Right Bol Loop 16.7.2.441 of order 16


0123456789101112131415
1032812764109155141311
2451211710151413631098
3812515601111314729104
4211155913141201108673
5127690321048141151113
6101013351214151127489
7901142125131115368410
8315111210141351094762
9714130415111512810326
1061314181115012549237
1115910714846230131251
1256710123984130111514
1314843159102671211015
1413482111093765151012
1511109613487321145120

Centre:   0

Centrum:   0   5

Nucleus:   0

Left Nucleus:   0   1   5   11   12   13   14   15

Middle Nucleus:   0

Right Nucleus:   0

1 Element of order 1:   0

7 Elements of order 2:   1   5   11   12   13   14   15

8 Elements of order 4:   2   3   4   6   7   8   9   10

Commutator Subloop:   0   5   13   15

Associator Subloop:   0   5   13   15

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 = (2,8)(3,4)(5,15,13)(6,9)(7,10)(11,12,14) is not an automorphism.   L1,2(1*5) neq L1,2(1)*L1,2(5)

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

Right (Left, Full) Mult Group Orders:   64 (18432, 36864)


/ revised November, 2001