Right Bol Loop 16.11.4.29 of order 16


0123456789101112131415
1032765491514108111312
2301547610141591181213
3210674511109813121514
4756023115121314910118
5647201313118121415910
6574310214131215109811
7465132012811131514109
8121011151314941537260
9151110121413874320651
1014891315121156013472
1113981412151062705143
1281413911101510654327
1311151210891423476015
1410121511981335142706
1591314810111207261534

Centre:   0   4

Centrum:   0   3   4   6

Nucleus:   0   4

Left Nucleus:   0   3   4   6

Middle Nucleus:   0   4

Right Nucleus:   0   4


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

11 Elements of order 2:   1   2   3   4   5   6   7   10   11   13   14

4 Elements of order 4:   8   9   12   15

Commutator Subloop:   0   4

Associator Subloop:   0   4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (2,5)(3,6) 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