Right Bol Loop 16.3.4.39 of order 16


0123456789101112131415
1032547698111015141312
2310675410118913121514
3201764511109814151213
4567012312151413811109
5476103215121314910118
6754231014131215118910
7645320113141512109811
8911101215141310325764
9810111512131401234675
1011891413151232106457
1110981314121523017546
1215131489101154761320
1314151211108967453102
1413121510119876542013
1512141398111045670231

Centre:   0   1

Centrum:   0   1   4   5

Nucleus:   0   1

Left Nucleus:   0   1   4   5

Middle Nucleus:   0   1

Right Nucleus:   0   1


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

3 Elements of order 2:   1   4   5

12 Elements of order 4:   2   3   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   1

Associator Subloop:   0   1

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*9)-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