Right Bol Loop 16.9.4.30 of order 16


0123456789101112131415
1036274591581413121110
2457160311141315810912
3670541214121110915813
4215037613111291081514
5764302115109121114138
6301725412131481591011
7542613010815131411129
8101214131511951762430
9151312111014875043621
1081411129131510534267
1114810912151363405712
1213159101181424350176
1312101581491132671054
1411981513101246217503
1591113148121007126345

Centre:   0   5

Centrum:   0   3   4   5

Nucleus:   0   5

Left Nucleus:   0   3   4   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   11   12   13   14

6 Elements of order 4:   2   6   8   9   10   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