Bol Loops of Order 30

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

a quick review of the relevant definitions;
a suitable list of references for further explanation, proofs, etc.;
a cross-reference list comparing this list with previously published lists of groups and loops;
descriptions of these loops in html format, found through the links below; and
the Cayley tables (15 KB) in plain text form.

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.)

The 5 Isotopy Classes of Bol Loops

Isotopy Class 0: The 2 Known Non-associative Bol Loops 30.1.2.0, 30.1.2.1

Isotopy Classes 1,2,3,4: The 4 Groups 30.1.30.0 30.3.5.0 30.5.3.0 30.15.1.0

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