The major function of group selection is presumably directly to promote the sustained reproductive success (lineal survival) of the group, in face of the spontaneous tendency for random change to promote the individual (and other lower level, below group) levels of selection.
For example, group selection would be of value in sustaining the cell in face of the tendency of cell components (for example the nucleus, or of evolvable organelles such as the mitochondria, chloroplast or centriole) to become 'free-riders' or parasites (taking net reproductive benefits from the cell, while contributing less than this to the cell, or nothing, or actively-harming the probability of the survival and ultimately reproduction of the cell).
A more clear cut example is the individual specialized cell in the context of a multicellular organism; there is a tendency for individual cells to evolve towards 'opting out' of the coordinated cooperation of the whole organism - and taking more than they give. This is termed neoplastic change, and the tendency is what leads to cancers - cancers constitute an internally-generated cellular parasite.
But the main posited role for group selection has been in the context of animal society - especially in social animals (social insects such as ants or bees, and social mammals such as many primates including Man - as well as other mammals with differentiated social roles such as naked mole rats or meerkats).
The problem for the sustained survival of social animals over many generations is that individuals tend to evolve to enhance their personal reproductive success at the expense of the group - taking benefits from social living while avoiding the costs and duties of social living - thereby destroying the social structure.
The fact that social animals are known to have existed over many generations is evidence that his problem has been solved historically - and the underpinning mechanism is usually regarded to be kin selection (aka inclusive fitness) together with reciprocity (the mutual benefits of cooperation).
The difficulty with such individual level mechanisms as kin selection is that they must themselves evolve in a context where the spontaneous tendency is for adaptations to be lost - on top of the spontaneous tendency for kin selection and reciprocity to be damaged by spontaneous mutations. In other words it is very difficult to evolve a high level mechanism of social living on top of all the other layers of cooperation at sub-cellular and cellular levels - all of which are vulnerable to destruction by spontaneous mutations.
This is presumably one reason why social animals have been a late arrival on the evolutionary scene, in the past couple of hundred thousand years - however, once a stable and sustainable adaptation had arisen to enforce sociality, these animals have more-or-less taken over the earth by becoming the dominant species. Thus ants and termites dominate the tropical regions (in terms of biomass) while more recently humans have come to dominate the temperate zones.
Clearly sociality is a tremendous advantage - the difficulties are in evolving it, and sustaining it in the face of continued spontaneous mutations with each generation; and the tendency of sub-lethal deleterious mutations to accumulate generation-upon-generation; plus any environmental change and variety which is itself a consequence of the high adaptiveness of these species.
However, the very success of social animals, their dominance, would be expected to contain the seeds of destruction - since the conditions for free-riding and parasitism are greatly increased by the expansion in numbers and the relative autonomy from environmental constraints such as food supply and predation.
(This can be seen very clearly in modern human society, where the large surplus of modern economies above subsistence allows for unprecedented levels of parasitic behaviour by individuals, and also groups - such as bureaucracies.)
A successful social species can therefore find itself in the situation when the main proximate constraint on reproductive success is competition within the species - and this creates many niches for more-or-less parasitic and exploitative behaviours (the individual profiting at the expense of the group).
In the short-term, the fastest and most secure route to enhanced reproductive success is to exploit other humans (rather than cooperate with them) - and this would tend to destroy the social structure by reproductively favouring the least social individual animals.
Group selection entails that the group has an identity, that this identity must have integrity over time, and that it be transmissible between generations. This group identity must be able to sustain itself and should also be potentially further-adaptive to some extent.
Group identity needs to be of a cognitive and behavioural nature - in other words there must be strategizing knowledge and also some kind of reasoning from this knowledge. In sum, group selection requires a group identity; and group identity requires a teleology, aim or purpose; and that purpose should 'know' (with better than random probability) how to implement itself in individuals within that group.
This is probably the basis of the intense modern suspicion of and hostility to group selection - this idea that group selection entails something like a group purpose, memory and 'mind' - which superficially sounds like a non-biological, maybe even supernatural, kind of thing.
However, social animals are based on communications between networks of individuals, and the idea of conceptualizing the complex interactions of individuals in terms of being a type of 'computational' or 'cognitive' process is actually fairly mainstream - for instance in the theories of complex systems, the mathematics of chaos and complexity and elsewhere.
So, in principle, there is no reason to exclude the possibility that webs of complexly interacting social animals can be considered as higher level, group entities - which have a tendency to sustain and reproduce themselves.
Furthermore, these networks of communications fall into patterns, and these patterns may be self-sustaining and with a tendency to expand - so there is a potential mechanism for non-genetic inter-generation transmission.
In other words, the group-level entity is a pattern of communications which is both influenced by and also influences the communications (and behaviours) of the individual components of that patter: the individual organisms. And this pattern of communications will tend to fall into relatively stable forms, forms that resist change.
(Such a stability of forms is something which has cropped up in many areas of science over more than 2000 years - since at least the time of Aristotle with his elaboration of a finite number of archetypal 'forms' or relatively stable conformations into which all things will tend to 'fall; modern conceptualizations of the same basic idea include 'strange attractors' and 'morphic fields'.)
I do not see any fatal difficulty in supposing that relatively stable and 'cognitive' patterns of inter-individual, group communications would be transmissible between generations of social animals - given that these generations are overlapping (with new group members incrementally arriving and maturing, while others are leaving and dying - but without a break in the continuity of communications).
Such a concept of 'group mind' would have implicit purpose (survival and self-propagation) implemented by problem solving and strategizing properties including memory and intelligent processing.
Therefore, in principle, this group mind entity could identify problems among individuals within the group, and (to a significant extent) suppress selfishness at the individual level - also it could foresee (with better than random probability) the need for (or potential benefits from) certain types of individual which would be useful to the group survival and reproduction. Then individuals of this type might be induced to arise from the group - perhaps by the kind of developmental switching posited by Life History theory.
So, for the putative example of genius - it seems possible that the group mind might detect and appreciate the need for, or potential benefits from, an increase in the production of geniuses (i.e. those individuals characterized by what I have termed an Endogenous personality comprising a triad of high intelligence, intuitive thinking and inner motivation).
Having calculated that such individuals would probably be of value to the group - it seems possible that either the developmental trajectory of individuals might be directed towards becoming a genius - or more fundamentally that suitable pairs of individual parents (especially those characterized by high intelligence - low mutational load) might (perhaps by broadly 'epigenetic' means, by affecting gene switching, activation, suppression etc) lead to the sexual conception of more potential geniuses who are designed to benefit the group survival and reproduction, even when this tends to reduce the probability of reproductive success in the individual geniuses.
So this above scheme could, in broad brush terms, provide a group selection mechanism by which the group benefits of genius might be acquired when the group circumstances require, despite that many or most geniuses have below average reproductive success due to their energies and efforts being directed at non-reproductive, non-social goals.