Right Bol Loop 16.5.4.18 of order 16


0123456789101112131415
1151413121090116348527
2141511131209107453816
3131215140111098126745
4121391514101105271638
5101109151213144762183
6901210111514131835472
7091011131415122584361
8111014091312153617254
9218347650111310121514
1034127856110914151213
1143612587109150141312
1285276341131401591011
1358761432121514901110
1467458123151210131109
1576583214141312111090

Centre:   0   15

Centrum:   0   10   13   15

Nucleus:   0   15

Left Nucleus:   0   10   13   15

Middle Nucleus:   0   15

Right Nucleus:   0   15


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

5 Elements of order 2:   9   10   13   14   15

10 Elements of order 4:   1   2   3   4   5   6   7   8   11   12

Commutator Subloop:   0   15

Associator Subloop:   0   15

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   FAILS.   (1-1)(5-1) neq (1*5)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,6)(9,14) 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:   64 (1024, 2048)


/ revised October, 2001