Right Bol Loop 16.5.6.1 of order 16


0123456789101112131415
1032547698141211151013
2406173511121389101514
3517062412111598141310
4260715313151110148129
5371604215131214109118
6745230110148131511912
7654321014109151312811
8101113121591476154302
9141215111381067045213
1081311151214910732564
1112891014131554376120
1211981410151345267031
1315101489111232510746
1491512131110801623475
1513141098121123401657

Centre:   0   7

Centrum:   0   7   11   12   13   15

Nucleus:   0   7

Left Nucleus:   0   1   6   7   11   12   13   15

Middle Nucleus:   0   2   5   7

Right Nucleus:   0   2   5   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

5 Elements of order 2:   1   2   5   6   7

10 Elements of order 4:   3   4   8   9   10   11   12   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:   32 (64, 256)


/ revised October, 2001