x4 x0 x1] [x3 x4 x0 x1 x2] [x4 x0 x1 x2 x3] ... of Multiplicative Abelian Group isomorphic to C5 T1 = [ 0 1 -1 -1 -1] [ 2 0 -1 -1 -1] [ 3 2 4 -1 -1] [ 1 4 3 -1 -1] [-1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x5 r2 = x3 r3 = x2 c0 = x0 c4 = x2 c4 = x2 s0 = x0 s1 = x2 s2 = x5 s3 = x3 s4 = x4 Cayley table: [x0 x1 x2 x3 x4 x5 x6] [x1 x2 x3 x4 x5 x6 x0] [x2 x3 x4 x5 x6 x0 x1] [x3 x4 x5 x6 x0 x1 x2] [x4 x5 x6 x0 x1 x2 x3] [x5 x6 x0 x1 x2 x3 x4] [x6 x0 x1 x2 x3 x4 x5] ... of Multiplicative Abelian Group isomorphic to C7 T1 = [ 0 1 2 -1] [ 3 -1 0 -1] [ 1 -1 -1 3] [-1 2 3 1] row, column, symbol relabelling: r0 = x0 r1 = x5 r2 = x2 r3 = x7 c0 = x0 c3 = x3 c3 = x3 c3 = x3 s0 = x0 s1 = x2 s2 = x6 s3 = x5 Cayley table: [x0 x1 x2 x3 x4 x5 x6 x7 x8] [x1 x2 x0 x4 x5 x3 x7 x8 x6] [x2 x0 x1 x5 x3 x4 x8 x6 x7] [x3 x4 x5 x6 x7 x8 x1 x2 x0] [x4 x5 x3 x7 x8 x6 x2 x0 x1] [x5 x3 x4 x8 x6 x7 x0 x1 x2] [x6 x7 x8 x1 x2 x0 x4 x5 x3] [x7 x8 x6 x2 x0 x1 x5 x3 x4] [x8 x6 x7 x0 x1 x2 x3 x4 x5] ... of Multiplicative Abelian Group isomorphic to C9 T1 = [ 0 1 2 -1 -1] [ 3 -1 0 4 -1] [ 1 2 4 3 -1] [-1 -1 -1 -1 -1] [-1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x3 r2 = x5 c0 = x0 c4 = x6 c4 = x6 c4 = x6 s0 = x0 s1 = x5 s2 = x2 s3 = x3 s4 = x7 Cayley table: [x0 x1 x2 x3 x4 x5 x6 x7] [x1 x0 x3 x2 x5 x4 x7 x6] [x2 x3 x1 x0 x6 x7 x5 x4] [x3 x2 x0 x1 x7 x6 x4 x5] [x4 x5 x6 x7 x2 x3 x1 x0] [x5 x4 x7 x6 x3 x2 x0 x1] [x6 x7 x5 x4 x1 x0 x3 x2] [x7 x6 x4 x5 x0 x1 x2 x3] ... of Multiplicative Abelian Group isomorphic to C8 T1 = [ 0 1 2 -1] [-1 -1 0 3] [ 3 -1 -1 0] [ 1 2 3 -1] row, column, symbol relabelling: r0 = x0 r1 = x3 r2 = x7 r3 = x5 c0 = x0 c3 = x4 c3 = x4 c3 = x4 s0 = x0 s1 = x5 s2 = x2 s3 = x7 Cayley table: [x0 x1 x2 x3 x4 x5 x6 x7] [x1 x0 x3 x2 x5 x4 x7 x6] [x2 x3 x1 x0 x6 x7 x5 x4] [x3 x2 x0 x1 x7 x6 x4 x5] [x4 x5 x6 x7 x2 x3 x1 x0] [x5 x4 x7 x6 x3 x2 x0 x1] [x6 x7 x5 x4 x1 x0 x3 x2] [x7 x6 x4 x5 x0 x1 x2 x3] ... of Multiplicative Abelian Group isomorphic to C8 T1 = [ 0 1 2 3] [ 1 -1 -1 0] [-1 -1 3 1] [-1 2 1 -1] row, column, symbol relabelling: r0 = x0 r1 = x7 r2 = x3 r3 = x1 c0 = x0 c3 = x4 c3 = x4 c3 = x4 s0 = x0 s1 = x7 s2 = x6 s3 = x4 Cayley table: [x0 x1 x2 x3 x4 x5 x6 x7] [x1 x0 x3 x2 x5 x4 x7 x6] [x2 x3 x1 x0 x6 x7 x5 x4] [x3 x2 x0 x1 x7 x6 x4 x5] [x4 x5 x6 x7 x2 x3 x1 x0] [x5 x4 x7 x6 x3 x2 x0 x1] [x6 x7 x5 x4 x1 x0 x3 x2] [x7 x6 x4 x5 x0 x1 x2 x3] ... of Multiplicative Abelian Group isomorphic to C8 T1 = [ 0 1 2 3] [ 1 -1 -1 0] [-1 3 -1 1] [-1 2 3 -1] row, column, symbol relabelling: r0 = x0 r1 = x6 r2 = x2 r3 = x7 c0 = x0 c3 = x4 c3 = x4 c3 = x4 s0 = x0 s1 = x6 s2 = x3 s3 = x4 Cayley table: [x0 x1 x2 x3 x4 x5 x6 x7] [x1 x0 x3 x2 x5 x4 x7 x6] [x2 x3 x0 x1 x6 x7 x4 x5] [x3 x2 x1 x0 x7 x6 x5 x4] [x4 x5 x6 x7 x2 x3 x0 x1] [x5 x4 x7 x6 x3 x2 x1 x0] [x6 x7 x4 x5 x0 x1 x2 x3] [x7 x6 x5 x4 x1 x0 x3 x2] ... of Multiplicative Abelian Group isomorphic to C4 x C2 T1 = [ 0 1 2 -1] [ 1 -1 0 3] [ 3 -1 -1 0] [-1 2 1 -1] row, column, symbol relabelling: r0 = x0 r1 = x3 r2 = x7 r3 = x1 c0 = x0 c3 = x4 c3 = x4 c3 = x4 s0 = x0 s1 = x3 s2 = x2 s3 = x7 Cayley table: [x0 x1 x2 x3 x4 x5 x6 x7] [x1 x0 x3 x2 x5 x4 x7 x6] [x2 x3 x1 x0 x6 x7 x5 x4] [x3 x2 x0 x1 x7 x6 x4 x5] [x4 x5 x6 x7 x2 x3 x1 x0] [x5 x4 x7 x6 x3 x2 x0 x1] [x6 x7 x5 x4 x1 x0 x3 x2] [x7 x6 x4 x5 x0 x1 x2 x3] ... of Multiplicative Abelian Group isomorphic to C8 T1 = [ 0 1 2 3 4 5] [ 1 -1 -1 -1 -1 0] [-1 2 3 4 5 1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x9 r2 = x4 c0 = x0 c5 = x5 c5 = x5 c5 = x5 c5 = x5 c5 = x5 s0 = x0 s1 = x9 s2 = x8 s3 = x7 s4 = x6 s5 = x5 Cayley table: [x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] [x1 x2 x3 x4 x0 x6 x7 x8 x9 x5] [x2 x3 x4 x0 x1 x7 x8 x9 x5 x6] [x3 x4 x0 x1 x2 x8 x9 x5 x6 x7] [x4 x0 x1 x2 x3 x9 x5 x6 x7 x8] [x5 x6 x7 x8 x9 x1 x2 x3 x4 x0] [x6 x7 x8 x9 x5 x2 x3 x4 x0 x1] [x7 x8 x9 x5 x6 x3 x4 x0 x1 x2] [x8 x9 x5 x6 x7 x4 x0 x1 x2 x3] [x9 x5 x6 x7 x8 x0 x1 x2 x3 x4] ... of Multiplicative Abelian Group isomorphic to C10 T1 = [ 0 1 2 3 4 -1] [ 5 -1 -1 -1 0 -1] [ 2 -1 3 4 5 -1] [ 1 2 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x6 r2 = x5 r3 = x9 c0 = x0 c5 = x11 c5 = x11 c5 = x11 c5 = x11 s0 = x0 s1 = x9 s2 = x5 s3 = x3 s4 = x1 s5 = x6 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [ x1 x2 x3 x4 x5 x6 x0 x8 x9 x10 x11 x12 x13 x7] [ x2 x3 x4 x5 x6 x0 x1 x9 x10 x11 x12 x13 x7 x8] [ x3 x4 x5 x6 x0 x1 x2 x10 x11 x12 x13 x7 x8 x9] [ x4 x5 x6 x0 x1 x2 x3 x11 x12 x13 x7 x8 x9 x10] [ x5 x6 x0 x1 x2 x3 x4 x12 x13 x7 x8 x9 x10 x11] [ x6 x0 x1 x2 x3 x4 x5 x13 x7 x8 x9 x10 x11 x12] [ x7 x8 x9 x10 x11 x12 x13 x1 x2 x3 x4 x5 x6 x0] [ x8 x9 x10 x11 x12 x13 x7 x2 x3 x4 x5 x6 x0 x1] [ x9 x10 x11 x12 x13 x7 x8 x3 x4 x5 x6 x0 x1 x2] [x10 x11 x12 x13 x7 x8 x9 x4 x5 x6 x0 x1 x2 x3] [x11 x12 x13 x7 x8 x9 x10 x5 x6 x0 x1 x2 x3 x4] [x12 x13 x7 x8 x9 x10 x11 x6 x0 x1 x2 x3 x4 x5] [x13 x7 x8 x9 x10 x11 x12 x0 x1 x2 x3 x4 x5 x6] ... of Multiplicative Abelian Group isomorphic to C14 T1 = [ 0 1 2 3 4 -1] [-1 -1 -1 -1 0 4] [ 2 -1 3 4 -1 0] [ 1 2 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x6 r2 = x5 r3 = x9 c0 = x0 c5 = x2 c5 = x2 c5 = x2 c5 = x2 c5 = x2 s0 = x0 s1 = x9 s2 = x5 s3 = x3 s4 = x1 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [ x1 x2 x3 x4 x5 x6 x0 x8 x9 x10 x11 x12 x13 x7] [ x2 x3 x4 x5 x6 x0 x1 x9 x10 x11 x12 x13 x7 x8] [ x3 x4 x5 x6 x0 x1 x2 x10 x11 x12 x13 x7 x8 x9] [ x4 x5 x6 x0 x1 x2 x3 x11 x12 x13 x7 x8 x9 x10] [ x5 x6 x0 x1 x2 x3 x4 x12 x13 x7 x8 x9 x10 x11] [ x6 x0 x1 x2 x3 x4 x5 x13 x7 x8 x9 x10 x11 x12] [ x7 x8 x9 x10 x11 x12 x13 x1 x2 x3 x4 x5 x6 x0] [ x8 x9 x10 x11 x12 x13 x7 x2 x3 x4 x5 x6 x0 x1] [ x9 x10 x11 x12 x13 x7 x8 x3 x4 x5 x6 x0 x1 x2] [x10 x11 x12 x13 x7 x8 x9 x4 x5 x6 x0 x1 x2 x3] [x11 x12 x13 x7 x8 x9 x10 x5 x6 x0 x1 x2 x3 x4] [x12 x13 x7 x8 x9 x10 x11 x6 x0 x1 x2 x3 x4 x5] [x13 x7 x8 x9 x10 x11 x12 x0 x1 x2 x3 x4 x5 x6] ... of Multiplicative Abelian Group isomorphic to C14 T1 = [ 0 1 2 3 4 -1] [ 2 -1 3 5 0 -1] [ 1 2 -1 -1 -1 -1] [-1 -1 -1 4 5 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x5 r2 = x9 r3 = x6 c0 = x0 c5 = x11 c5 = x11 c5 = x11 c5 = x11 s0 = x0 s1 = x9 s2 = x5 s3 = x3 s4 = x2 s5 = x1 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [ x1 x2 x3 x4 x5 x6 x0 x8 x9 x10 x11 x12 x13 x7] [ x2 x3 x4 x5 x6 x0 x1 x9 x10 x11 x12 x13 x7 x8] [ x3 x4 x5 x6 x0 x1 x2 x10 x11 x12 x13 x7 x8 x9] [ x4 x5 x6 x0 x1 x2 x3 x11 x12 x13 x7 x8 x9 x10] [ x5 x6 x0 x1 x2 x3 x4 x12 x13 x7 x8 x9 x10 x11] [ x6 x0 x1 x2 x3 x4 x5 x13 x7 x8 x9 x10 x11 x12] [ x7 x8 x9 x10 x11 x12 x13 x1 x2 x3 x4 x5 x6 x0] [ x8 x9 x10 x11 x12 x13 x7 x2 x3 x4 x5 x6 x0 x1] [ x9 x10 x11 x12 x13 x7 x8 x3 x4 x5 x6 x0 x1 x2] [x10 x11 x12 x13 x7 x8 x9 x4 x5 x6 x0 x1 x2 x3] [x11 x12 x13 x7 x8 x9 x10 x5 x6 x0 x1 x2 x3 x4] [x12 x13 x7 x8 x9 x10 x11 x6 x0 x1 x2 x3 x4 x5] [x13 x7 x8 x9 x10 x11 x12 x0 x1 x2 x3 x4 x5 x6] ... of Multiplicative Abelian Group isomorphic to C14 T1 = [ 0 1 2 3 4 -1] [ 5 -1 3 