Right Bol Loop 16.7.4.30 of order 16


0123456789101112131415
1036274591581413121110
2457160311141289151013
3670541214131198101512
4215037612111310159814
5764302115109131411128
6301725413121415108911
7542613010815121114139
8101114121513957164230
9151413111012870546321
1081211139141515032467
1114151091381264351072
1213915814101136215704
1312891011151423407516
1411108151291342670153
1591312148111001723645

Centre:   0   5

Centrum:   0   5   9   10

Nucleus:   0   5

Left Nucleus:   0   5   9   10

Middle Nucleus:   0   5

Right Nucleus:   0   5


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   3   4   5   7   9   10

8 Elements of order 4:   2   6   8   11   12   13   14   15

Commutator Subloop:   0   5

Associator Subloop:   0   5

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