Right Bol Loop 16.11.2.165 of order 16


0123456789101112131415
1032547698141211151013
2406173511131214910158
3517062412151110814139
4260715313111591481210
5371604215121381091114
6745230110148131511912
7654321014109151312811
8101113121591401654372
9141215111381010745263
1081311151214967032514
1112891014131524306157
1211981410151335217046
1315101489111242560731
1491512131110876123405
1513141098121153471620

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

11 Elements of order 2:   1   2   5   6   7   8   9   10   11   14   15

4 Elements of order 4:   3   4   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