Right Bol Loop 16.7.2.117 of order 16


0123456789101112131415
1230547691181013121514
2301765411109815141312
3012674510811914151213
4675213012141315119108
5467302114151213911810
6754120313121514108119
7546031215131412810911
8101191214131523104657
9810111412151330216475
1011981315121412035746
1198101513141201327564
1214151311910876542130
1312141591181057463021
1415131210811964751203
1513121481091145670312

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

Middle Nucleus:   0   2

Right Nucleus:   0   2


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:   2   5   6   9   10   13   14

8 Elements of order 4:   1   3   4   7   8   11   12   15

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (4-1)(9-1) neq (4*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6)(8,11)(9,10)(12,15)(13,14) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (1024, 2048)


/ revised October, 2001