Middle class populist movement that punches up, but predominantly kicks down. Aside from the kicking down part (well, and some punching up at prominent democratic leaders), none of these apply. The Thirty were ultimate elitists seeking to create a very narrow, very tight, oligarchy. There was nothing middle class or populist about them. Theramenes, it is true, appears to have favored a moderate oligarchy that would admit all men of hoplite status or above. Given different circumstances, one can imaging him inciting the hoplites to resent that navy rabble that ruined the city by getting them into this senseless war and refused to get out when the going was good.* In such a case, Theramenes might have made a pretty good right-wing populist, or even a proto-fascist. But it would also be unthinkable in the context of Ancient Greece, where "respectable" figures like Theramenes despised rabble rousers, and the whole idea of a populist movement based mostly on kicking down does not seem to have occurred to anyone.
Driven by both fear and ambition, but fear predominates. Once again, oligarchy in Classical Greek appears to have been altogether driven by ambition.
A paramilitary party seizing power and claiming an effective monopoly on political activity. That is a fair description of the 400. The Thirty went through the outward forms of participating in the democracy before seizing power, but they were effectively agents of a foreign power.
A. The fascist negations:
Anti-radical: Fear of radical revolution does not seem to have been at issue, so no. If anything, the Thirty were the radicals.
Anti-liberal: If by this we mean seeking to narrow the circle of people who morally matter, then yes, the Thirty were anti-liberal, in the extreme.
Anti-conservative: Although minimal lip service was paid to the "ancestral constitution," it is clear that Critias in particular, and no doubt many others, had no respect whatever for tradition, for traditional values, conventional religion and morality, and the like. They are quite properly described as anti-conservative.
B. Ideology and goals:
-- Creation of a new nationalist authoritarian state based not merely on traditional principles or models
-- Organization of some new kind of regulated, multiclass, integrated national economic structure, whether called national corporatist, national socialist, or national syndicalist
-- The goal of empire or a radical change in the nation’s relationship with other powers
-- Specific espousal of an idealist, voluntarist creed, normally involving the attempt to realize a new form of modern, self-determined, secular culture.
Except for the part about empire or radical change in international relations, there are all modern concepts quite foreign to Ancient Greece. They presuppose a society in which all members are citizens (though not participants in the decision-making process). As for international matters, the Thirty showed no interest in the subject and were faithfully subservient to Sparta.
C. Style and organization:
- Emphasis on aesthetic structure of meetings, symbols, and political choreography, stressing romantic and mystical aspects. There is nothing to suggest this, nor should we expect it. This is a populist feature of fascism, and the Thirty were anything but populist.
-- Attempted mass mobilization with militarization of political relationships and style and with the goal of a mass party militia. Once again, no. The goal was a narrow military rule over a passive population.
-- Positive evaluation and use of, or willingness to use, violence. Taken to the extreme. The Thirty were nothing if not violent.
-- Extreme stress on the masculine principle and male dominance, while espousing the organic view of society. On the one hand, I would say no more than any other Ancient Greeks. On the other hand, if this means the sort of organization that sees reason, morality, constraint, and even thought as emasculating, I suppose you might see it to some extent among the Thirty.
-- Exaltation of youth above other phases of life, emphasizing the conflict of generations, at least in effecting the initial political transformation. This is a bit hard to say, although there are some hints that the Thirty, like the 400 before them, drew their support particularly among the young. First and foremost, the extreme violence of their government suggests that it was one of young men. Second is simply the vague impression that it would be young men, who never saw the democracy in its glory day but only in its ruin under the Peloponnesian War who would be most likely to be disillusioned with democracy and think an oligarchy could do better. And there were the audacious young men with daggers sent to intimidate the Council. So maybe.
-- Specific tendency toward an authoritarian, charismatic, personal style of command, whether or not the command is to some degree initially elective. There appears to have been at least some degree of this with Critias, who offered a very person, authoritarian style of leadership. The movement appears to have started to break down once he was killed. And Theramenes, in saying that Critias made enemies of democrats and oligarchs alike, seems to have been accusing him of wanting a personal dictatorship. But he never quite achieved that. He still had to carry the approval of at least a majority of the Thirty.
