Right Bol Loop 16.7.2.443 of order 16


0123456789101112131415
1032674598111014151213
2301547610118913121514
3210765411109815141312
4657021315131412119108
5746203114121513911810
6475130213151214108119
7564312012141315810911
8912131011151410325476
9814151110131201237654
1011131289141532104567
1110151498121323016745
1214810131511957461302
1315108121491146573120
1412911151310875640213
1513119141281064752031

Centre:   0

Centrum:   0   1

Nucleus:   0

Left Nucleus:   0   1   2   3   4   5   6   7

Middle Nucleus:   0

Right Nucleus:   0

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   1   2   3   4   5   6   7

Associator Subloop:   0   1   2   3   4   5   6   7

1 Conjugacy Class of size 1:

1 Conjugacy Class of size 7:

1 Conjugacy Class of size 8:

Automorphic Inverse Property:   HOLDS

Al Property:   FAILS. The left inner mapping L1,8 = (2,6,5)(3,7,4) is not an automorphism.   L1,8(1*2) neq L1,8(1)*L1,8(2)

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

Right (Left, Full) Mult Group Orders:   128 (1625702400, 3251404800)


/ revised November, 2001