Right Bol Loop 16.9.4.28 of order 16


0123456789101112131415
1091312101415116348527
2915111012014137453816
3101115140121398126745
4111390141012155271638
5131209151110144762183
6140121311159101835472
7151410111390122584361
8121014159131103617254
9278541630111310121514
1034127856110914151213
1145672381109150141312
1283216547131401591011
1358761432121514901110
1461438725151210131109
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

9 Elements of order 2:   1   4   7   8   9   10   13   14   15

6 Elements of order 4:   2   3   5   6   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)(3-1) neq (1*3)-1

Al Property:   FAILS. The left inner mapping L1,1 = (2,6)(3,5)(4,8)(9,14)(10,13)(11,12) 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