Right Bol Loop 16.15.4.4 of order 16


0123456789101112131415
1032674591511141081213
2301547610118913121514
3210765411149158101312
4657021313812101415119
5746203112101381514911
6475130215131412119108
7564312014121513911810
8910121311151404253176
9811141510131210327654
1011813129141525041367
1110915148121332106745
1214138101511957460213
1315121081491146572031
1412159111310873614502
1513141191281061735420

Centre:   0   6

Centrum:   0   2   6   7

Nucleus:   0   6

Left Nucleus:   0   2   6   7

Middle Nucleus:   0   6

Right Nucleus:   0   6


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

15 Elements of order 2:   1   2   3   4   5   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   6

Associator Subloop:   0   6

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (2,7)(3,5)(8,15)(9,13)(10,14)(11,12) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001