Right Bol Loop 16.7.2.383 of order 16


0123456789101112131415
1035247698111510141312
2401673510118139121514
3517062411109814151213
4260715312151314810119
5376104215121491311108
6742530113141210158911
7654321014131512119810
8910121115131406543172
9811101512141317425063
1012813914111524716350
1115981413101235670241
1210131489151142107536
1314121510118960352714
1413151112109871234605
1511149138121053061427

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.


1 Element of order 1:   0

7 Elements of order 2:   1   2   5   6   7   8   14

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