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Dear Gordon, dear GAP-Forum,

- is the order in which the groups appear arbitrary or are

there some principles underlying it? I notice that the

abelian groups don't seem to appear as the first few groups

of each order; this is mildly surprising for lists of groups,

but maybe there is a deeper underlying principle of which I

am not aware.

There are some principles. They are induced by the algorithms used

to construct the groups. Since we employed four different construction

methods, the ordering principles for the groups may depend on the

considered group order.

Most of the groups have been constructed using the p-group generation

algorithm or the Frattini extension method. In these two cases the

first sorting criteria is the order of the socle of the Frattini factor

of the given group. For example, for the groups of order 6 we obtain

that both groups are equal to their Frattini factors and for their socles

we find that |Soc( S_3 )| = 3 and |Soc( C_2 x C_3 )| = 6. Thus the

non-abelian group S_3 is listed first.

Further sorting principles and an overview on the construction and

setup of the Small Groups library can be found in 'A millenium project:

constructing small groups' by Hans Ulrich Besche, myself and Eamonn

O'Brien. This article is going to appear in the IJAC journal and can

also be found on my web page http://www.mathematik.uni-kassel.de/~eick.

- is this order guaranteed to remain unchanged (so that if I

refer in a paper to "the 5044th group of order 512" then this

can definitely be recovered by the future reader)

Yes, the ordering of the groups contained in the Small Groups library

is guaranteed to remain unchanged! The authors of the Small Groups library

all believe that this is a very important feature of this library and

hence we are not going to change the ordering of the groups.

Best wishes, Bettina

Miles-Receive-Header: reply

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