Right Bol Loop 16.7.4.52 of order 16


0123456789101112131415
1035247698121311101514
2401673510131581491211
3517062412111498151013
4260715313109141581112
5376104211128159141310
6742530114151312101189
7654321015141110131298
8911131210141576524310
9813101112151467432501
1013151498121153071642
1112891415131024706135
1211148159101342167053
1310915814111235610724
1415121110138910345276
1514101213119801253467

Centre:   0   7

Centrum:   0   7   12   13

Nucleus:   0   7

Left Nucleus:   0   7   12   13

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   10   11

8 Elements of order 4:   3   4   8   9   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:   64 (128, 512)


/ revised October, 2001