Right Bol Loop 16.7.2.9 of order 16


0123456789101112131415
1032765498141315111012
2301547610148121115913
3210674511131281091514
4756023115121314910118
5647201313111591481210
6574310214109151312811
7465132012151110814139
8121314151011947561230
9151413121110874320651
1014151213891153416072
1113121514981062145703
1281110914131510654327
1311891015121426073415
1410981112151335702146
1591011813141201237564

Centre:   0   4

Centrum:   0   4

Nucleus:   0   4

Left Nucleus:   0   4

Middle Nucleus:   0   4

Right Nucleus:   0   4


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

7 Elements of order 2:   1   2   3   4   5   6   7

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

Commutator Subloop:   0   4

Associator Subloop:   0   4

2 Conjugacy Classes of size 1:

7 Conjugacy Classes of size 2:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (2,5)(3,6)(8,15)(9,12)(10,13)(11,14) is not an automorphism.   L1,8(2*8) neq L1,8(2)*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