Right Bol Loop 16.11.4.38 of order 16


0123456789101112131415
1032547691581314121110
2406173511141315891012
3517062413111210915814
4260715314121191081513
5371604212131481510911
6745230110815141311129
7654321015109121114138
8101213141191506125437
9151411121381010734256
1081312111415967043521
1113151098141223470615
1214891015131154307162
1311101589121435261074
1412981510111342516703
1591114131210871652340

Centre:   0   7

Centrum:   0   7   11   12

Nucleus:   0   7

Left Nucleus:   0   7   11   12

Middle Nucleus:   0   7

Right Nucleus:   0   7


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets.


1 Element of order 1:   0

11 Elements of order 2:   1   2   5   6   7   8   9   10   13   14   15

4 Elements of order 4:   3   4   11   12

Commutator Subloop:   0   7

Associator Subloop:   0   7

2 Conjugacy Classes of size 1:

7 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:   64 (128, 512)


/ revised October, 2001