Right Bol Loop 16.7.4.58 of order 16


0123456789101112131415
1230574691181013141512
2301765411109814151213
3012647510811915121314
4576013212131514111089
5764120313141215108911
6457302115121413911108
7645231014151312891110
8911101215131403124675
9111081312141510235467
1089111514121332016754
1110891413151221307546
1213141581091146572103
1314151298111054763210
1415121311910875640321
1512131410118967451032

Centre:   0   2

Centrum:   0   1   2   3

Nucleus:   0   2

Left Nucleus:   0   1   2   3

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   4   7   8   9   10   11

8 Elements of order 4:   1   3   5   6   12   13   14   15

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)(9-1) neq (1*9)-1

Al Property:   FAILS. The left inner mapping L1,8 = (4,7)(5,6)(8,11)(9,10)(12,14)(13,15) 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