Right Bol Loop 16.9.2.68 of order 16


0123456789101112131415
1121415111013902568473
2140111013151291657384
3151112140913104875261
4131591214010113786152
5101309121411156123748
6111014091215135214837
7912131511100148432516
8091013151114127341625
9286345170111014151213
1036178245110915141312
1143782156109013121514
1287563421141513011910
1365217834151412110109
1471456382121315910011
1554821763131214109110

Centre:   0   12

Centrum:   0   12

Nucleus:   0   12

Left Nucleus:   0   12

Middle Nucleus:   0   12

Right Nucleus:   0   12


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

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

6 Elements of order 4:   1   3   4   5   6   8

Commutator Subloop:   0   12

Associator Subloop:   0   12

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:   FAILS. The left inner mapping L1,1 = (3,5)(10,15) is not an automorphism.   L1,1(2*3) neq L1,1(2)*L1,1(3)

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

Right (Left, Full) Mult Group Orders:   128 (1024, 2048)


/ revised October, 2001