Right Bol Loop 16.15.2.24 of order 16


0123456789101112131415
1032547698111013121514
2301674510118914151213
3210765411109815141312
4567012312131415891011
5476103213121514981110
6745230114151213101189
7654321015141312111098
8109121113151401234567
9118131012141510325476
1081114915131223016745
1191015814121332107654
1214138159111045670123
1315129148101154761032
1412151013119867452301
1513141112108976543210

Centre:   0

Centrum:   0   5

Nucleus:   0

Left Nucleus:   0   1   2   3   4   5   6   7

Middle Nucleus:   0

Right Nucleus:   0

1 Element of order 1:   0

15 Elements of order 2:   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   2   4   6

Associator Subloop:   0   1   2   3   4   5   6   7

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 7:

1 Conjugacy Class of size 8:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (2,7,5)(3,4,6)(8,11)(9,10)(12,15)(13,14) is not an automorphism.   L1,8(1*2) neq L1,8(1)*L1,8(2)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (1625702400, 3251404800)


/ revised November, 2001