Right Bol Loop 16.9.2.38 of order 16


0123456789101112131415
1032547698151314111210
2406173511141315891012
3517062413121110981514
4260715314111291015813
5371604212131481510911
6745230110158141312119
7654321015109121114138
8101214131191571652430
9151412111381060743521
1081311121415917034256
1113159108141254307612
1214810915131123470165
1311108159121445216703
1412915810111332561074
1591113141210806125347

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

9 Elements of order 2:   1   2   5   6   7   9   10   11   12

6 Elements of order 4:   3   4   8   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