Right Bol Loop 16.5.2.20 of order 16


0123456789101112131415
1036274598121311101514
2457160310131581491211
3670541213109141581112
4215037612111498151013
5764302115141110131298
6301725411128159141310
7542613014151312101189
8911131215101457263410
9812111014131575432601
1012814911151364501732
1113159141081223057146
1210141581391132715064
1311981512141046170523
1415131011912810346257
1514101213811901624375

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

5 Elements of order 2:   1   3   4   5   7

10 Elements of order 4:   2   6   8   9   10   11   12   13   14   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