Right Bol Loop 16.3.4.5 of order 16


0123456789101112131415
1032548967111013121514
2310684115109714151312
3201865104117915141213
4579101321231415861110
5497011231321514681011
6810113214015113124579
7954121301411523111068
8611102315114012135497
9745131211501432101186
1011861415312213107954
1110681514213312019745
1213141597105114681032
1312151479114105860123
1415131211107698543201
1514121310119876452310

Centre:   0   1   14   15

Centrum:   0   1   14   15

Nucleus:   0   1   14   15

Left Nucleus:   0   1   6   7   8   9   14   15

Middle Nucleus:   0   1   14   15

Right Nucleus:   0   1   14   15

1 Element of order 1:   0

3 Elements of order 2:   1   14   15

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

Commutator Subloop:   0   1   14   15

Associator Subloop:   0   1

4 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (2-1)(5-1) neq (2*5)-1

Al Property:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

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

Right (Left, Full) Mult Group Orders:   32 (64, 256)


/ revised October, 2001