Right Bol Loop 16.9.2.195 of order 16


0123456789101112131415
1032547698121310111514
2406173510121581491311
3517062412101491581113
4260715313119148151012
5371604211138159141210
6745230114151312111089
7654321015141110131298
8911131210141501253467
9813111012151410342576
1013159148121123706145
1112814915131054071632
1211148159101332617054
1310915814111245160723
1415121011138967435201
1514101213119876524310

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   1   6   7

Middle Nucleus:   0   7

Right Nucleus:   0   7


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

9 Elements of order 2:   1   2   5   6   7   8   9   14   15

6 Elements of order 4:   3   4   10   11   12   13

Commutator Subloop:   0   7

Associator Subloop:   0   7

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