Right Bol Loop 16.7.2.337 of order 16


0123456789101112131415
1230547691181013121514
2301765411109814151213
3012674510811915141312
4576031212131514810119
5764120313141215911108
6457302115121413108911
7645213014151312119810
8911101215131401327645
9111081314121512036754
1089111512141330215467
1110891413151223104576
1213141589101145672103
1314151298111057463012
1415121311109876540321
1512131410118964751230

Centre:   0   2

Centrum:   0   2

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   4   7   8   11   13   15

8 Elements of order 4:   1   3   5   6   9   10   12   14

Commutator Subloop:   0   2

Associator Subloop:   0   2

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (4-1)(9-1) neq (4*9)-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