Right Bol Loop 16.11.4.14 of order 16


0123456789101112131415
1230547698111013151214
2301765411109815141312
3012674510118914121513
4675013212131415810911
5467102313121514981110
6754320114151213101189
7546231015141312119108
8101191513141221304567
9810111412151330215746
1011981315121412036475
1198101214131503127654
1213151411910875640312
1315141210811964751023
1412131591181057463201
1514121381091146572130

Centre:   0   2

Centrum:   0   2   5   6

Nucleus:   0   2

Left Nucleus:   0   2   5   6

Middle Nucleus:   0   2

Right Nucleus:   0   2


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

11 Elements of order 2:   2   4   5   6   7   9   10   12   13   14   15

4 Elements of order 4:   1   3   8   11

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,8 = (12,15)(13,14) is not an automorphism.   L1,8(4*8) neq L1,8(4)*L1,8(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   64 (1024, 2048)


/ revised October, 2001