4 0 -1] [-1 2 5 -1 -1 -1] [ 1 5 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x14 r2 = x13 r3 = x7 c0 = x0 c5 = x12 c5 = x12 c5 = x12 c5 = x12 s0 = x0 s1 = x7 s2 = x1 s3 = x10 s4 = x5 s5 = x14 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [ x1 x2 x3 x4 x0 x6 x7 x8 x9 x5 x11 x12 x13 x14 x10] [ x2 x3 x4 x0 x1 x7 x8 x9 x5 x6 x12 x13 x14 x10 x11] [ x3 x4 x0 x1 x2 x8 x9 x5 x6 x7 x13 x14 x10 x11 x12] [ x4 x0 x1 x2 x3 x9 x5 x6 x7 x8 x14 x10 x11 x12 x13] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x1 x2 x3 x4 x0] [ x6 x7 x8 x9 x5 x11 x12 x13 x14 x10 x2 x3 x4 x0 x1] [ x7 x8 x9 x5 x6 x12 x13 x14 x10 x11 x3 x4 x0 x1 x2] [ x8 x9 x5 x6 x7 x13 x14 x10 x11 x12 x4 x0 x1 x2 x3] [ x9 x5 x6 x7 x8 x14 x10 x11 x12 x13 x0 x1 x2 x3 x4] [x10 x11 x12 x13 x14 x1 x2 x3 x4 x0 x6 x7 x8 x9 x5] [x11 x12 x13 x14 x10 x2 x3 x4 x0 x1 x7 x8 x9 x5 x6] [x12 x13 x14 x10 x11 x3 x4 x0 x1 x2 x8 x9 x5 x6 x7] [x13 x14 x10 x11 x12 x4 x0 x1 x2 x3 x9 x5 x6 x7 x8] [x14 x10 x11 x12 x13 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] ... of Multiplicative Abelian Group isomorphic to C15 T1 = [ 0 1 2 3 4 -1] [ 2 -1 3 4 0 -1] [ 1 -1 -1 -1 -1 2] [-1 2 -1 -1 -1 1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x8 r2 = x5 r3 = x11 c0 = x0 c5 = x11 c5 = x11 c5 = x11 c5 = x11 c5 = x11 s0 = x0 s1 = x5 s2 = x8 s3 = x4 s4 = x9 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] [ x1 x2 x0 x4 x5 x3 x7 x8 x6 x10 x11 x9] [ x2 x0 x1 x5 x3 x4 x8 x6 x7 x11 x9 x10] [ x3 x4 x5 x1 x2 x0 x9 x10 x11 x7 x8 x6] [ x4 x5 x3 x2 x0 x1 x10 x11 x9 x8 x6 x7] [ x5 x3 x4 x0 x1 x2 x11 x9 x10 x6 x7 x8] [ x6 x7 x8 x9 x10 x11 x3 x4 x5 x1 x2 x0] [ x7 x8 x6 x10 x11 x9 x4 x5 x3 x2 x0 x1] [ x8 x6 x7 x11 x9 x10 x5 x3 x4 x0 x1 x2] [ x9 x10 x11 x7 x8 x6 x1 x2 x0 x4 x5 x3] [x10 x11 x9 x8 x6 x7 x2 x0 x1 x5 x3 x4] [x11 x9 x10 x6 x7 x8 x0 x1 x2 x3 x4 x5] ... of Multiplicative Abelian Group isomorphic to C12 T1 = [ 0 1 2 3 4 5] [ 4 -1 -1 -1 5 0] [ 1 2 3 4 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x1 r2 = x6 c0 = x0 c5 = x2 c5 = x2 c5 = x2 c5 = x2 c5 = x2 s0 = x0 s1 = x6 s2 = x3 s3 = x9 s4 = x1 s5 = x2 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] [ x1 x2 x0 x4 x5 x3 x7 x8 x6 x10 x11 x9] [ x2 x0 x1 x5 x3 x4 x8 x6 x7 x11 x9 x10] [ x3 x4 x5 x1 x2 x0 x9 x10 x11 x7 x8 x6] [ x4 x5 x3 x2 x0 x1 x10 x11 x9 x8 x6 x7] [ x5 x3 x4 x0 x1 x2 x11 x9 x10 x6 x7 x8] [ x6 x7 x8 x9 x10 x11 x3 x4 x5 x1 x2 x0] [ x7 x8 x6 x10 x11 x9 x4 x5 x3 x2 x0 x1] [ x8 x6 x7 x11 x9 x10 x5 x3 x4 x0 x1 x2] [ x9 x10 x11 x7 x8 x6 x1 x2 x0 x4 x5 x3] [x10 x11 x9 x8 x6 x7 x2 x0 x1 x5 x3 x4] [x11 x9 x10 x6 x7 x8 x0 x1 x2 x3 x4 x5] ... of Multiplicative Abelian Group isomorphic to C12 T1 = [ 0 1 2 3 4 -1] [ 3 -1 -1 4 0 -1] [ 5 2 3 -1 -1 -1] [ 1 5 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x11 r2 = x10 r3 = x5 c0 = x0 c5 = x14 c5 = x14 c5 = x14 c5 = x14 s0 = x0 s1 = x5 s2 = x1 s3 = x11 s4 = x8 s5 = x10 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [ x1 x2 x3 x4 x0 x6 x7 x8 x9 x5 x11 x12 x13 x14 x10] [ x2 x3 x4 x0 x1 x7 x8 x9 x5 x6 x12 x13 x14 x10 x11] [ x3 x4 x0 x1 x2 x8 x9 x5 x6 x7 x13 x14 x10 x11 x12] [ x4 x0 x1 x2 x3 x9 x5 x6 x7 x8 x14 x10 x11 x12 x13] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x1 x2 x3 x4 x0] [ x6 x7 x8 x9 x5 x11 x12 x13 x14 x10 x2 x3 x4 x0 x1] [ x7 x8 x9 x5 x6 x12 x13 x14 x10 x11 x3 x4 x0 x1 x2] [ x8 x9 x5 x6 x7 x13 x14 x10 x11 x12 x4 x0 x1 x2 x3] [ x9 x5 x6 x7 x8 x14 x10 x11 x12 x13 x0 x1 x2 x3 x4] [x10 x11 x12 x13 x14 x1 x2 x3 x4 x0 x6 x7 x8 x9 x5] [x11 x12 x13 x14 x10 x2 x3 x4 x0 x1 x7 x8 x9 x5 x6] [x12 x13 x14 x10 x11 x3 x4 x0 x1 x2 x8 x9 x5 x6 x7] [x13 x14 x10 x11 x12 x4 x0 x1 x2 x3 x9 x5 x6 x7 x8] [x14 x10 x11 x12 x13 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] ... of Multiplicative Abelian Group isomorphic to C15 T1 = [ 0 1 2 3 4 -1] [-1 -1 -1 4 0 3] [-1 2 3 -1 -1 1] [ 1 -1 -1 -1 -1 0] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x16 r2 = x11 r3 = x14 c0 = x0 c5 = x3 c5 = x3 c5 = x3 c5 = x3 c5 = x3 s0 = x0 s1 = x14 s2 = x8 s3 = x2 s4 = x1 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16] [ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0] [ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1] [ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2] [ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4] [ x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5] [ x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6] [ x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7] [ x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8] [x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] [x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10] [x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] [x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12] [x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] ... of Multiplicative Abelian Group isomorphic to C17 T1 = [ 0 1 2 3 4 -1] [-1 -1 -1 -1 0 4] [ 3 -1 -1 4 -1 0] [ 1 2 3 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x4 r2 = x3 r3 = x9 c0 = x0 c5 = x2 c5 = x2 c5 = x2 c5 = x2 c5 = x2 s0 = x0 s1 = x9 s2 = x13 s3 = x3 s4 = x1 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [ x1 x2 x3 x4 x0 x6 x7 x8 x9 x5 x11 x12 x13 x14 x10] [ x2 x3 x4 x0 x1 x7 x8 x9 x5 x6 x12 x13 x14 x10 x11] [ x3 x4 x0 x1 x2 x8 x9 x5 x6 x7 x13 x14 x10 x11 x12] [ x4 x0 x1 x2 x3 x9 x5 x6 x7 x8 x14 x10 x11 x12 x13] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x1 x2 x3 x4 x0] [ x6 x7 x8 x9 x5 x11 x12 x13 x14 x10 x2 x3 x4 x0 x1] [ x7 x8 x9 x5 x6 x12 x13 x14 x10 x11 x3 x4 x0 x1 x2] [ x8 x9 x5 x6 x7 x13 x14 x10 x11 x12 x4 x0 x1 x2 x3] [ x9 x5 x6 x7 x8 x14 x10 x11 x12 x13 x0 x1 x2 x3 x4] [x10 x11 x12 x13 x14 x1 x2 x3 x4 x0 x6 x7 x8 x9 x5] [x11 x12 x13 x14 x10 x2 x3 x4 x0 x1 x7 x8 x9 x5 x6] [x12 x13 x14 x10 x11 x3 x4 x0 x1 x2 x8 x9 x5 x6 x7] [x13 x14 x10 x11 x12 x4 x0 x1 x2 x3 x9 x5 x6 x7 x8] [x14 x10 x11 x12 x13 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] ... of Multiplicative Abelian Group isomorphic to C15 T1 = [ 0 1 2 3 -1] [-1 -1 -1 0 4] [-1 -1 3 4 2] [-1 2 -1 -1 1] [ 1 -1 -1 -1 0] row, column, symbol relabelling: r0 = x0 r1 = x16 r2 = x18 r3 = x9 r4 = x14 c0 = x0 c4 = x5 c4 = x5 c4 = x5 c4 = x5 s0 = x0 s1 = x14 s2 = x4 s3 = x3 s4 = x2 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18] [ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0] [ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1] [ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2] [ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4] [ x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5] [ x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6] [ x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7] [ x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8] [x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] [x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10] [x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] [x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12] [x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16] [x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17] ... of