for n at most 6 and p prime; those of order p7 for p = 3, 5, 7, 11 (907 489 groups); those of order pqn where qn divides 28, 36, 55 or 74 and p is an arbitrary prime which differs from q; those whose orders factorise into at most 3 primes (not necessarily distinct). It contains explicit descriptions of the available groups in computer readable format. The smallest order for which the SmallGroups library does not have information is 1024. See also Classification of finite simple groups Composition series List of finite simple groups Number of groups of a given order Small Latin squares and quasigroups Sylow theorems Notes References , Table 1, Nonabelian groups order<32. External links Particular groups in the Group Properties Wiki Groups of given order GroupNames database Groups that are small Groups that are small Finite groups