[GAP Forum] Accessing groups up to isoclinism

[Vipul Naik]

Dear GAP Forum,

Two related questions:

(1) Is there an existing function in GAP or one of the available GAP
packages to check whether two given finite groups are isoclinic? I
could write a function, but I'm guessing something already written
would be more efficient.

(2) If (1) exists, this can be done in terms of (1), but it would
still be nice to have this as a standalone: access to the equivalence
classes of groups of a given order under isoclinism. 

Background: As I understand, the original classification of groups of
small prime power orders (e.g., the Hall-Senior classification up to
2^6 and the later classification for 2^7) was done by first
classifying groups up to isoclinism and then finding all the groups
within a given family of isoclinic groups. However, the ordering of
groups used by the SmallGroup library is based on somewhat different
criteria than isoclinism, so all groups in a single family under
isoclinism do not have adjacent IDs in the SmallGroup librar. I have
worked out the relation between the SmallGroup IDs and the isoclinism
families for small prime power orders, but it would be great to be
able to access the isoclinism information in pre-computed form through
GAP.

Vipul