effectively

adv. productively, efficiently; impressively

In mathematics, a symmetry group describes all symmetries of objects. This is formalized by the notion of a group action: every element of the group "acts" like a bijective map (or "symmetry") on some set. In this case, the group is also called a permutation group (especially if the set is finite or not a vector space) or transformation group (especially if the set is a vector space and the group acts like linear transformations of the set). A permutation representation of a group G is a representation of G as a group of permutations of the set (usually if the set is finite), and may be described as a group representation of G by permutation matrices, and is usually considered in the finite-dimensional case—it is the same as a group action of G on an ordered basis of a vector space.
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Adverb
1. in an effective manner; "these are real problems that can be dealt with most effectively by rational discussion"
(synonym) efficaciously
(antonym) inefficaciously, ineffectively
(pertainym) effective, effectual, efficacious
2. in actuality or reality or fact; "she is effectively his wife"; "in effect, they had no choice"
(synonym) in effect
(pertainym) effective

(adv.)
With effect; powerfully; completely; thoroughly.
  

Synonyms and related words:
ably, adequately, advantageously, ardently, capably, cogently, competently, conveniently, dynamically, effectually, efficiently, eloquently, energetically, expressively, fervently, fluently, forcefully, forcibly, functionally, glibly, glowingly, graphically, handily, impressively, in glowing terms, meaningfully, mightily, passionately, potently, powerfully, practically, productively, profitably, serviceably, smoothly, spiritedly, strikingly, tellingly, to advantage, to good account, to good effect, to good purpose, to good use, to profit, usefully, vehemently, vigorously, vividly, warmly, well, with a vengeance, with telling effect,