Right Bol Loop 16.7.2.260 of order 16


0123456789101112131415
1230547698111014121513
2301765411109815141312
3012674510118913151214
4576031212131415810911
5764120313121514101189
6457302114151213981110
7645213015141312119108
8101191513141221307654
9810111412151330215746
1011981315121412036475
1198101214131503124567
1214151311109875642130
1312141510118964751023
1415131298111057463201
1513121489101146570312

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

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.


1 Element of order 1:   0

7 Elements of order 2:   2   4   7   9   10   13   14

8 Elements of order 4:   1   3   5   6   8   11   12   15

Commutator Subloop:   0   2

Associator Subloop:   0   2

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 = (12,15)(13,14) 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:   128 (1024, 2048)


/ revised October, 2001