Right Bol Loop 16.7.2.59 of order 16


0123456789101112131415
1032547691481215111013
2406173511121314109158
3517062412151110814139
4260715313111591481210
5371604215131289101114
6745230110814131115912
7654321014109151312811
8101112131591401624375
9141211151381017032564
1081315111214960745213
1112810914131523471650
1211914810151335267041
1315108149111242510736
1491513121110876153402
1513149108121154306127

Centre:   0   7

Centrum:   0   7

Nucleus:   0   7

Left Nucleus:   0   7

Middle Nucleus:   0   7

Right Nucleus:   0   7


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

7 Elements of order 2:   1   2   5   6   7   8   14

8 Elements of order 4:   3   4   9   10   11   12   13   15

Commutator Subloop:   0   7

Associator Subloop:   0   7

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:   128 (128, 1024)


/ revised October, 2001