Right Bol Loop 16.5.2.48 of order 16


0123456789101112131415
1091011121514132435876
2901110131415121348567
3101190151213144127658
4111009141312153216785
5121314159111008671243
6151412131190107854312
7141513121009116583421
8131215140101195762134
9214387650111013121514
1034216587119014151213
1143127856100915141312
1258762431131415091110
1385671342121514901011
1476853124151312101190
1567584213141213111009

Centre:   0   9

Centrum:   0   9

Nucleus:   0   9

Left Nucleus:   0   9   14   15

Middle Nucleus:   0   9

Right Nucleus:   0   9


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

5 Elements of order 2:   1   2   9   12   13

10 Elements of order 4:   3   4   5   6   7   8   10   11   14   15

Commutator Subloop:   0   9

Associator Subloop:   0   9

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(6-1) neq (1*6)-1

Al Property:   FAILS. The left inner mapping L1,1 = (3,4)(10,11) is not an automorphism.   L1,1(3*5) neq L1,1(3)*L1,1(5)

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

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001