Right Bol Loop 16.7.8.2 of order 16


0123456789101112131415
1035247691481211151013
2401673511121381091514
3517062412151191481310
4260715313111510814129
5376104215131214910118
6742530110814131511912
7654321014109151312811
8101112131591476153402
9141215111381060742513
1081311151214917035264
1112891014131554376120
1211914810151342567031
1315108149111235210746
1491513121110801624375
1513141098121123401657

Centre:   0   7   11   15

Centrum:   0   3   4   7   9   10   11   15

Nucleus:   0   7   11   15

Left Nucleus:   0   3   4   7   9   10   11   15

Middle Nucleus:   0   7   11   15

Right Nucleus:   0   7   11   15

1 Element of order 1:   0

7 Elements of order 2:   1   2   5   6   7   9   10

8 Elements of order 4:   3   4   8   11   12   13   14   15

Commutator Subloop:   0   7

Associator Subloop:   0   7

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