Contents of Database of Groups of Order Dividing 256

This database contains descriptions for the groups of order dividing 256. The descriptions are stored in files according to the first three entries. If the second entry N is 7 or less, the group will have an order O = 2^N and the description will be found in the file twogpO. If the group has order 256 (i.e., N is 8), then the descriptions are split up according to generator number first, and sometimes by exponent-p class as well. Thus the files twogpdD contain the D generator groups of order 256, while the files twogpdDX contain the D generator groups of order 256 and exponent-p class of Num(X) where Num(X) is the position of X in the alphabet (i.e., Num(a) is 1).

The files are:

twogp2          twogpd1         twogpd4a        twogpd5c
twogp4          twogpd2         twogpd4b        twogpd5d
twogp8          twogpd3a        twogpd4c        twogpd5e
twogp16         twogpd3b        twogpd4d        twogpd6
twogp32         twogpd3c        twogpd4e        twogpd7
twogp64         twogpd3d        twogpd5a        twogpd8
twogp128        twogpd3e        twogpd5b

A procedure, gen2, is also supplied with the database.

The groups are arranged as a sequence gps. The following criteria are used, in turn, to determine the index of a group in the sequence:

1. increasing generator number (the generator number d of a group G is the smallest cardinality of a set of generators of G);
2. increasing exponent-p class;
3. the position of its parent in the sequence of the appropriate order;
4. the sequence in which the implementation of the p-group generation algorithm outputs the immediate descendants of a group.

The compact description for a group encodes the exponents of the pcp of the group. There are (n-1).n.(n+1)/6 such exponents for a group of order 2^n, each of which is either 0 or 1. Each compact description is a sequence of 4 integers. The first entry is the generator number, the second is the number of pcp generators, the third is the exponent-p class of the group and the fourth is an integer encoding the exponents for the pcp. The compact description of each group is stored as an element of a sequence gps. For further details, consult the decoding procedure gen2.