Example for Database of Groups of Order Dividing 729

These are examples of how to use the thrgps database.

To obtain the P-CP for the 57th group of order 729, first restore the appropriate library file and the procedure gen3:

> load thrgp729;
Loading "thrgps/thrgp729"
Library of 504 groups of order 729 set up
> load gen3;
Loading "thrgps/gen3"

> GP := gen3(gps[57], 1);
Lower exponent-3 central series for G
Group: G to lower exponent-3 central class 1 has order 3^2
Group: G to lower exponent-3 central class 2 has order 3^3
Group: G to lower exponent-3 central class 3 has order 3^5
Group: G to lower exponent-3 central class 4 has order 3^6

The following example (output not shown) illustrates looping over all the groups:

> for x in gps do
>     GP := gen3(x, 0);
>     print Order(Centre(GP));
> end for;