Right Bol Loop 16.9.4.24 of order 16


0123456789101112131415
1036274591511101312814
2457160310111598141312
3670541213109151481211
4215037611121489151013
5764302115141213101198
6301725412138141591110
7542613014813121110159
8910131115121401246375
9813121014111515423607
1011151491281324510736
1110915813141246701523
1213891410151163075142
1312148151191032157064
1415111012913870364251
1514121113810957632410

Centre:   0   5

Centrum:   0   5   8   15

Nucleus:   0   5

Left Nucleus:   0   5   8   15

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

9 Elements of order 2:   1   3   4   5   7   8   11   13   15

6 Elements of order 4:   2   6   9   10   12   14

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:   64 (128, 512)


/ revised October, 2001