Right Bol Loop 16.11.2.41 of order 16


0123456789101112131415
1036274598111213101514
2457160310111598141312
3670541213129814151011
4215037611101415981213
5764302115141213101198
6301725412138141591110
7542613014151310111289
8910111315121451632470
9813101214111570324651
1011159141281364075132
1110981513141232107564
1213814910151123510746
1312141581191046751023
1415111210913815463207
1514121311810907246315

Centre:   0   5

Centrum:   0   5

Nucleus:   0   5

Left Nucleus:   0   5

Middle Nucleus:   0   5

Right Nucleus:   0   5


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   3   4   5   7   9   10   11   12   13   14

4 Elements of order 4:   2   6   8   15

Commutator Subloop:   0   5

Associator Subloop:   0   5

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