Right Bol Loop 16.7.4.13 of order 16


0123456789101112131415
1032548967111013121514
2310681141059714151312
3201861051147915141213
4579012133121514861110
5497103122131415681011
6810112314015112134579
7954131201411532111068
8611103215114013125497
9745121311501423101186
1011861514123132017954
1110681415132123109745
1213141597510411681032
1312151479411510860123
1415131211107698543201
1514121310119876452310

Centre:   0   1   14   15

Centrum:   0   1   14   15

Nucleus:   0   1   14   15

Left Nucleus:   0   1   14   15

Middle Nucleus:   0   1   14   15

Right Nucleus:   0   1   14   15

1 Element of order 1:   0

7 Elements of order 2:   1   4   5   10   11   14   15

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

Commutator Subloop:   0   1   14   15

Associator Subloop:   0   1   14   15

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 (256, 1024)


/ revised October, 2001