Right Bol Loop 16.5.2.253 of order 16


0123456789101112131415
1032547698151314111210
2406173511131415810912
3517062413111210915814
4260715314121191081513
5371604212141381591011
6745230110158141312119
7654321015109121114138
8101213141191576125340
9151411121381067034251
1081312111415910743526
1113151098141254370612
1214891015131123407165
1311101589121445261703
1412981510111332516074
1591114131210801652437

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

5 Elements of order 2:   1   2   5   6   7

10 Elements of order 4:   3   4   8   9   10   11   12   13   14   15

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