I've been working on a classification of Bol loops of small order. Here is a list of the 6 known Bol loops of order 30. This includes the 4 groups of order 30 and the 2 known non-associative Bol loops of order 30 (neither of which is Moufang). The two known non-associative examples are isotopic to one another.
I have made available
In listing elements of the commutator (resp. associator) subloop of each of these loops, we have printed in italics
any elements which are not actual commutators (resp. associators). (I haven't checked, however, whether in fact this
phenomenon occurs among any the loops of order 30 in our list.)
Isotopy Class 0: The 2 Known Non-associative Bol Loops
Isotopy Classes 1,2,3,4: The 4 Groups
The 5 Isotopy Classes of Bol Loops
Naming of the Loops
For each of the loops of order 30, I have used a name 30.i.c.k where i=|I(L)|,
c=|C(L)| and the index k=0,1,2,... indicates merely the order in which each isomorphism
class of loop was first encountered by my computer.
/ revised March, 2004
Isotopy Class 0: The 2 Known Non-associative Bol Loops 18.104.22.168, 22.214.171.124
Isotopy Classes 1,2,3,4: The 4 Groups 126.96.36.199 188.8.131.52 184.108.40.206 220.127.116.11