Multiplicative Abelian Group isomorphic to C19 T1 = [ 0 1 2 3 -1 -1] [ 4 -1 -1 0 -1 -1] [ 5 -1 -1 4 -1 -1] [ 2 -1 3 5 -1 -1] [ 1 2 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x6 r2 = x5 r3 = x4 r4 = x12 c0 = x0 c5 = x3 c5 = x3 c5 = x3 s0 = x0 s1 = x12 s2 = x4 s3 = x1 s4 = x6 s5 = x5 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [ x1 x2 x3 x4 x5 x6 x0 x8 x9 x10 x11 x12 x13 x7] [ x2 x3 x4 x5 x6 x0 x1 x9 x10 x11 x12 x13 x7 x8] [ x3 x4 x5 x6 x0 x1 x2 x10 x11 x12 x13 x7 x8 x9] [ x4 x5 x6 x0 x1 x2 x3 x11 x12 x13 x7 x8 x9 x10] [ x5 x6 x0 x1 x2 x3 x4 x12 x13 x7 x8 x9 x10 x11] [ x6 x0 x1 x2 x3 x4 x5 x13 x7 x8 x9 x10 x11 x12] [ x7 x8 x9 x10 x11 x12 x13 x1 x2 x3 x4 x5 x6 x0] [ x8 x9 x10 x11 x12 x13 x7 x2 x3 x4 x5 x6 x0 x1] [ x9 x10 x11 x12 x13 x7 x8 x3 x4 x5 x6 x0 x1 x2] [x10 x11 x12 x13 x7 x8 x9 x4 x5 x6 x0 x1 x2 x3] [x11 x12 x13 x7 x8 x9 x10 x5 x6 x0 x1 x2 x3 x4] [x12 x13 x7 x8 x9 x10 x11 x6 x0 x1 x2 x3 x4 x5] [x13 x7 x8 x9 x10 x11 x12 x0 x1 x2 x3 x4 x5 x6] ... of Multiplicative Abelian Group isomorphic to C14 T1 = [ 0 1 2 3 -1] [-1 -1 -1 0 3] [ 2 -1 3 -1 4] [ 1 2 -1 -1 -1] [ 4 -1 -1 -1 0] row, column, symbol relabelling: r0 = x0 r1 = x8 r2 = x7 r3 = x15 r4 = x5 c0 = x0 c4 = x6 c4 = x6 c4 = x6 c4 = x6 s0 = x0 s1 = x15 s2 = x7 s3 = x3 s4 = x5 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17] [ x1 x2 x0 x4 x5 x3 x7 x8 x6 x10 x11 x9 x13 x14 x12 x16 x17 x15] [ x2 x0 x1 x5 x3 x4 x8 x6 x7 x11 x9 x10 x14 x12 x13 x17 x15 x16] [ x3 x4 x5 x6 x7 x8 x1 x2 x0 x12 x13 x14 x15 x16 x17 x10 x11 x9] [ x4 x5 x3 x7 x8 x6 x2 x0 x1 x13 x14 x12 x16 x17 x15 x11 x9 x10] [ x5 x3 x4 x8 x6 x7 x0 x1 x2 x14 x12 x13 x17 x15 x16 x9 x10 x11] [ x6 x7 x8 x1 x2 x0 x4 x5 x3 x15 x16 x17 x10 x11 x9 x13 x14 x12] [ x7 x8 x6 x2 x0 x1 x5 x3 x4 x16 x17 x15 x11 x9 x10 x14 x12 x13] [ x8 x6 x7 x0 x1 x2 x3 x4 x5 x17 x15 x16 x9 x10 x11 x12 x13 x14] [ x9 x10 x11 x12 x13 x14 x15 x16 x17 x3 x4 x5 x6 x7 x8 x1 x2 x0] [x10 x11 x9 x13 x14 x12 x16 x17 x15 x4 x5 x3 x7 x8 x6 x2 x0 x1] [x11 x9 x10 x14 x12 x13 x17 x15 x16 x5 x3 x4 x8 x6 x7 x0 x1 x2] [x12 x13 x14 x15 x16 x17 x10 x11 x9 x6 x7 x8 x1 x2 x0 x4 x5 x3] [x13 x14 x12 x16 x17 x15 x11 x9 x10 x7 x8 x6 x2 x0 x1 x5 x3 x4] [x14 x12 x13 x17 x15 x16 x9 x10 x11 x8 x6 x7 x0 x1 x2 x3 x4 x5] [x15 x16 x17 x10 x11 x9 x13 x14 x12 x1 x2 x0 x4 x5 x3 x7 x8 x6] [x16 x17 x15 x11 x9 x10 x14 x12 x13 x2 x0 x1 x5 x3 x4 x8 x6 x7] [x17 x15 x16 x9 x10 x11 x12 x13 x14 x0 x1 x2 x3 x4 x5 x6 x7 x8] ... of Multiplicative Abelian Group isomorphic to C18 T1 = [ 0 1 2 3 -1] [ 4 -1 -1 0 -1] [ 2 -1 -1 4 3] [ 1 2 -1 -1 -1] [-1 -1 3 -1 2] row, column, symbol relabelling: r0 = x0 r1 = x14 r2 = x6 r3 = x15 r4 = x12 c0 = x0 c4 = x12 c4 = x12 c4 = x12 c4 = x12 s0 = x0 s1 = x15 s2 = x6 s3 = x8 s4 = x14 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x0 x1 x6 x7 x4 x5 x10 x11 x8 x9 x14 x15 x12 x13] [ x3 x2 x1 x0 x7 x6 x5 x4 x11 x10 x9 x8 x15 x14 x13 x12] [ x4 x5 x6 x7 x2 x3 x0 x1 x12 x13 x14 x15 x10 x11 x8 x9] [ x5 x4 x7 x6 x3 x2 x1 x0 x13 x12 x15 x14 x11 x10 x9 x8] [ x6 x7 x4 x5 x0 x1 x2 x3 x14 x15 x12 x13 x8 x9 x10 x11] [ x7 x6 x5 x4 x1 x0 x3 x2 x15 x14 x13 x12 x9 x8 x11 x10] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x0 x1] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x1 x0] [x10 x11 x8 x9 x14 x15 x12 x13 x6 x7 x4 x5 x0 x1 x2 x3] [x11 x10 x9 x8 x15 x14 x13 x12 x7 x6 x5 x4 x1 x0 x3 x2] [x12 x13 x14 x15 x10 x11 x8 x9 x2 x3 x0 x1 x6 x7 x4 x5] [x13 x12 x15 x14 x11 x10 x9 x8 x3 x2 x1 x0 x7 x6 x5 x4] [x14 x15 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x15 x14 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] ... of Multiplicative Abelian Group isomorphic to C8 x C2 T1 = [ 0 1 2 3 -1] [ 4 -1 -1 0 -1] [ 2 -1 -1 -1 4] [ 1 2 -1 -1 -1] [-1 -1 3 4 2] row, column, symbol relabelling: r0 = x0 r1 = x5 r2 = x2 r3 = x14 r4 = x7 c0 = x0 c4 = x3 c4 = x3 c4 = x3 c4 = x3 s0 = x0 s1 = x14 s2 = x2 s3 = x6 s4 = x5 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17] [ x1 x2 x0 x4 x5 x3 x7 x8 x6 x10 x11 x9 x13 x14 x12 x16 x17 x15] [ x2 x0 x1 x5 x3 x4 x8 x6 x7 x11 x9 x10 x14 x12 x13 x17 x15 x16] [ x3 x4 x5 x6 x7 x8 x1 x2 x0 x12 x13 x14 x15 x16 x17 x10 x11 x9] [ x4 x5 x3 x7 x8 x6 x2 x0 x1 x13 x14 x12 x16 x17 x15 x11 x9 x10] [ x5 x3 x4 x8 x6 x7 x0 x1 x2 x14 x12 x13 x17 x15 x16 x9 x10 x11] [ x6 x7 x8 x1 x2 x0 x4 x5 x3 x15 x16 x17 x10 x11 x9 x13 x14 x12] [ x7 x8 x6 x2 x0 x1 x5 x3 x4 x16 x17 x15 x11 x9 x10 x14 x12 x13] [ x8 x6 x7 x0 x1 x2 x3 x4 x5 x17 x15 x16 x9 x10 x11 x12 x13 x14] [ x9 x10 x11 x12 x13 x14 x15 x16 x17 x3 x4 x5 x6 x7 x8 x1 x2 x0] [x10 x11 x9 x13 x14 x12 x16 x17 x15 x4 x5 x3 x7 x8 x6 x2 x0 x1] [x11 x9 x10 x14 x12 x13 x17 x15 x16 x5 x3 x4 x8 x6 x7 x0 x1 x2] [x12 x13 x14 x15 x16 x17 x10 x11 x9 x6 x7 x8 x1 x2 x0 x4 x5 x3] [x13 x14 x12 x16 x17 x15 x11 x9 x10 x7 x8 x6 x2 x0 x1 x5 x3 x4] [x14 x12 x13 x17 x15 x16 x9 x10 x11 x8 x6 x7 x0 x1 x2 x3 x4 x5] [x15 x16 x17 x10 x11 x9 x13 x14 x12 x1 x2 x0 x4 x5 x3 x7 x8 x6] [x16 x17 x15 x11 x9 x10 x14 x12 x13 x2 x0 x1 x5 x3 x4 x8 x6 x7] [x17 x15 x16 x9 x10 x11 x12 x13 x14 x0 x1 x2 x3 x4 x5 x6 x7 x8] ... of Multiplicative Abelian Group isomorphic to C18 T1 = [ 0 1 2 3 -1 -1] [ 4 -1 -1 0 5 -1] [ 2 -1 3 5 4 -1] [ 1 2 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x3 r2 = x5 r3 = x11 c0 = x0 c5 = x12 c5 = x12 c5 = x12 c5 = x12 s0 = x0 s1 = x11 s2 = x5 s3 = x2 s4 = x3 s5 = x7 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 3 -1] [-1 -1 -1 0 4] [ 4 -1 -1 -1 0] [ 2 -1 3 4 -1] [ 1 2 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x3 r2 = x7 r3 = x5 r4 = x11 c0 = x0 c4 = x4 c4 = x4 c4 = x4 c4 = x4 s0 = x0 s1 = x11 s2 = x5 s3 = x2 s4 = x7 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 3 4 -1] [ 5 -1 -1 4 0 -1] [ 2 -1 3 5 -1 -1] [ 1 2 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x7 r2 = x5 r3 = x11 c0 = x0 c5 = x12 c5 = x12 c5 = x12 c5 = x12 s0 = x0 s1 = x11 s2 = x5 s3 = x2 s4 = x4 s5 = x7 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 3 -1] [-1 -1 -1 0 4] [-1 -1 3 4 1] [-1 2 1 -1 -1] [ 1 -1 -1 -1 0] row, column, symbol relabelling: r0 = x0 r1 = x14 r2 = x5 r3 = x13 r4 = x8 c0 = x0 c4 = x3 c4 = x3 c4 = x3 c4 = x3 s0 = x0 s1 = x8 s2 = x10 s3 = x12 s4 = x17 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17] [ x1 x2 x0 x4 x5 x3 x7 x8 x6 x10 x11 x9 x13 x14 x12 x16 x17 x15] [ x2 x0 x1 x5 x3 x4 x8 x6 x7 x11 x9 x10 x14 x12 x13 x17 x15 x16] [ x3 x4 x5 x6 x7 x8 x1 x2 x0 x12 x13 x14 x15 x16 x17 x10 x11 x9] [ x4 x5 x3 x7 x8 x6 x2 x0 x1 x13 x14 x12 x16 x17 x15 x11 x9 x10] [ x5 x3 x4 x8 x6 x7 x0 x1 x2 x14 x12 x13 x17 x15 x16 x9 x10 x11] [ x6 x7 x8 x1 x2 x0 x4 x5 x3 x15 x16 x17 x10 x11 x9 x13 x14 x12] [ x7 x8 x6 x2 x0 x1 x5 x3 x4 x16 x17 x15 x11 x9 x10 x14 x12 x13] [ x8 x6 x7 x0 x1 x2 x3 x4 x5 x17 x15 x16 x9 x10 x11 x12 x13 x14] [ x9 x10 x11 x12 x13 x14 x15 x16 x17 x3 x4 x5 