Right Bol Loop 16.7.2.438 of order 16


0123456789101112131415
1032674591011814151312
2301547610118913121514
3210765411891015141213
4657021313151214810911
5746203112141315108119
6475130214131512119810
7564312015121413911108
8121013119151421035476
9151114108121332106754
1013812911141503214567
1114915810131210327645
1281310141591146572013
1310128151411957460231
1411159121310874653120
1591411131281065741302

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2   6   7

Middle Nucleus:   0   2

Right Nucleus:   0   2


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

7 Elements of order 2:   1   2   3   4   5   6   7

8 Elements of order 4:   8   9   10   11   12   13   14   15

Commutator Subloop:   0   2   6   7

Associator Subloop:   0   2   6   7

2 Conjugacy Classes of size 1:

1 Conjugacy Class of size 2:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (4,5)(6,7)(8,14)(9,13)(10,15)(11,12) is not an automorphism.   L1,8(4*8) neq L1,8(4)*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, 4096)


/ revised October, 2001