Right Bol Loop 16.7.4.53 of order 16


0123456789101112131415
1230547691181015141312
2301765411109814151213
3012674510811913121514
4675231012131514119810
5467320115121413108911
6754102313141215911108
7546013214151312810119
8911101415131201327546
9111081312141512036457
1089111514121330215764
1110891213151423104675
1213141581091146570321
1314151210811967453012
1415121311910875642103
1512131491181054761230

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

7 Elements of order 2:   2   8   11   12   13   14   15

8 Elements of order 4:   1   3   4   5   6   7   9   10

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 = (4,7)(5,6) 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