These tables provide a lot of information about finite groups of orders up to 100, excluding groups of order 64 and 72

For each group there's a presentsation in terms of generators and relations

For smaller groups a group table is given

For all groups, except the larger abelian groups, the character table is given

Among other information provided are the number of elements of each order, the conjugacy classes, the normal subgroups and the quotient groups, the ascending central series and the derived series.

The catalogue at the moment only extends to orders 1 to 63. Further sizes will be added progressively.

  • Groups of Orders 1-16
  • Groups of Orders 17-31
  • Groups of Order 32
  • Groups of Orders 33-47
  • Groups of Order 48
  • Groups of Orders 49-63
  • The following table helps to identify a group given the orders of its elements, sizes of its conjugacy classes and other numerical information.

  • Identifying Groups
  • The following table identifies groups that are part of a family, such as dihedral groups or symmetric groups.

  • Isomorphic Groups
  • The following table summarises the Order Profiles (numbers of elements of each order) and Class Equations

  • Orders and Class Equations