Right Bol Loop 16.7.4.35 of order 16


0123456789101112131415
1036274598151213141110
2457160311141289151013
3670541214111310891512
4215037612131191510814
5764302115109131411128
6301725413121415108911
7542613010158141112139
8101112141513957163240
9151411131012875032461
1081213119141510546327
1114159101381264357012
1213981514101132670154
1312810911151423401576
1411101581291346215703
1591314128111001724635

Centre:   0   5

Centrum:   0   5   12   14

Nucleus:   0   5

Left Nucleus:   0   5   12   14

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   12   14

8 Elements of order 4:   2   6   8   9   10   11   13   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