Right Bol Loop 16.7.8.3 of order 16


0123456789101112131415
1032116587121349101514
2341069011214751581113
3211135121091586147410
4116503215141312110987
5619310114137142815012
6501221341110815371419
7812015111013452146391
8791144131011631552120
9121415137856011101423
1013781214152311094156
1145612314151090131278
1291514108765141301132
1310879151432411211065
1415131180912125736104
1514104711290368251311

Centre:   0

Centrum:   0   1   4   9   10   11   12   13

Nucleus:   0

Left Nucleus:   0   1   4   9   10   11   12   13

Middle Nucleus:   0

Right Nucleus:   0

1 Element of order 1:   0

7 Elements of order 2:   1   4   9   10   11   12   13

8 Elements of order 4:   2   3   5   6   7   8   14   15

Commutator Subloop:   0   1   9   12

Associator Subloop:   0   1   9   12

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 3:

3 Conjugacy Classes of size 4:

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

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

Ar Property:   FAILS. The right inner mapping R1,2 = (2,14)(3,15)(5,7)(6,8) is not an automorphism.   R1,2(2*2) neq R1,2(2)*R1,2(2)

Right (Left, Full) Mult Group Orders:   64 (9216, 9216)


/ revised November, 2001