The Magma group has developed efficient methods for obtaining the
O'Nan-Scott decomposition of a primitive group. The elementary
abelian regular normal subgroup of an affine primitive group is
constructed by a polynomial-time algorithm based on ideas published
by P. Neumann. For example, Magma finds the EARNS of
AGL(10, 3) which
has degree 59,049 and order
17046196453240220939126401085378073952125928970649600in 36 seconds. The construction of the socle and the analysis of a
non-affine primitive group is performed by algorithms based on ideas
of Cannon, Holt and Kantor. A 2-transitive group is identified as
an abstract group using an algorithm published by Cameron and
Cannon.