Right Bol Loop 16.3.4.2 of order 16


0123456789101112131415
1032547698111015141312
2310675410111512148913
3201764511101215139814
4567012312151413811109
5476103215121314910118
6754231014139810121511
7645320113148911151210
8911101215131410675324
9810111512141301764235
1011891413121532107456
1110981314151223016547
1215131489111054231760
1314151211109867452103
1413121510118976543012
1512141398101145320671

Centre:   0   1   4   5

Centrum:   0   1   4   5

Nucleus:   0   1   4   5

Left Nucleus:   0   1   4   5   10   11   13   14

Middle Nucleus:   0   1   4   5

Right Nucleus:   0   1   4   5

1 Element of order 1:   0

3 Elements of order 2:   1   4   5

12 Elements of order 4:   2   3   6   7   8   9   10   11   12   13   14   15

Commutator Subloop:   0   1   4   5

Associator Subloop:   0   4

4 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (2-1)(9-1) neq (2*9)-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:   32 (64, 256)


/ revised October, 2001