Right Bol Loop 16.9.4.23 of order 16


0123456789101112131415
1036274598151314121110
2457160311131481510912
3670541214121110915813
4215037613111291081514
5764302115109121114138
6301725412141315891011
7542613010158141311129
8101214131511957126430
9151312111014875043621
1081411129131510534267
1114810912151363405712
1213159101181424350176
1312101581491136217054
1411981513101242671503
1591113148121001762345

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