Right Bol Loop 16.3.2.49 of order 16


0123456789101112131415
1230547698111014121513
2301765411109815141312
3012674510118913151214
4675231012131415119108
5467320114151213101189
6754102313121514981110
7546013215141312810911
8101191214131521304567
9810111412151330215746
1011981315121412036475
1198101513141203127654
1214151311109876542310
1312141598111054761203
1415131210118967453021
1513121489101145670132

Centre:   0   2

Centrum:   0   2

Nucleus:   0   2

Left Nucleus:   0   2

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

3 Elements of order 2:   2   9   10

12 Elements of order 4:   1   3   4   5   6   7   8   11   12   13   14   15

Commutator Subloop:   0   2

Associator Subloop:   0   2

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 L1,8 = (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:   128 (1024, 2048)


/ revised October, 2001