GAP Data Library "small"
[WWW homepage]
This library has the status of an accepted GAP package,
communicated in January 2002 by
Mike F. Newman, Canberra. It is part of the main
GAP distribution.
Authors
Hans Ulrich Besche,
Bettina Eick, and
Eamonn O'Brien.
Description
The small groups library contains all groups of certain ``small''
orders. The groups are sorted by their orders and they are listed up to
isomorphism; that is, for each of the available orders a complete and
irredundant list of isomorphism type representatives of groups is given.
Currently, the library contains the following groups:
- those of order at most 2000 except 1024 (423 164 062 groups);
- those of order 5^5 and 7^4 (92 groups);
- those of order q^n * p where q^n divides 2^8, 3^6, 5^5 or 7^4
and p is an arbitrary prime different to q;
- those whose order factorises into at most 3 primes.
The library also has an identification function: it returns the library
number of a given group. Currently, this function is available for all
orders in the library except 512 and 1536.
The library is organised in 8 layers. Each layer contains the groups of
certain orders and their corresponding group identification routines. It
is possible to install the first $n$ layers of the group library and the
first $m$ layers of the group identification for each
$1 <= m <= n <= 8$. In summary, the layers are:
- the groups whose order factorises into at most 3 primes.
- the remaining groups of order at most 1000 except 512 and 768.
- the remaining groups of order 2^n * p with n < 9 and p an odd
prime.
- the groups of order 5^5 and 7^4 and the remaining groups of order
q^n * p where q^n divides 3^6, 5^5 or 7^4 and p is a prime with p
not equal to q.
- the remaining groups of order at most 2000 except 1024, 1152, 1536
and 1920.
- the groups of orders 1152 and 1920.
- the groups of order 512.
- the groups of order 1536.
GAP Manual section
Small Groups
Contact addresses
Hans Ulrich Besche
Institut Computational Mathematics
Universität Braunschweig
Pockelsstr. 14
38106 Braunschweig
Germany
email: hubesche@tu-bs.de
Bettina Eick
Institut Computational Mathematics
TU Braunschweig
Pockelsstr. 14
D-38106 Braunschweig
Germany
email: beick@tu-bs.de
Eamonn O'Brien
Department of Mathematics
University of Auckland
Auckland, Private Bag 92019
New Zealand
email: obrien@math.auckland.ac.nz
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