Right Bol Loop 16.5.2.85 of order 16


0123456789101112131415
1032547698141315111012
2406173511121314109158
3517062412111598141310
4260715313151110148129
5371604215131289101114
6745230110148121115913
7654321014109151312811
8101112131591476124305
9141211151381067042513
1081315111214910735264
1112810914131554371620
1211914810151345217036
1315108149111232560741
1491513121110801653472
1513149108121123406157

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   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:   128 (128, 1024)


/ revised October, 2001