FiSGO.OrderSearch.candidates_2E

candidates_2E(prime_bounds, abs_bound=None, return_codes=True)

Returns a list of all exceptional Steinberg \({}^2E_6(q^2)\), simple groups of Lie type, whose order divides prime_bounds and is less than or equal to abs_bound.

Parameters:

• prime_bounds (list[int]) – Contains a list with the maximum powers for each prime, example: [2,0,1,0,3] means the order of the group must divide 2^2*5^1*11^3.

• abs_bound – An integer providing an upper bound to the order of the group, if None, then it is constructed from prime_bounds.

• return_codes – If False, the function returns a list of derived objects from the SimpleGroup class. If True, the function returns a list of strings, each string represents a simple group code. See SimpleGroups.simple_group_ids.

Returns:

Returns a list, the contents depend on the return_codes parameter.