x6 x7 x8 x1 x2 x0] [x10 x11 x9 x13 x14 x12 x16 x17 x15 x4 x5 x3 x7 x8 x6 x2 x0 x1] [x11 x9 x10 x14 x12 x13 x17 x15 x16 x5 x3 x4 x8 x6 x7 x0 x1 x2] [x12 x13 x14 x15 x16 x17 x10 x11 x9 x6 x7 x8 x1 x2 x0 x4 x5 x3] [x13 x14 x12 x16 x17 x15 x11 x9 x10 x7 x8 x6 x2 x0 x1 x5 x3 x4] [x14 x12 x13 x17 x15 x16 x9 x10 x11 x8 x6 x7 x0 x1 x2 x3 x4 x5] [x15 x16 x17 x10 x11 x9 x13 x14 x12 x1 x2 x0 x4 x5 x3 x7 x8 x6] [x16 x17 x15 x11 x9 x10 x14 x12 x13 x2 x0 x1 x5 x3 x4 x8 x6 x7] [x17 x15 x16 x9 x10 x11 x12 x13 x14 x0 x1 x2 x3 x4 x5 x6 x7 x8] ... of Multiplicative Abelian Group isomorphic to C18 T1 = [ 0 1 2 3 -1 -1] [ 4 -1 -1 0 -1 -1] [ 5 -1 -1 4 -1 -1] [ 1 -1 3 5 -1 -1] [-1 2 1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x13 r2 = x6 r3 = x12 r4 = x10 c0 = x0 c5 = x5 c5 = x5 c5 = x5 s0 = x0 s1 = x12 s2 = x2 s3 = x7 s4 = x13 s5 = x6 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [ x1 x2 x3 x4 x5 x6 x0 x8 x9 x10 x11 x12 x13 x7] [ x2 x3 x4 x5 x6 x0 x1 x9 x10 x11 x12 x13 x7 x8] [ x3 x4 x5 x6 x0 x1 x2 x10 x11 x12 x13 x7 x8 x9] [ x4 x5 x6 x0 x1 x2 x3 x11 x12 x13 x7 x8 x9 x10] [ x5 x6 x0 x1 x2 x3 x4 x12 x13 x7 x8 x9 x10 x11] [ x6 x0 x1 x2 x3 x4 x5 x13 x7 x8 x9 x10 x11 x12] [ x7 x8 x9 x10 x11 x12 x13 x1 x2 x3 x4 x5 x6 x0] [ x8 x9 x10 x11 x12 x13 x7 x2 x3 x4 x5 x6 x0 x1] [ x9 x10 x11 x12 x13 x7 x8 x3 x4 x5 x6 x0 x1 x2] [x10 x11 x12 x13 x7 x8 x9 x4 x5 x6 x0 x1 x2 x3] [x11 x12 x13 x7 x8 x9 x10 x5 x6 x0 x1 x2 x3 x4] [x12 x13 x7 x8 x9 x10 x11 x6 x0 x1 x2 x3 x4 x5] [x13 x7 x8 x9 x10 x11 x12 x0 x1 x2 x3 x4 x5 x6] ... of Multiplicative Abelian Group isomorphic to C14 T1 = [ 0 1 2 3 -1] [-1 -1 -1 0 3] [ 1 -1 3 -1 4] [-1 2 1 -1 -1] [ 4 -1 -1 -1 0] row, column, symbol relabelling: r0 = x0 r1 = x17 r2 = x5 r3 = x13 r4 = x8 c0 = x0 c4 = x3 c4 = x3 c4 = x3 c4 = x3 s0 = x0 s1 = x5 s2 = x15 s3 = x9 s4 = x8 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17] [ x1 x2 x0 x4 x5 x3 x7 x8 x6 x10 x11 x9 x13 x14 x12 x16 x17 x15] [ x2 x0 x1 x5 x3 x4 x8 x6 x7 x11 x9 x10 x14 x12 x13 x17 x15 x16] [ x3 x4 x5 x6 x7 x8 x1 x2 x0 x12 x13 x14 x15 x16 x17 x10 x11 x9] [ x4 x5 x3 x7 x8 x6 x2 x0 x1 x13 x14 x12 x16 x17 x15 x11 x9 x10] [ x5 x3 x4 x8 x6 x7 x0 x1 x2 x14 x12 x13 x17 x15 x16 x9 x10 x11] [ x6 x7 x8 x1 x2 x0 x4 x5 x3 x15 x16 x17 x10 x11 x9 x13 x14 x12] [ x7 x8 x6 x2 x0 x1 x5 x3 x4 x16 x17 x15 x11 x9 x10 x14 x12 x13] [ x8 x6 x7 x0 x1 x2 x3 x4 x5 x17 x15 x16 x9 x10 x11 x12 x13 x14] [ x9 x10 x11 x12 x13 x14 x15 x16 x17 x3 x4 x5 x6 x7 x8 x1 x2 x0] [x10 x11 x9 x13 x14 x12 x16 x17 x15 x4 x5 x3 x7 x8 x6 x2 x0 x1] [x11 x9 x10 x14 x12 x13 x17 x15 x16 x5 x3 x4 x8 x6 x7 x0 x1 x2] [x12 x13 x14 x15 x16 x17 x10 x11 x9 x6 x7 x8 x1 x2 x0 x4 x5 x3] [x13 x14 x12 x16 x17 x15 x11 x9 x10 x7 x8 x6 x2 x0 x1 x5 x3 x4] [x14 x12 x13 x17 x15 x16 x9 x10 x11 x8 x6 x7 x0 x1 x2 x3 x4 x5] [x15 x16 x17 x10 x11 x9 x13 x14 x12 x1 x2 x0 x4 x5 x3 x7 x8 x6] [x16 x17 x15 x11 x9 x10 x14 x12 x13 x2 x0 x1 x5 x3 x4 x8 x6 x7] [x17 x15 x16 x9 x10 x11 x12 x13 x14 x0 x1 x2 x3 x4 x5 x6 x7 x8] ... of Multiplicative Abelian Group isomorphic to C18 T1 = [ 0 1 2 3 -1 -1] [ 4 -1 -1 0 -1 -1] [ 1 -1 5 4 -1 -1] [-1 -1 3 5 -1 -1] [-1 2 1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x15 r2 = x6 r3 = x14 r4 = x3 c0 = x0 c5 = x7 c5 = x7 c5 = x7 s0 = x0 s1 = x6 s2 = x5 s3 = x9 s4 = x15 s5 = x1 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x0 x1 x6 x7 x4 x5 x10 x11 x8 x9 x14 x15 x12 x13] [ x3 x2 x1 x0 x7 x6 x5 x4 x11 x10 x9 x8 x15 x14 x13 x12] [ x4 x5 x6 x7 x2 x3 x0 x1 x12 x13 x14 x15 x10 x11 x8 x9] [ x5 x4 x7 x6 x3 x2 x1 x0 x13 x12 x15 x14 x11 x10 x9 x8] [ x6 x7 x4 x5 x0 x1 x2 x3 x14 x15 x12 x13 x8 x9 x10 x11] [ x7 x6 x5 x4 x1 x0 x3 x2 x15 x14 x13 x12 x9 x8 x11 x10] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x0 x1] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x1 x0] [x10 x11 x8 x9 x14 x15 x12 x13 x6 x7 x4 x5 x0 x1 x2 x3] [x11 x10 x9 x8 x15 x14 x13 x12 x7 x6 x5 x4 x1 x0 x3 x2] [x12 x13 x14 x15 x10 x11 x8 x9 x2 x3 x0 x1 x6 x7 x4 x5] [x13 x12 x15 x14 x11 x10 x9 x8 x3 x2 x1 x0 x7 x6 x5 x4] [x14 x15 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x15 x14 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] ... of Multiplicative Abelian Group isomorphic to C8 x C2 T1 = [ 0 1 2 3 -1 -1] [ 4 -1 -1 0 -1 -1] [ 1 -1 3 4 -1 -1] [-1 5 1 -1 -1 -1] [-1 2 5 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x9 r2 = x13 r3 = x11 r4 = x8 c0 = x0 c5 = x3 c5 = x3 c5 = x3 s0 = x0 s1 = x13 s2 = x2 s3 = x10 s4 = x9 s5 = x5 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [ x1 x2 x3 x4 x0 x6 x7 x8 x9 x5 x11 x12 x13 x14 x10] [ x2 x3 x4 x0 x1 x7 x8 x9 x5 x6 x12 x13 x14 x10 x11] [ x3 x4 x0 x1 x2 x8 x9 x5 x6 x7 x13 x14 x10 x11 x12] [ x4 x0 x1 x2 x3 x9 x5 x6 x7 x8 x14 x10 x11 x12 x13] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x1 x2 x3 x4 x0] [ x6 x7 x8 x9 x5 x11 x12 x13 x14 x10 x2 x3 x4 x0 x1] [ x7 x8 x9 x5 x6 x12 x13 x14 x10 x11 x3 x4 x0 x1 x2] [ x8 x9 x5 x6 x7 x13 x14 x10 x11 x12 x4 x0 x1 x2 x3] [ x9 x5 x6 x7 x8 x14 x10 x11 x12 x13 x0 x1 x2 x3 x4] [x10 x11 x12 x13 x14 x1 x2 x3 x4 x0 x6 x7 x8 x9 x5] [x11 x12 x13 x14 x10 x2 x3 x4 x0 x1 x7 x8 x9 x5 x6] [x12 x13 x14 x10 x11 x3 x4 x0 x1 x2 x8 x9 x5 x6 x7] [x13 x14 x10 x11 x12 x4 x0 x1 x2 x3 x9 x5 x6 x7 x8] [x14 x10 x11 x12 x13 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] ... of Multiplicative Abelian Group isomorphic to C15 T1 = [ 0 1 2 3 -1] [ 4 -1 -1 0 -1] [ 1 -1 3 4 -1] [-1 -1 1 -1 2] [-1 2 -1 -1 1] row, column, symbol relabelling: r0 = x0 r1 = x14 r2 = x9 r3 = x8 r4 = x11 c0 = x0 c4 = x12 c4 = x12 c4 = x12 c4 = x12 s0 = x0 s1 = x9 s2 = x1 s3 = x5 s4 = x14 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [ x1 x2 x3 x4 x0 x6 x7 x8 x9 x5 x11 x12 x13 x14 x10] [ x2 x3 x4 x0 x1 x7 x8 x9 x5 x6 x12 x13 x14 x10 x11] [ x3 x4 x0 x1 x2 x8 x9 x5 x6 x7 x13 x14 x10 x11 x12] [ x4 x0 x1 x2 x3 x9 x5 x6 x7 x8 x14 x10 x11 x12 x13] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x1 x2 x3 x4 x0] [ x6 x7 x8 x9 x5 x11 x12 x13 x14 x10 x2 x3 x4 x0 x1] [ x7 x8 x9 x5 x6 x12 x13 x14 x10 x11 x3 x4 x0 x1 x2] [ x8 x9 x5 x6 x7 x13 x14 x10 x11 x12 x4 x0 x1 x2 x3] [ x9 x5 x6 x7 x8 x14 x10 x11 x12 x13 x0 x1 x2 x3 x4] [x10 x11 x12 x13 x14 x1 x2 x3 x4 x0 x6 x7 x8 x9 x5] [x11 x12 x13 x14 x10 x2 x3 x4 x0 x1 x7 x8 x9 x5 x6] [x12 x13 x14 x10 x11 x3 x4 x0 x1 x2 x8 x9 x5 x6 x7] [x13 x14 x10 x11 x12 x4 x0 x1 x2 x3 x9 x5 x6 x7 x8] [x14 x10 x11 x12 x13 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] ... of Multiplicative Abelian Group isomorphic to C15 T1 = [ 0 1 2 3 -1 -1] [ 4 -1 -1 0 5 -1] [ 1 -1 3 5 4 -1] [-1 2 1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x7 r2 = x11 r3 = x1 c0 = x0 c5 = x12 c5 = x12 c5 = x12 c5 = x12 s0 = x0 s1 = x11 s2 = x10 s3 = x4 s4 = x7 s5 = x15 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 3 4 -1] [ 5 -1 -1 4 0 -1] [ 1 -1 3 5 -1 -1] [-1 2 1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x15 r2 = x11 r3 = x1 c0 = x0 c5 = x12 c5 = x12 c5 = x12 c5 = x12 s0 = x0 s1 = x11 s2 = x10 s3 = x4 s4 = x8 s5 = x15 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 3 -1] [ 4 2 -1 0 -1] [ 1 -1 -1 -1 4] [-1 4 -1 -1 1] [-1 -1 3 2 -1] row, column, symbol relabelling: r0 = x0 r1 = x12 r2 = x4 r3 = x8 r4 = x1 c0 = x0 c4 = x8 c4 = x8 c4 = x8 c4 = x8 s0 = x0 s1 = x4 s2 = x10 s3 = x11 s4 = x12 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 -1 -1] [ 1 -1 0 4 3] [ 3 -1 -1 0 -1] [-1 -1 -1 3 4] [-1 2 1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x7 r2 = x15 r3 = x6 r4 = x2 c0 = x0 c4 = x8 c4 = x8 c4 = x8 c4 = x8 s0 = x0 s1 = x7 s2 = x5 s3 = x15 s4 = x14 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x0 x1 x6 x7 x4 x5 x10 x11 x8 x9 x14 x15 x12 x13] [ x3 x2 x1 x0 x7 x6 x5 x4 x11 x10 x9 x8 x15 x14 x13 x12] [ x4 x5 x6 x7 x2 x3 x0 x1 x12 x13 x14 x15 x10 x11 x8 x9] [ x5 x4 x7 x6 x3 x2 x1 x0 x13 x12 x15 x14 x11 x10 x9 x8] [ x6 x7 x4 x5 x0 x1 x2 x3 x14 x15 x12 x13 x8 x9 x10 x11] [ x7 x6 x5 x4 x1 x0 x3 x2 x15 x14 x13 x12 x9 x8 x11 x10] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x0 x1] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x1 x0] [x10 x11 x8 x9 x14 x15 x12 x13 x6 x7 x4 x5 x0 x1 x2 x3] [x11 x10 x9 x8 x15 x14 x13 x12 x7 x6 x5 x4 x1 x0 x3 x2] [x12 x13 x14 x15 x10 x11 x8 x9 x2 x3 x0 x1 x6 x7 x4 x5] [x13 x12 x15 x14 x11 x10 x9 x8 x3 x2 x1 x0 x7 x6 x5 x4] [x14 x15 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x15 x14 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] ... of Multiplicative Abelian Group isomorphic to C8 x C2 T1 = [ 0 1 2 3 4] [-1 -1 -1 4 0] [ 3 -1 -1 0 -1] [ 1 -1 3 -1 -1] [-1 2 1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x3 r2 = x1 r3 = x15 r4 = x4 c0 = x0 c4 = x2 c4 = x2 c4 = x2 c4 = x2 s0 = x0 s1 = x15 s2 = x11 s3 = x1 s4 = x2 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x0 x1 x2 x3 x12 x13 x14 x15 x8 x9 x10 x11] [ x5 x4 x7 x6 x1 x0 x3 x2 x13 x12 x15 x14 x9 x8 x11 x10] [ x6 x7 x5 x4 x2 x3 x1 x0 x14 x15 x13 x12 x10 x11 x9 x8] [ x7 x6 x4 x5 x3 x2 x0 x1 x15 x14 x12 x13 x11 x10 x8 x9] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x0 x1 x2 x3] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x1 x0 x3 x2] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x2 x3 x1 x0] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x3 x2 x0 x1] [x12 x13 x14 x15 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x13 x12 x15 x14 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x14 x15 x13 x12 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x15 x14 x12 x13 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] ... of Multiplicative Abelian Group isomorphic to C4 x C4 T1 = [ 0 1 2 3 -1 -1] [ 1 4 -1 0 -1 -1] [-1 -1 3 4 -1 -1] [-1 5 4 -1 -1 -1] [-1 2 5 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x11 r2 = x14 r3 = x7 r4 = x15 c0 = x0 c5 = x2 c5 = x2 c5 = x2 s0 = x0 s1 = x11 s2 = x3 s3 = x12 s4 = x5 s5 = x13 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 3 -1] [ 1 -1 -1 0 4] [-1 -1 3 4 -1] [-1 -1 4 -1 2] [-1 2 -1 -1 1] row, column, symbol relabelling: r0 = x0 r1 = x4 r2 = x19 r3 = x9 r4 = x12 c0 = x0 c4 = x16 c4 = x16 c4 = x16 c4 = x16 s0 = x0 s1 = x4 s2 = x11 s3 = x1 s4 = x15 Cayley table: 20 x 20 dense matrix over Multivariate Polynomial Ring in x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19 over Rational Field ... of Multiplicative Abelian Group isomorphic to C20 T1 = [ 0 1 2 3 -1 -1] [ 5 4 -1 0 -1 -1] [-1 -1 3 4 -1 -1] [-1 2 4 -1 -1 -1] [ 1 5 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x5 r2 = x17 r3 = x8 r4 = x10 c0 = x0 c5 = x11 c5 = x11 c5 = x11 s0 = x0 s1 = x10 s2 = x15 s3 = x6 s4 = x12 s5 = x5 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17] [ x1 x2 x0 x4 x5 x3 x7 x8 x6 x10 x11 x9 x13 x14 x12 x16 x17 x15] [ x2 x0 x1 x5 x3 x4 x8 x6 x7 x11 x9 x10 x14 x12 x13 x17 x15 x16] [ x3 x4 x5 x6 x7 x8 x1 x2 x0 x12 x13 x14 x15 x16 x17 x10 x11 x9] [ x4 x5 x3 x7 x8 x6 x2 x0 x1 x13 x14 x12 x16 x17 x15 x11 x9 x10] [ x5 x3 x4 x8 x6 x7 x0 x1 x2 x14 x12 x13 x17 x15 x16 x9 x10 x11] [ x6 x7 x8 x1 x2 x0 x4 x5 x3 x15 x16 x17 x10 x11 x9 x13 x14 x12] [ x7 x8 x6 x2 x0 x1 x5 x3 x4 x16 x17 x15 x11 x9 x10 x14 x12 x13] [ x8 x6 x7 x0 x1 x2 x3 x4 x5 x17 x15 x16 x9 x10 x11 x12 x13 x14] [ x9 x10 x11 x12 x13 x14 x15 x16 x17 x3 x4 x5 x6 x7 x8 x1 x2 x0] [x10 x11 x9 x13 x14 x12 x16 x17 x15 x4 x5 x3 x7 x8 x6 x2 x0 x1] [x11 x9 x10 x14 x12 x13 x17 x15 x16 x5 x3 x4 x8 x6 x7 x0 x1 x2] [x12 x13 x14 x15 x16 x17 x10 x11 x9 x6 x7 x8 x1 x2 x0 x4 x5 x3] [x13 x14 x12 x16 x17 x15 x11 x9 x10 x7 x8 x6 x2 x0 x1 x5 x3 x4] [x14 x12 x13 x17 x15 x16 x9 x10 x11 x8 x6 x7 x0 x1 x2 x3 x4 x5] [x15 x16 x17 x10 x11 x9 x13 x14 x12 x1 x2 x0 x4 x5 x3 x7 x8 x6] [x16 x17 x15 x11 x9 x10 x14 x12 x13 x2 x0 x1 x5 x3 x4 x8 x6 x7] [x17 x15 x16 x9 x10 x11 x12 x13 x14 x0 x1 x2 x3 x4 x5 x6 x7 x8] ... of Multiplicative Abelian Group isomorphic to C18 T1 = [ 0 1 2 3 -1] [-1 4 -1 0 1] [-1 -1 3 4 -1] [-1 2 4 -1 -1] [ 1 -1 -1 -1 0] row, column, symbol relabelling: r0 = x0 r1 = x7 r2 = x10 r3 = x5 r4 = x15 c0 = x0 c4 = x11 c4 = x11 c4 = x11 c4 = x11 s0 = x0 s1 = x15 s2 = x9 s3 = x4 s4 = x14 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17] [ x1 x2 x0 x4 x5 x3 x7 x8 x6 x10 x11 x9 x13 x14 x12 x16 x17 x15] [ x2 x0 x1 x5 x3 x4 x8 x6 x7 x11 x9 x10 x14 x12 x13 x17 x15 x16] [ x3 x4 x5 x6 x7 x8 x1 x2 x0 x12 x13 x14 x15 x16 x17 x10 x11 x9] [ x4 x5 x3 x7 x8 x6 x2 x0 x1 x13 x14 x12 x16 x17 x15 x11 x9 x10] [ x5 x3 x4 x8 x6 x7 x0 x1 x2 x14 x12 x13 x17 x15 x16 x9 x10 x11] [ x6 x7 x8 x1 x2 x0 x4 x5 x3 x15 x16 x17 x10 x11 x9 x13 x14 x12] [ x7 x8 x6 x2 x0 x1 x5 x3 x4 x16 x17 x15 x11 x9 x10 x14 x12 x13] [ x8 x6 x7 x0 x1 x2 x3 x4 x5 x17 x15 x16 x9 x10 x11 x12 x13 x14] [ x9 x10 x11 x12 x13 x14 x15 x16 x17 x3 x4 x5 x6 x7 x8 x1 x2 x0] [x10 x11 x9 x13 x14 x12 x16 x17 x15 x4 x5 x3 x7 x8 x6 x2 x0 x1] [x11 x9 x10 x14 x12 x13 x17 x15 x16 x5 x3 x4 x8 x6 x7 x0 x1 x2] [x12 x13 x14 x15 x16 x17 x10 x11 x9 x6 x7 x8 x1 x2 x0 x4 x5 x3] [x13 x14 x12 x16 x17 x15 x11 x9 x10 x7 x8 x6 x2 x0 x1 x5 x3 x4] [x14 x12 x13 x17 x15 x16 x9 x10 x11 x8 x6 x7 x0 x1 x2 x3 x4 x5] [x15 x16 x17 x10 x11 x9 x13 x14 x12 x1 x2 x0 x4 x5 x3 x7 x8 x6] [x16 x17 x15 x11 x9 x10 x14 x12 x13 x2 x0 x1 x5 x3 x4 x8 x6 x7] [x17 x15 x16 x9 x10 x11 x12 x13 x14 x0 x1 x2 x3 x4 x5 x6 x7 x8] ... of Multiplicative Abelian Group isomorphic to C18 T1 = [ 0 1 2 3 -1] [ 1 4 -1 0 -1] [-1 -1 -1 4 3] [-1 -1 3 -1 2] [-1 2 -1 -1 4] row, column, symbol relabelling: r0 = x0 r1 = x12 r2 = x17 r3 = x18 r4 = x15 c0 = x0 c4 = x9 c4 = x9 c4 = x9 c4 = x9 s0 = x0 s1 = x12 s2 = x8 s3 = x7 s4 = x5 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18] [ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0] [ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1] [ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2] [ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4] [ x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5] [ x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6] [ x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7] [ x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8] [x10 x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] [x11 x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10] [x12 x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] [x13 x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12] [x14 x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [x15 x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [x16 x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [x17 x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16] [x18 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17] ... of Multiplicative Abelian Group isomorphic to C19 T1 = [ 0 1 2 3 -1] [ 1 -1 -1 0 3] [-1 -1 3 -1 2] [-1 2 -1 -1 4] [-1 4 -1 -1 1] row, column, symbol relabelling: r0 = x0 r1 = x13 r2 = x15 r3 = x10 r4 = x5 c0 = x0 c4 = x8 c4 = x8 c4 = x8 c4 = x8 s0 = x0 s1 = x13 s2 = x6 s3 = x4 s4 = x1 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16] [ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0] [ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1] [ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2] [ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4] [ x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5] [ x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6] [ x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7] [ x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8] [x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] [x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10] [x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] [x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12] [x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] ... of Multiplicative Abelian Group isomorphic to C17 T1 = [ 0 1 2 3 -1 -1] [ 1 -1 4 0 -1 -1] [-1 -1 3 4 -1 -1] [-1 5 1 -1 -1 -1] [-1 2 5 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x13 r2 = x9 r3 = x11 r4 = x8 c0 = x0 c5 = x3 c5 = x3 c5 = x3 s0 = x0 s1 = x13 s2 = x2 s3 = x6 s4 = x10 s5 = x5 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [ x1 x2 x3 x4 x0 x6 x7 x8 x9 x5 x11 x12 x13 x14 x10] [ x2 x3 x4 x0 x1 x7 x8 x9 x5 x6 x12 x13 x14 x10 x11] [ x3 x4 x0 x1 x2 x8 x9 x5 x6 x7 x13 x14 x10 x11 x12] [ x4 x0 x1 x2 x3 x9 x5 x6 x7 x8 x14 x10 x11 x12 x13] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x1 x2 x3 x4 x0] [ x6 x7 x8 x9 x5 x11 x12 x13 x14 x10 x2 x3 x4 x0 x1] [ x7 x8 x9 x5 x6 x12 x13 x14 x10 x11 x3 x4 x0 x1 x2] [ x8 x9 x5 x6 x7 x13 x14 x10 x11 x12 x4 x0 x1 x2 x3] [ x9 x5 x6 x7 x8 x14 x10 x11 x12 x13 x0 x1 x2 x3 x4] [x10 x11 x12 x13 x14 x1 x2 x3 x4 x0 x6 x7 x8 x9 x5] [x11 x12 x13 x14 x10 x2 x3 x4 x0 x1 x7 x8 x9 x5 x6] [x12 x13 x14 x10 x11 x3 x4 x0 x1 x2 x8 x9 x5 x6 x7] [x13 x14 x10 x11 x12 x4 x0 x1 x2 x3 x9 x5 x6 x7 x8] [x14 x10 x11 x12 x13 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] ... of Multiplicative Abelian Group isomorphic to C15 T1 = [ 0 1 2 3 -1] [-1 -1 3 0 1] [-1 4 1 -1 -1] [-1 2 4 -1 -1] [ 1 -1 -1 -1 0] row, column, symbol relabelling: r0 = x0 r1 = x13 r2 = x11 r3 = x8 r4 = x9 c0 = x0 c4 = x10 c4 = x10 c4 = x10 c4 = x10 s0 = x0 s1 = x9 s2 = x12 s3 = x6 s4 = x1 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [ x1 x2 x3 x4 x0 x6 x7 x8 x9 x5 x11 x12 x13 x14 x10] [ x2 x3 x4 x0 x1 x7 x8 x9 x5 x6 x12 x13 x14 x10 x11] [ x3 x4 x0 x1 x2 x8 x9 x5 x6 x7 x13 x14 x10 x11 x12] [ x4 x0 x1 x2 x3 x9 x5 x6 x7 x8 x14 x10 x11 x12 x13] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x1 x2 x3 x4 x0] [ x6 x7 x8 x9 x5 x11 x12 x13 x14 x10 x2 x3 x4 x0 x1] [ x7 x8 x9 x5 x6 x12 x13 x14 x10 x11 x3 x4 x0 x1 x2] [ x8 x9 x5 x6 x7 x13 x14 x10 x11 x12 x4 x0 x1 x2 x3] [ x9 x5 x6 x7 x8 x14 x10 x11 x12 x13 x0 x1 x2 x3 x4] [x10 x11 x12 x13 x14 x1 x2 x3 x4 x0 x6 x7 x8 x9 x5] [x11 x12 x13 x14 x10 x2 x3 x4 x0 x1 x7 x8 x9 x5 x6] [x12 x13 x14 x10 x11 x3 x4 x0 x1 x2 x8 x9 x5 x6 x7] [x13 x14 x10 x11 x12 x4 x0 x1 x2 x3 x9 x5 x6 x7 x8] [x14 x10 x11 x12 x13 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] ... of Multiplicative Abelian Group isomorphic to C15 T1 = [ 0 1 2 3 4] [-1 -1 -1 4 0] [-1 2 -1 0 -1] [ 1 0 -1 -1 -1] [-1 -1 3 2 -1] row, column, symbol relabelling: r0 = x0 r1 = x15 r2 = x6 r3 = x3 r4 = x1 c0 = x0 c4 = x9 c4 = x9 c4 = x9 c4 = x9 s0 = x0 s1 = x3 s2 = x5 s3 = x4 s4 = x9 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x0 x1 x6 x7 x4 x5 x10 x11 x8 x9 x14 x15 x12 x13] [ x3 x2 x1 x0 x7 x6 x5 x4 x11 x10 x9 x8 x15 x14 x13 x12] [ x4 x5 x6 x7 x2 x3 x0 x1 x12 x13 x14 x15 x10 x11 x8 x9] [ x5 x4 x7 x6 x3 x2 x1 x0 x13 x12 x15 x14 x11 x10 x9 x8] [ x6 x7 x4 x5 x0 x1 x2 x3 x14 x15 x12 x13 x8 x9 x10 x11] [ x7 x6 x5 x4 x1 x0 x3 x2 x15 x14 x13 x12 x9 x8 x11 x10] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x0 x1] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x1 x0] [x10 x11 x8 x9 x14 x15 x12 x13 x6 x7 x4 x5 x0 x1 x2 x3] [x11 x10 x9 x8 x15 x14 x13 x12 x7 x6 x5 x4 x1 x0 x3 x2] [x12 x13 x14 x15 x10 x11 x8 x9 x2 x3 x0 x1 x6 x7 x4 x5] [x13 x12 x15 x14 x11 x10 x9 x8 x3 x2 x1 x0 x7 x6 x5 x4] [x14 x15 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x15 x14 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] ... of Multiplicative Abelian Group isomorphic to C8 x C2 T1 = [ 0 1 2 3 -1] [ 2 -1 -1 0 4] [ 4 -1 -1 -1 0] [ 1 2 -1 -1 -1] [-1 -1 3 2 -1] row, column, symbol relabelling: r0 = x0 r1 = x6 r2 = x14 r3 = x15 r4 = x2 c0 = x0 c4 = x8 c4 = x8 c4 = x8 c4 = x8 s0 = x0 s1 = x15 s2 = x6 s3 = x4 s4 = x14 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x0 x1 x6 x7 x4 x5 x10 x11 x8 x9 x14 x15 x12 x13] [ x3 x2 x1 x0 x7 x6 x5 x4 x11 x10 x9 x8 x15 x14 x13 x12] [ x4 x5 x6 x7 x2 x3 x0 x1 x12 x13 x14 x15 x10 x11 x8 x9] [ x5 x4 x7 x6 x3 x2 x1 x0 x13 x12 x15 x14 x11 x10 x9 x8] [ x6 x7 x4 x5 x0 x1 x2 x3 x14 x15 x12 x13 x8 x9 x10 x11] [ x7 x6 x5 x4 x1 x0 x3 x2 x15 x14 x13 x12 x9 x8 x11 x10] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x0 x1] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x1 x0] [x10 x11 x8 x9 x14 x15 x12 x13 x6 x7 x4 x5 x0 x1 x2 x3] [x11 x10 x9 x8 x15 x14 x13 x12 x7 x6 x5 x4 x1 x0 x3 x2] [x12 x13 x14 x15 x10 x11 x8 x9 x2 x3 x0 x1 x6 x7 x4 x5] [x13 x12 x15 x14 x11 x10 x9 x8 x3 x2 x1 x0 x7 x6 x5 x4] [x14 x15 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x15 x14 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] ... of Multiplicative Abelian Group isomorphic to C8 x C2 T1 = [ 0 1 2 3 4] [ 2 -1 -1 -1 0] [ 1 2 -1 -1 -1] [-1 -1 3 -1 2] [-1 -1 -1 4 3] row, column, symbol relabelling: r0 = x0 r1 = x7 r2 = x14 r3 = x3 r4 = x1 c0 = x0 c4 = x4 c4 = x4 c4 = x4 c4 = x4 s0 = x0 s1 = x14 s2 = x7 s3 = x5 s4 = x4 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 3 -1] [ 3 -1 -1 0 -1] [ 2 -1 3 -1 -1] [ 1 4 -1 -1 2] [-1 2 -1 -1 4] row, column, symbol relabelling: r0 = x0 r1 = x2 r2 = x5 r3 = x9 r4 = x8 c0 = x0 c4 = x8 c4 = x8 c4 = x8 c4 = x8 s0 = x0 s1 = x9 s2 = x5 s3 = x2 s4 = x4 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x0 x1 x6 x7 x4 x5 x10 x11 x8 x9 x14 x15 x12 x13] [ x3 x2 x1 x0 x7 x6 x5 x4 x11 x10 x9 x8 x15 x14 x13 x12] [ x4 x5 x6 x7 x2 x3 x0 x1 x12 x13 x14 x15 x10 x11 x8 x9] [ x5 x4 x7 x6 x3 x2 x1 x0 x13 x12 x15 x14 x11 x10 x9 x8] [ x6 x7 x4 x5 x0 x1 x2 x3 x14 x15 x12 x13 x8 x9 x10 x11] [ x7 x6 x5 x4 x1 x0 x3 x2 x15 x14 x13 x12 x9 x8 x11 x10] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x0 x1] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x1 x0] [x10 x11 x8 x9 x14 x15 x12 x13 x6 x7 x4 x5 x0 x1 x2 x3] [x11 x10 x9 x8 x15 x14 x13 x12 x7 x6 x5 x4 x1 x0 x3 x2] [x12 x13 x14 x15 x10 x11 x8 x9 x2 x3 x0 x1 x6 x7 x4 x5] [x13 x12 x15 x14 x11 x10 x9 x8 x3 x2 x1 x0 x7 x6 x5 x4] [x14 x15 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x15 x14 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] ... of Multiplicative Abelian Group isomorphic to C8 x C2 T1 = [ 0 1 2 3 -1] [-1 -1 3 0 -1] [-1 2 0 -1 -1] [ 1 0 -1 -1 4] [ 4 -1 -1 -1 0] row, column, symbol relabelling: r0 = x0 r1 = x15 r2 = x6 r3 = x2 r4 = x7 c0 = x0 c4 = x5 c4 = x5 c4 = x5 c4 = x5 s0 = x0 s1 = x2 s2 = x4 s3 = x9 s4 = x7 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x0 x1 x6 x7 x4 x5 x10 x11 x8 x9 x14 x15 x12 x13] [ x3 x2 x1 x0 x7 x6 x5 x4 x11 x10 x9 x8 x15 x14 x13 x12] [ x4 x5 x6 x7 x2 x3 x0 x1 x12 x13 x14 x15 x10 x11 x8 x9] [ x5 x4 x7 x6 x3 x2 x1 x0 x13 x12 x15 x14 x11 x10 x9 x8] [ x6 x7 x4 x5 x0 x1 x2 x3 x14 x15 x12 x13 x8 x9 x10 x11] [ x7 x6 x5 x4 x1 x0 x3 x2 x15 x14 x13 x12 x9 x8 x11 x10] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x0 x1] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x1 x0] [x10 x11 x8 x9 x14 x15 x12 x13 x6 x7 x4 x5 x0 x1 x2 x3] [x11 x10 x9 x8 x15 x14 x13 x12 x7 x6 x5 x4 x1 x0 x3 x2] [x12 x13 x14 x15 x10 x11 x8 x9 x2 x3 x0 x1 x6 x7 x4 x5] [x13 x12 x15 x14 x11 x10 x9 x8 x3 x2 x1 x0 x7 x6 x5 x4] [x14 x15 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x15 x14 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] ... of Multiplicative Abelian Group isomorphic to C8 x C2 T1 = [ 0 1 2 3 4] [-1 -1 -1 4 0] [-1 -1 3 0 -1] [-1 2 0 -1 -1] [ 1 0 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x15 r2 = x7 r3 = x3 r4 = x1 c0 = x0 c4 = x8 c4 = x8 c4 = x8 c4 = x8 s0 = x0 s1 = x1 s2 = x2 s3 = x4 s4 = x8 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 3 -1] [-1 -1 3 0 -1] [ 2 -1 0 -1 4] [ 1 2 -1 -1 -1] [-1 -1 4 -1 2] row, column, symbol relabelling: r0 = x0 r1 = x13 r2 = x4 r3 = x14 r4 = x8 c0 = x0 c4 = x8 c4 = x8 c4 = x8 c4 = x8 s0 = x0 s1 = x14 s2 = x4 s3 = x9 s4 = x12 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x0 x1 x6 x7 x4 x5 x10 x11 x8 x9 x14 x15 x12 x13] [ x3 x2 x1 x0 x7 x6 x5 x4 x11 x10 x9 x8 x15 x14 x13 x12] [ x4 x5 x6 x7 x0 x1 x2 x3 x12 x13 x14 x15 x8 x9 x10 x11] [ x5 x4 x7 x6 x1 x0 x3 x2 x13 x12 x15 x14 x9 x8 x11 x10] [ x6 x7 x4 x5 x2 x3 x0 x1 x14 x15 x12 x13 x10 x11 x8 x9] [ x7 x6 x5 x4 x3 x2 x1 x0 x15 x14 x13 x12 x11 x10 x9 x8] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x0 x1 x2 x3] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x1 x0 x3 x2] [x10 x11 x8 x9 x14 x15 x12 x13 x6 x7 x4 x5 x2 x3 x0 x1] [x11 x10 x9 x8 x15 x14 x13 x12 x7 x6 x5 x4 x3 x2 x1 x0] [x12 x13 x14 x15 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x13 x12 x15 x14 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x14 x15 x12 x13 x10 x11 x8 x9 x2 x3 x0 x1 x6 x7 x4 x5] [x15 x14 x13 x12 x11 x10 x9 x8 x3 x2 x1 x0 x7 x6 x5 x4] ... of Multiplicative Abelian Group isomorphic to C4 x C2 x C2 T1 = [ 0 1 2 3 -1] [-1 -1 3 0 -1] [ 2 -1 0 -1 -1] [ 1 4 -1 -1 2] [-1 2 -1 -1 4] row, column, symbol relabelling: r0 = x0 r1 = x12 r2 = x4 r3 = x15 r4 = x14 c0 = x0 c4 = x14 c4 = x14 c4 = x14 c4 = x14 s0 = x0 s1 = x15 s2 = x4 s3 = x8 s4 = x5 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x0 x1 x2 x3 x12 x13 x14 x15 x8 x9 x10 x11] [ x5 x4 x7 x6 x1 x0 x3 x2 x13 x12 x15 x14 x9 x8 x11 x10] [ x6 x7 x5 x4 x2 x3 x1 x0 x14 x15 x13 x12 x10 x11 x9 x8] [ x7 x6 x4 x5 x3 x2 x0 x1 x15 x14 x12 x13 x11 x10 x8 x9] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x0 x1 x2 x3] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x1 x0 x3 x2] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x2 x3 x1 x0] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x3 x2 x0 x1] [x12 x13 x14 x15 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] [x13 x12 x15 x14 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x14 x15 x13 x12 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x15 x14 x12 x13 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] ... of Multiplicative Abelian Group isomorphic to C4 x C4 T1 = [ 0 1 2 -1 -1] [-1 2 0 -1 -1] [ 3 0 -1 1 -1] [ 1 -1 -1 4 3] [-1 -1 -1 3 4] row, column, symbol relabelling: r0 = x0 r1 = x15 r2 = x7 r3 = x4 r4 = x5 c0 = x0 c4 = x3 c4 = x3 c4 = x3 c4 = x3 s0 = x0 s1 = x4 s2 = x8 s3 = x7 s4 = x6 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 -1 -1] [ 1 -1 0 3 4] [ 3 -1 -1 0 -1] [ 4 -1 -1 -1 3] [-1 2 1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x3 r2 = x7 r3 = x11 r4 = x1 c0 = x0 c4 = x8 c4 = x8 c4 = x8 c4 = x8 s0 = x0 s1 = x3 s2 = x2 s3 = x7 s4 = x11 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] [ x1 x0 x3 x2 x5 x4 x7 x6 x9 x8 x11 x10 x13 x12 x15 x14] [ x2 x3 x1 x0 x6 x7 x5 x4 x10 x11 x9 x8 x14 x15 x13 x12] [ x3 x2 x0 x1 x7 x6 x4 x5 x11 x10 x8 x9 x15 x14 x12 x13] [ x4 x5 x6 x7 x2 x3 x1 x0 x12 x13 x14 x15 x10 x11 x9 x8] [ x5 x4 x7 x6 x3 x2 x0 x1 x13 x12 x15 x14 x11 x10 x8 x9] [ x6 x7 x5 x4 x1 x0 x3 x2 x14 x15 x13 x12 x9 x8 x11 x10] [ x7 x6 x4 x5 x0 x1 x2 x3 x15 x14 x12 x13 x8 x9 x10 x11] [ x8 x9 x10 x11 x12 x13 x14 x15 x4 x5 x6 x7 x2 x3 x1 x0] [ x9 x8 x11 x10 x13 x12 x15 x14 x5 x4 x7 x6 x3 x2 x0 x1] [x10 x11 x9 x8 x14 x15 x13 x12 x6 x7 x5 x4 x1 x0 x3 x2] [x11 x10 x8 x9 x15 x14 x12 x13 x7 x6 x4 x5 x0 x1 x2 x3] [x12 x13 x14 x15 x10 x11 x9 x8 x2 x3 x1 x0 x6 x7 x5 x4] [x13 x12 x15 x14 x11 x10 x8 x9 x3 x2 x0 x1 x7 x6 x4 x5] [x14 x15 x13 x12 x9 x8 x11 x10 x1 x0 x3 x2 x5 x4 x7 x6] [x15 x14 x12 x13 x8 x9 x10 x11 x0 x1 x2 x3 x4 x5 x6 x7] ... of Multiplicative Abelian Group isomorphic to C16 T1 = [ 0 1 2 -1 -1 -1] [ 3 -1 0 2 4 5] [ 1 2 -1 4 5 3] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x10 r2 = x8 c0 = x0 c5 = x2 c5 = x2 c5 = x2 c5 = x2 c5 = x2 s0 = x0 s1 = x8 s2 = x3 s3 = x10 s4 = x1 s5 = x12 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12] [ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x0] [ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x0 x1] [ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x0 x1 x2] [ x4 x5 x6 x7 x8 x9 x10 x11 x12 x0 x1 x2 x3] [ x5 x6 x7 x8 x9 x10 x11 x12 x0 x1 x2 x3 x4] [ x6 x7 x8 x9 x10 x11 x12 x0 x1 x2 x3 x4 x5] [ x7 x8 x9 x10 x11 x12 x0 x1 x2 x3 x4 x5 x6] [ x8 x9 x10 x11 x12 x0 x1 x2 x3 x4 x5 x6 x7] [ x9 x10 x11 x12 x0 x1 x2 x3 x4 x5 x6 x7 x8] [x10 x11 x12 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] [x11 x12 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10] [x12 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] ... of