Right Bol Loop 16.9.2.35 of order 16


0123456789101112131415
1036274591581413121110
2457160311141289151013
3670541214131198101512
4215037612111310159814
5764302115109131411128
6301725413121415108911
7542613010815121114139
8101112141513957124630
9151411131012870536421
1081213119141515042367
1114159101381264301572
1213981514101136275104
1312810911151423457016
1411101581291342610753
1591314128111001763245

Centre:   0   5

Centrum:   0   5

Nucleus:   0   5

Left Nucleus:   0   5

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

9 Elements of order 2:   1   3   4   5   7   9   10   11   13

6 Elements of order 4:   2   6   8   12   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:   128 (128, 1024)


/ revised October, 2001