Right Bol Loop 16.7.2.442 of order 16


0123456789101112131415
1032674598151211141310
2457160311121389151014
3675041212111498101513
4210537613141110159812
5764302115109141312118
6301725414131215108911
7546213010158131411129
8101211141513957123640
9151112131014875032461
1081413129111510546327
1112101581491364301752
1211151091381446210573
1314891012151132675014
1413981511101223457106
1591314118121001764235

Centre:   0

Centrum:   0   5

Nucleus:   0

Left Nucleus:   0   1   5   7

Middle Nucleus:   0

Right Nucleus:   0

1 Element of order 1:   0

7 Elements of order 2:   1   5   7   11   12   13   14

8 Elements of order 4:   2   3   4   6   8   9   10   15

Commutator Subloop:   0   1   5   7

Associator Subloop:   0   1   5   7

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 3:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,2 = (2,6)(3,4)(8,15)(9,10)(11,13)(12,14) is not an automorphism.   L1,2(2*8) neq L1,2(2)*L1,2(8)

Ar Property:   HOLDS (i.e. every right inner mapping Ra,b is an automorphism)

Right (Left, Full) Mult Group Orders:   128 (18432, 36864)


/ revised November, 2001