Right Bol Loop 16.13.2.98 of order 16


0123456789101112131415
1032547691411151081312
2406173510121491311158
3517062411101314815129
4260715312159814101113
5371604215118139121014
6745230113812101514911
7654321014131512119810
8910121115131406543172
9811151012141310425763
1012891314111523061457
1115981413101235107246
1210131489151142670531
1314121015118967352014
1413151112109871234605
1511141398121054716320

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

13 Elements of order 2:   1   2   5   6   7   8   9   10   11   12   13   14   15

2 Elements of order 4:   3   4

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