37.14 The Small Groups Library

This library contains all groups of order at most 1000 except for 512 and 768 up to isomorphism. There are a total of 174366 such groups.

SmallGroup( size, i )

The function SmallGroup( size, i ) returns the ith group of order size in the catalogue. It will return an AgGroup, if the group is soluble and a PermGroup otherwise.

NumberSmallGroups( size )

The function NumberSmallGroups( size ) returns the number of groups of the order size.

AllSmallGroups( size )

The function AllSmallGroups( size ) returns the list of all groups of the order size.

UnloadSmallGroups( list of sizes )

It is possible to work with the catalogue of groups of small order just using the functions described above. However, the catalogue is rather large even though the groups are stored in a very compact description. Thus it might be helpful for a space efficient usage of the catalogue, to know a little bit about unloading parts of the catalogue by hand.

At the first call of one of the functions described above, the groups of order size are loaded and stored in a compact description. GAP will not unload them itsself again. Thus if one calls one of the above functions for a lot of different orders, then all the groups of these orders are stored. Even though the description of the groups is space efficient, this might use a lot of space. For example, if one uses the above functions to load the complete catalogue, then GAP will grow to about 12 MB of workspace.

Thus it might be interesting to unload the groups of some orders again, if they are not used anymore. This can be done by calling the function UnloadSmallGroups( list of sizes )

If the groups of order size are unloaded by hand, then GAP will of course load them again at the next call of SmallGroup( size, i ) or one of the other functions described at the beginning of this section.

IdGroup( G )

Let G be a PermGroup or AgGroup of order at most 1000, but not of order 256, 512 or 768. Then the function call IdGroup( G ) returns a tuple [size, i] meaning that G is isomorphic to the i-th group in the catalogue of groups of order size.

Note that this package calls and uses the ANUPQ share library of GAP in a few cases.

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