Right Bol Loop 16.7.4.59 of order 16


0123456789101112131415
1035247698111510141312
2401673510128913111514
3517062411159148101213
4260715312101381415119
5376104215111413912108
6742530113141210158911
7654321014131512119810
8910111215131406534172
9811151012141317452063
1012891314111523716450
1115914813101232670541
1210138149151145107236
1314121015118960325714
1413151211109871243605
1511141398121054061327

Centre:   0   7

Centrum:   0   3   4   7

Nucleus:   0   7

Left Nucleus:   0   3   4   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

7 Elements of order 2:   1   2   5   6   7   8   14

8 Elements of order 4:   3   4   9   10   11   12   13   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:   64 (128, 512)


/ revised October, 2001