Right Bol Loop 16.7.4.12 of order 16


0123456789101112131415
1039810421575131411126
2451106011131231589714
3610131241011142815795
4211213310514116971580
5106430215981141312117
6301012514121347981511
7814051511131109643212
8713141191210501532641
9151211148131057462310
1054891367150121114132
1113726141594312010158
1214815713942611100513
1311971512836214150104
1412156211783413511009
1591150714121018234613

Centre:   0   5   12   13

Centrum:   0   5   12   13

Nucleus:   0   5   12   13

Left Nucleus:   0   2   5   6   8   9   12   13

Middle Nucleus:   0   5   12   13

Right Nucleus:   0   5   12   13

1 Element of order 1:   0

7 Elements of order 2:   1   5   10   11   12   13   14

8 Elements of order 4:   2   3   4   6   7   8   9   15

Commutator Subloop:   0   5   12   13

Associator Subloop:   0   13

4 Conjugacy Classes of size 1:

3 Conjugacy Classes of size 4:

Automorphic Inverse Property:   FAILS.   (1-1)(3-1) neq (1*3)-1

Al Property:   HOLDS (i.e. every left inner mapping La,b is an automorphism)

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

Right (Left, Full) Mult Group Orders:   32 (64, 256)


/ revised October, 2001