Multiplicative Abelian Group isomorphic to C13 T1 = [ 0 1 2 3 -1 -1] [ 5 -1 3 0 2 4] [ 1 2 -1 -1 4 5] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x6 r2 = x11 c0 = x0 c5 = x8 c5 = x8 c5 = x8 c5 = x8 c5 = x8 s0 = x0 s1 = x11 s2 = x2 s3 = x1 s4 = x7 s5 = x6 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [ x1 x2 x3 x4 x5 x6 x0 x8 x9 x10 x11 x12 x13 x7] [ x2 x3 x4 x5 x6 x0 x1 x9 x10 x11 x12 x13 x7 x8] [ x3 x4 x5 x6 x0 x1 x2 x10 x11 x12 x13 x7 x8 x9] [ x4 x5 x6 x0 x1 x2 x3 x11 x12 x13 x7 x8 x9 x10] [ x5 x6 x0 x1 x2 x3 x4 x12 x13 x7 x8 x9 x10 x11] [ x6 x0 x1 x2 x3 x4 x5 x13 x7 x8 x9 x10 x11 x12] [ x7 x8 x9 x10 x11 x12 x13 x1 x2 x3 x4 x5 x6 x0] [ x8 x9 x10 x11 x12 x13 x7 x2 x3 x4 x5 x6 x0 x1] [ x9 x10 x11 x12 x13 x7 x8 x3 x4 x5 x6 x0 x1 x2] [x10 x11 x12 x13 x7 x8 x9 x4 x5 x6 x0 x1 x2 x3] [x11 x12 x13 x7 x8 x9 x10 x5 x6 x0 x1 x2 x3 x4] [x12 x13 x7 x8 x9 x10 x11 x6 x0 x1 x2 x3 x4 x5] [x13 x7 x8 x9 x10 x11 x12 x0 x1 x2 x3 x4 x5 x6] ... of Multiplicative Abelian Group isomorphic to C14 T1 = [ 0 1 2 -1 -1 -1] [ 3 -1 0 2 5 -1] [ 4 -1 -1 -1 3 -1] [ 1 2 -1 5 4 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x14 r2 = x12 r3 = x10 c0 = x0 c5 = x7 c5 = x7 c5 = x7 c5 = x7 s0 = x0 s1 = x10 s2 = x3 s3 = x14 s4 = x12 s5 = x16 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16] [ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0] [ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1] [ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2] [ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4] [ x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5] [ x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6] [ x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7] [ x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8] [x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] [x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10] [x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] [x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12] [x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] ... of Multiplicative Abelian Group isomorphic to C17 T1 = [ 0 1 2 -1 -1 -1] [ 3 -1 0 -1 4 2] [ 1 -1 -1 3 -1 -1] [-1 2 -1 1 3 4] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x10 r2 = x1 r3 = x15 c0 = x0 c5 = x6 c5 = x6 c5 = x6 c5 = x6 c5 = x6 s0 = x0 s1 = x1 s2 = x16 s3 = x10 s4 = x13 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17] [ x1 x2 x0 x4 x5 x3 x7 x8 x6 x10 x11 x9 x13 x14 x12 x16 x17 x15] [ x2 x0 x1 x5 x3 x4 x8 x6 x7 x11 x9 x10 x14 x12 x13 x17 x15 x16] [ x3 x4 x5 x6 x7 x8 x1 x2 x0 x12 x13 x14 x15 x16 x17 x10 x11 x9] [ x4 x5 x3 x7 x8 x6 x2 x0 x1 x13 x14 x12 x16 x17 x15 x11 x9 x10] [ x5 x3 x4 x8 x6 x7 x0 x1 x2 x14 x12 x13 x17 x15 x16 x9 x10 x11] [ x6 x7 x8 x1 x2 x0 x4 x5 x3 x15 x16 x17 x10 x11 x9 x13 x14 x12] [ x7 x8 x6 x2 x0 x1 x5 x3 x4 x16 x17 x15 x11 x9 x10 x14 x12 x13] [ x8 x6 x7 x0 x1 x2 x3 x4 x5 x17 x15 x16 x9 x10 x11 x12 x13 x14] [ x9 x10 x11 x12 x13 x14 x15 x16 x17 x3 x4 x5 x6 x7 x8 x1 x2 x0] [x10 x11 x9 x13 x14 x12 x16 x17 x15 x4 x5 x3 x7 x8 x6 x2 x0 x1] [x11 x9 x10 x14 x12 x13 x17 x15 x16 x5 x3 x4 x8 x6 x7 x0 x1 x2] [x12 x13 x14 x15 x16 x17 x10 x11 x9 x6 x7 x8 x1 x2 x0 x4 x5 x3] [x13 x14 x12 x16 x17 x15 x11 x9 x10 x7 x8 x6 x2 x0 x1 x5 x3 x4] [x14 x12 x13 x17 x15 x16 x9 x10 x11 x8 x6 x7 x0 x1 x2 x3 x4 x5] [x15 x16 x17 x10 x11 x9 x13 x14 x12 x1 x2 x0 x4 x5 x3 x7 x8 x6] [x16 x17 x15 x11 x9 x10 x14 x12 x13 x2 x0 x1 x5 x3 x4 x8 x6 x7] [x17 x15 x16 x9 x10 x11 x12 x13 x14 x0 x1 x2 x3 x4 x5 x6 x7 x8] ... of Multiplicative Abelian Group isomorphic to C18 T1 = [ 0 1 2 -1 -1 -1] [ 3 -1 0 2 4 -1] [ 1 2 -1 5 3 -1] [-1 -1 -1 4 5 -1] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x14 r2 = x10 r3 = x12 c0 = x0 c5 = x7 c5 = x7 c5 = x7 c5 = x7 s0 = x0 s1 = x10 s2 = x3 s3 = x14 s4 = x1 s5 = x16 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16] [ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0] [ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1] [ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2] [ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4] [ x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5] [ x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6] [ x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7] [ x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8] [x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] [x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10] [x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] [x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12] [x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] ... of Multiplicative Abelian Group isomorphic to C17 T1 = [ 0 1 2 -1 -1 -1] [ 3 -1 0 -1 -1 2] [ 1 -1 -1 3 -1 -1] [-1 -1 -1 1 3 -1] [-1 2 -1 -1 1 3] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x14 r2 = x12 r3 = x10 r4 = x8 c0 = x0 c5 = x6 c5 = x6 c5 = x6 c5 = x6 c5 = x6 s0 = x0 s1 = x12 s2 = x3 s3 = x14 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16] [ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0] [ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1] [ x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2] [ x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3] [ x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4] [ x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5] [ x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6] [ x8 x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7] [ x9 x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8] [x10 x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9] [x11 x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10] [x12 x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11] [x13 x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12] [x14 x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13] [x15 x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14] [x16 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15] ... of Multiplicative Abelian Group isomorphic to C17 T1 = [ 0 1 2 -1 -1] [ 3 -1 0 -1 2] [ 1 -1 -1 3 -1] [-1 4 -1 1 3] [-1 2 -1 -1 4] row, column, symbol relabelling: r0 = x0 r1 = x19 r2 = x9 r3 = x17 r4 = x12 c0 = x0 c4 = x2 c4 = x2 c4 = x2 c4 = x2 s0 = x0 s1 = x9 s2 = x11 s3 = x19 s4 = x14 Cayley table: 20 x 20 dense matrix over Multivariate Polynomial Ring in x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19 over Rational Field ... of Multiplicative Abelian Group isomorphic to C10 x C2 T1 = [ 0 1 2 -1 -1 -1] [ 3 -1 0 -1 -1 2] [ 1 -1 -1 4 3 -1] [-1 2 -1 1 4 3] [-1 -1 -1 -1 -1 -1] [-1 -1 -1 -1 -1 -1] row, column, symbol relabelling: r0 = x0 r1 = x16 r2 = x12 r3 = x10 c0 = x0 c5 = x6 c5 = x6 c5 = x6 c5 = x6 c5 = x6 s0 = x0 s1 = x12 s2 = x3 s3 = x16 s4 = x14 Cayley table: [ x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18] [ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 x0] [ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x