Right Bol Loop 16.9.4.46 of order 16


0123456789101112131415
1032547691481311151012
2406173511131214910158
3517062412111598141310
4260715313151110148129
5371604215121381091114
6745230110814121511913
7654321014109151312811
8101113121591476154302
9141215111381060735214
1081311151214917042563
1112891014131553406127
1211981410151345267031
1315101489111232510746
1491512131110801623475
1513141098121124371650

Centre:   0   7

Centrum:   0   7   12   13

Nucleus:   0   7

Left Nucleus:   0   7   12   13

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

9 Elements of order 2:   1   2   5   6   7   9   10   11   15

6 Elements of order 4:   3   4   8   12   13   14

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