database for the structure of groups I am looking for a database where I can look up the structure of any small
 group (lets say to order 100). I know that SAGE has such a database, but 4-7
 Gigabyte-downloads definitely take to long with my modem. Does anyone know
 an online database for the groups ?
 A: As @Mariano suggested correctly, you can download GAP, and then you will have:

48.7 Small Groups
The Small Groups library gives access to 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 cubefree order at most 50 000   (395   703 groups);
those of order pn for n ≤ 6 and all primes p
those of order qn ·p for qn dividing 28, 36, 55 or 74 and all primes p with p ≠ q;
those of squarefree order;
those whose order factorises into at most 3 primes.

And some useful codes:
SmallGroup( order, i ) F 

SmallGroup( [order, i] ) F 


which returns the i-th group of order order in the catalogue.

AllSmallGroups( arg ) F 


which returns all groups with certain properties as specified by arg. And many othe useful codes.

The following examples are noted here fram GAP manual.
gap> G := SmallGroup( 768, 1000000 );
                    <pc group of size 768 with 9 generators>
gap> G := SmallGroup( [768, 1000000] );
                     <pc group of size 768 with 9 generators> 

A: I like these one: 


*

*Groupprops, The Group Properties Wiki

*MAGMA Online Calculator
