Alivia Sureka is one of the few perpetuals in the galaxy, as well as being one of the least grimdark characters in the grim darkness of the far future. She also happens to be the Emperor's Waifu, and much like himself, she is a total badass, when she gets the chance to show off her skills, which is not very often (in fact we only have two accounts of her feats, one of which ended with her getting impaled by Horus...)
Not much is known of her history, other than she is one of the perpetuals to have traveled with Emps to the planet Molech during the dark age of technology, where he acquired all his knowledge about gene modifications and the like, then subsequently abandoned her there to watch over the portal while he got a one way ticket back to Terra. She is Younger than the Emperor by about 9000 years, which still makes her old as fuck, But much easier to relate to, seeing as she spent her first years in the 20th and 21st century on Terra, and regularly speaks using modern English slang and abbreviations (Despite being born in Denmark...) Apparently she really liked this era, as she carries around various items that we could easily walk down the street and find today, including a copy of Hans Christian Andersen Fairy tales, because apparently, no one has written a better book in 30 thousand years.
When Emps finally returned to Molech during his great crusade, he fortified it so much to protect the portal that he essentially made Alivia Jobless, forcing her to retire, and she retreated to live a quiet life and adopt 2 children. That is until Horus' fuck up happened. Horus wanted to use the portal to acquire the same powers as his father, And now Alivia had a chance to demonstrate why you shouldn't fuck with the Emperor's friends. Returning to the portal before Horus could reach it, she Started a ritual to shut it using her psychic might, Much like Emps did on Terra with the golden throne, except she did it without a glorified toilet, and in a fraction of the time... almost. Horus arrived just before she could complete the ritual, and because she couldn't divert her attention to fight, she got royally fucked over (as in, impaled with Horus' talon.), which doesn't really matter because the portal was rendered unusable anyway. At this point she was assumed to be dead, because only the Emperor himself knew who she was, and she disappeared for much of the Heresy.
She was revealed to be alive towards the end, but she had grown tired of trying to cover up Emps fuck ups, so she was essentially living a normal family life, Until her daughters got kidnapped by a slaaneshi cult, and she got royally pissed off. However, Unlike Big E, She didn't go on a murderous rampage, she played things very sneakily, and pretended to be a defenseless women and allowed herself to be captured by that same cult in order to learn the location of her daughters. Everything was going just as planned, until Severian of the knights errant (later named Grey Knights) came along and killed most of the cultists in the area, completely fucking up her plan. However, she didn't fret too much, This badass simply switched into battle mode, learned her daughter's location by force and then murdered her way towards the ritual chamber. She then interrupted the ritual, saving her daughter and several others, murdered all the cultists in the room and fought of some warp entities. Then she was Confronted by a daemonette, which she allowed to possess her, then proceeded to destroy her own body to kill the fiend and regenerated on the spot. If that's not badass, I don't know what is.
Like the emperor, Alivia Sureka is a very strong psyker, if we go by the fact that she closed a webway portal faster than the former, and without the aid of ancient technology. However her powers are largely empathic, meaning she can make others like her in order to control them. The downside to this is that she can feel everything her target feels, including pain and death. She is also supposedly proficient in hand to hand combat, but there's not much to go by. Oh, and she's also a perpetual, making her immortal.