Right Bol Loop 16.5.2.273 of order 16


0123456789101112131415
1036274598151213141110
2457160311121481015913
3670541214131110159812
4215037612111398101514
5764302115109131411128
6301725413141215981011
7542613010158141112139
8101112141513957163240
9151411131012875032461
1081213119141510546327
1114159101381263451072
1213981514101136275104
1312810911151424307516
1411101581291342610753
1591314128111001724635

Centre:   0   5

Centrum:   0   5

Nucleus:   0   5

Left Nucleus:   0   3   4   5

Middle Nucleus:   0   5

Right Nucleus:   0   5


Comm(L):   This graph has as its 7 vertices the nontrivial cosets of the centre. Edges represent non-commuting cosets. Here we print (in reverse video) the complementary graph, in which edges represent commuting cosets.


1 Element of order 1:   0

5 Elements of order 2:   1   3   4   5   7

10 Elements of order 4:   2   6   8   9   10   11   12   13   14   15

Commutator Subloop:   0   5

Associator Subloop:   0   5

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:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

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

Right (Left, Full) Mult Group Orders:   64 (128, 512)


/ revised October, 2001