Summary of computations of minimal generating sets of invariant rings of transitive permutation groups

Common notations:
n
number of variables
i
ith transitive group on n variables
p
characteristic
G
group
betap
a priori degree bound
beta
real degree bound

Characteristic 0 (actually 32749)

Characteristic 2

Characteristic 3

Benchmark

The computations were done with four different methods: