Right Bol Loop 16.7.8.1 of order 16


0123456789101112131415
1032116587121349101514
2341069011214751581113
3211135121091586147410
4116503214151091131278
5611231311410815271409
6509210411137143815112
7890144101311621553121
8712115111310453146290
9121415108765041311123
1013789151423401211165
1145612315141312010987
1291514137856111100432
1310871214153211194056
1415104709121268351311
1514131181129035726104

Centre:   0   4   12   13

Centrum:   0   1   4   9   10   11   12   13

Nucleus:   0   4   12   13

Left Nucleus:   0   1   4   9   10   11   12   13

Middle Nucleus:   0   4   12   13

Right Nucleus:   0   4   12   13

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   12

Associator Subloop:   0   12

4 Conjugacy Classes of size 1:

6 Conjugacy Classes of size 2:

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 (64, 128)


/ revised October, 2001