I like to refer to this one, because it’s the most specific one unlike Umberto Eco’s definition which is more open ended and applies to almost every political movement in the 21st century depending on your perspective and are more about the characteristics needed for a fascist movement to rise rather than the characteristics possesd by fascism itself.

Italian historian of fascism Emilio Gentile described fascism in 1996 as the “sacralization of politics” through totalitarian methods and argued the following ten constituent elements: a mass movement with multiclass membership in which prevail, among the leaders and the militants, the middle sectors, in large part new to political activity, organized as a party militia, that bases its identity not on social hierarchy or class origin but on a sense of comradeship, believes itself invested with a mission of national regeneration, considers itself in a state of war against political adversaries and aims at conquering a monopoly of political power by using terror, parliamentary tactics, and deals with leading groups, to create a new regime that destroys parliamentary democracy; an “anti-ideological” and pragmatic ideology that proclaims itself antimaterialist, anti-individualist, anti-liberal, antidemocratic, anti-Marxist, populist and anticapitalist, and expresses itself aesthetically more than theoretically by means of a new political style and by myths, rites, and symbols as a lay religion designed to acculturate, socialize, and integrate the faith of the masses with the goal of creating a “new man”; a culture founded on mystical thought and the tragic and activist sense of life conceived of as the manifestation of the will to power, on the myth of youth as artificer of history, and on the exaltation of the militarization of politics as the model of life and collective activity; a totalitarian conception of the primacy of politics, conceived of as an integrating experience to carry out the fusion of the individual and the masses in the organic and mystical unity of the nation as an ethnic and moral community, adopting measures of discrimination and persecution against those considered to be outside this community either as enemies of the regime or members of races considered to be inferior or otherwise dangerous for the integrity of the nation; a civil ethic founded on total dedication to the national community, on discipline, virility, comradeship, and the warrior spirit; a single state party that has the task of providing for the armed defense of the regime, selecting its directing cadres, and organizing the masses within the state in a process of permanent mobilization of emotion and faith; a police apparatus that prevents, controls, and represses dissidence and opposition, including through the use of organized terror; a political system organized by hierarchy of functions named from the top and crowned by the figure of the “leader”, invested with a sacred charisma, who commands, directs, and coordinates the activities of the party and the regime; corporative organization of the economy that suppresses trade union liberty, broadens the sphere of state intervention, and seeks to achieve, by principles of technocracy and solidarity, the collaboration of the “productive sectors” under control of the regime, to achieve its goals of power, yet preserving private property and class divisions; a foreign policy inspired by the myth of national power and greatness, with the goal of imperialist expansion

Christian authoritarianism while having some overlap of course would argue the primacy of the bible, while fascism is more about the primacy of the state and even religion is subjected to the state.