Right Bol Loop 16.11.4.13 of order 16


0123456789101112131415
1032674598151211141310
2301765410111413815129
3210547611109813121514
4675031213141110158912
5764302112158914111013
6457120314131215109811
7546213015121314910118
8910111312141504235167
9811101415131216753042
1011891514121327640351
1110981213151435104276
1215141311810953016724
1314151281191040327615
1413121591081161572403
1512131410911872461530

Centre:   0   6

Centrum:   0   3   6   7

Nucleus:   0   6

Left Nucleus:   0   3   6   7

Middle Nucleus:   0   6

Right Nucleus:   0   6


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

11 Elements of order 2:   1   2   3   4   5   6   7   8   11   14   15

4 Elements of order 4:   9   10   12   13

Commutator Subloop:   0   6

Associator Subloop:   0   6

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

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

Al Property:   FAILS. The left inner mapping L1,8 = (8,14)(9,13) is not an automorphism.   L1,8(2*8) neq L1,8(2)*L1,8(8)

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