is it like a human supremacist group

Yes and it's also meant to be a satire of them and the obviously horrifying implications of fascism drawn out on a 40 thousand year timeline.

The Imperium of Man is a space empire run by Earth (or Terra). It was formerly ruled by the Emperor, an autocrat with superpowers, but because of a combination of him being a terrible dad, his failsons being unable to communicate, and just fuckery from evil gods throughout the universe, he was brainkilled by one of his sons, and half of his sons turned evil. But his corpse still has JUST enough superpowers within that it's able to power transportation throughout the galaxy

Now, officially, his corpse still rules the Imperium, but now, there's a state religion devoted to him, and multiple bureaucrats pretend to speak for him, and of course, everything he wants is in the interest of the capitalists and the imperialists. It's implied that one guy sneezing wrong in his throne room would destroy him, making the galactic transportation impossibile, thus destroying the Imperium, if it's not destroyed by either it imploding on itself or destroyed by an external forcem

Now, it's supposed to be an obvious satire of fascism. The Imperium sucks. The one thing it's supposed to do, destroy all external threats, it's terrible at. But fascists either don't see the satire or don't care.

Now, don't get me wrong, the writers are not completely innocent here. First off, the marketing is almost exclusively Space Marines looking awesome. And many of the writers can't decide between three different, contradictory messages:

1. The Imperium is a shitshow, and it's all because absolute power was given to an autocrat and his failsons.

2. The Imperium is pretty bad, but it's necessary for mankind to exist.

3. The heroic Space Marines save the humans from danger.

This obfuscates the satire pretty hard. Another thing is obsession with making it "gramdark enough". Like, originally, the Tau Empire was another faction that was as close as 40k had to good guys. It was not fascist. It wasn't perfect, but it had a good place in the story. It had the message "even though the Tau Empire isn't perfect, it's proof you don't need to be fascist to survive the universe of 40k". But people complained it wasn't grimdark enough, so it was made more evil (personally, I disagree that the concept is not grimdark, it makes the universe seem bleak that the one good faction stands no chance against the Imperium). But here's the thing: Fascists claim they like grimdark. They do not. What they think grimdarkness is is cruelty to the others. It's not. Probably the most famous story described as grimdark is George R. R. Martin's A Song of Ice and Fire, and it's not just mindless cruelty. It's a highly nuanced story in which you look into all sides. Fascists don't like that.

(As a side note, a fun way to make people who say the Imperium is fine because they're justified is to remind them that the Dark Eldar are much more justified.)

They don't get sarcasm. Art in general totally evades them. I remember looking at some Nazi poster from the 30s of the ideal German family and there was a 3 year old with the proportions of an adult man, like the kind of shit you'd see in Medieval illuminations. It was like looking at a version of American Gothic painted by an alien who had only met The Duggars.

another thing that nobody mentioned yet is that the imperium has the space marines who are the heavily-armoured genetically-modified superhuman special forces guys, and then the vaaaast majority of the army are the imperial guard who are mostly just conscripts with shitty guns who get sent in human wave style to die en masse

there are various themed imperial guard regiments that have distinctive uniforms and fighting styles of their planet. the most popular amongst warhammer nerds are the death korps of krieg, who resemble gas-masked wwi soldiers with a german-style helmet. purely coincidentally, they seem to be most commonly painted in feldgrau colour schemes

Fascists are morons who are too stupid to understand they're being made fun of

Everyone here is talking about the stories, but I want to add a point about how the hobby itself makes you really buy into the universe.

There's this concept in tabletop that sometimes called "Your Dudes", which basically describes how incredibly attached you get as a player to an army if you take the opportunity to customize them. My own Sisters of Battle aren't just pixels on a screen that I spawn in when I have enough command points, I remember painting literally every single on of their guns, liveries, and armored corsets. I've thought of names for each of the squads and applied little color variations to them so I can tell them apart on the board. I know the names of the sergeants and exactly what bits and pieces of wargear I attached to each of them so I can swap them in and out based on my army list. I have a whole backstory about how they come from a feudal planet and their liveries are super colorful because it's their family's banner.

Anyway I think that people who actually play the game get way more attached to the universe than in other hobbies, and that drives them to want to bend over backwards to explain why their faction is the Good Guys, actually.

Its numberless legions of soldiers and zealots bludgeon their way across the galaxy, delivering death to anyone and anything that doesn’t adhere to their blinkered view of purity. Almost every man and woman toils in misery either on the battlefield – where survival is measured in hours – or in the countless manufactorums and hive slums that fuel the Imperial war machine. All of this in slavish servitude to the living corpse of a God-Emperor whose commandments are at best only half-remembered, twisted by time and the fallibility of Humanity.

Warhammer 40,000 isn’t just grimdark. It’s the grimmest, darkest.

The Imperium of Man stands as a cautionary tale of what could happen should the very worst of Humanity’s lust for power and extreme, unyielding xenophobia set in. Like so many aspects of Warhammer 40,000, the Imperium of Man is satirical.

https://www.warhammer-community.com/2021/11/19/the-imperium-is-driven-by-hate-warhammer-is-not/