Right Bol Loop 16.7.4.9 of order 16


0123456789101112131415
1031071596248141312115
2451511710121413639108
3915130614151112724810
4211013851214151109367
5157680324109121114131
6101145313150121127849
7801122155111314361094
8712514401113115910632
9314111510121315084276
1061312191114150548723
1114829127410630515113
1213471011289365011514
1312943148106271510511
1411108613493721155012
1556921103784131411120

Centre:   0   5   13   14

Centrum:   0   5   13   14

Nucleus:   0   5   13   14

Left Nucleus:   0   5   13   14

Middle Nucleus:   0   5   13   14

Right Nucleus:   0   5   13   14

1 Element of order 1:   0

7 Elements of order 2:   1   5   11   12   13   14   15

8 Elements of order 4:   2   3   4   6   7   8   9   10

Commutator Subloop:   0   5   13   14

Associator Subloop:   0   5   13   14

4 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-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