Mobilizing passions of fascism:
-- a sense of overwhelming crisis beyond the reach of any traditional solutions; No, at least not at first. This is part of the fear side of fascism, and the Thirty were based mostly on ambition. Then again, when Thrasybulus and the exiles showed up and started defeating them, this sense of crisis did begin. And Critias certainly felt no restriction to "traditional solutions"!
-- the primacy of the group, toward which one has duties superior to every right, whether universal or individual, and the subordination of the individual to it; This seems like a fair description of Critias' outlook, at least to the extent of placing his group (whether the Thirty or his small citizen body) ahead of any individual or universal right and giving zero moral weight to anyone who stood in their way. Subordination of the individual -- probably yes, unless that individual is named Critias! Most others, by contrast, were probably not prepared to take things so far.
-- the belief that one's group is a victim, a sentiment which justifies any action, without legal or moral limits, against the group's enemies, both internal and external; Clearly Critias was ready to take any action, without legal or moral limits, against his group's enemies, internal or external. Most of the others were probably not prepared to go quite so far. But seeing one's group as a victim is more of the overall fear-based aspect of fascism, which does not seem to have applied as much here. More at work was the belief that the oligarchs were the best rulers (in the case of some), or simply raw lust for power (in the case of Critias, and perhaps others).
-- dread of the group's decline under the corrosive effect of individualistic liberalism, class conflict, and alien influences; Probably.
-- the need for closer integration of a purer community, by consent if possible, or by exclusionary violence if necessary; Yes, I would say. Not in the same manner as modern fascism, but the Thirty were shrinking the citizen body down to 3000 like-minded eligible participants, with the tight bond of mutual criminality and fear of retaliation.
-- the need for authority by natural leaders (always male), culminating in a national chief who alone is capable of incarnating the group's destiny; Well, Critias saw things in those terms anyhow. Not so sure about the others.
-- the superiority of the leader's instincts over abstract and universal reason; Ditto.
-- the beauty of violence and the efficacy of will, when they are devoted to the group's success; In spades!
-- the right of the chosen people to dominate others without restraint from any kind of human or divine law, right being decided by the sole criterion of the group's prowess in a Darwinian struggle. Well, once again, that seems like a fair description of how Critias saw things. Most oligarchs, it seems reasonable to say, were not prepared to go so far and preferred to ground their claimed right to power on moral grounds, particularly the claim that they were "the good and the fair" and other such terms the applied to themselves, basically, on claims of moral superiority. But there is ample evidence that, like elites everywhere and always, the aristocracy in classical times confused its own privileges with the public good. When they claimed to better serve the public good, most aristocrats did not classify the lower classes as part of the "public."**
In short, the Thirty had none of the populist features of fascism, few of its fear-based features (and then only when they had so provoked the general public as to give themselves ample grounds for fear), and probably not most of its paramilitary features, as fascist paramilitaries are essentially populist. What it had in common with fascism was (1) violence, (2) a powerful leader, and (3) its amorality, or at least definition of morality solely in terms of advancing the interest of one's group. But while fascism defines its "group" as a nation, the Thirty defined it as, at best, a narrow and tight oligarchy and at worst (by Critias) a clique of conspirators.
Yet surprisingly, the Thirty has a different trait in common with some of the lesser-known and less successful fascist movements, ones like the Hungarian Arrow Cross, the Romanian Iron Guard, and the Croatian Ustasha. These were fascist movement that never acquired the sort of popular following seen in Germany or Italy and were never able to take power on their own. But they were installed in power by Nazi occupiers and had brief but extraordinarily savage reigns as despised collaborationists. This was particularly ironic in the case of modern fascism, which is a form of hyper-nationalism. Critias and the Thirty were not nationalists, and Critias at least was a known Laconophile (Spartophile), so the irony is not present in their case. Nonetheless, although the Thirty had little in common with modern fascism, it is well to keep those movements in the back of one's mind, just as reminders that even fascism is not always what we expect.
*Of course, this would go contrary to actual, historical fascism, which is quite militaristic.
**Just as most democrats did not fit slaves into that category, and all invariably saw the best role of women as maximum subjugation to men).