Right Bol Loop 16.5.2.106 of order 16


0123456789101112131415
1035247691581314111210
2401673511141315810912
3517062413111210915814
4260715314121191081513
5376104212131481591011
6742530110815141312119
7654321015109121114138
8101214131191571625340
9151411121381067034251
1081312111415910743526
1113151098141254370612
1214891015131123407165
1311108159121442561703
1412915810111335216074
1591113141210806152437

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   7

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

5 Elements of order 2:   1   2   5   6   7

10 Elements of order 4:   3   4   8   9   10   11   12   13   14   15

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:   128 (128, 1024)


/ revised October, 2001