It’s 7:45 a.m. below Union Square, and one of the city’s keystone subway hubs is teeming with commuters in the Wednesday morning rush.

Stone-faced businessmen, yawning schoolkids and nannies pushing their young charges’ strollers jostle for space on an island between the muttering homeless man and the mystery liquid dripping from the ceiling.

But among the crowds on the uptown IRT platform, there are two other groups, locked in a game of cat-and-mouse invisible to most commuters: perverts and pickpockets hunting for their next victims, and plainclothes cops hunting for the creeps.

“It’s a weird, lonely job,” said Sgt. Paul Gratton, an 18-year NYPD vet who accompanied The Post for an exclusive look at a day in the life of a transit anti-crime team based in the sprawling Union Square complex. “They don’t talk. They have to watch each other.”

Communicating mostly with sideways glances, whistles and subtle hand signals, these teams have honed a wordless synergy, and made an art of fighting crime in the city’s subway system.

Though the underground undercovers keep their eyes peeled for any criminals, including pickpockets, many thieves are too cagey to get caught, employing their own experience to spot the cops among the crowds.

Consequently, the anti-crime teams more often find themselves busting the subway system’s gropers and grinders, whose focus is divided, said Lt. Nik Dedvukaj.

“The sex offender isn’t paying attention to us,” said Dedvukaj. “He’s only got one thing on his mind.”

Sexual assault reports have been steadily on the rise across the city in 2019, with 438 rapes tallied through the start of April — or 9.5 percent more than the 400 at the same point last year, according to NYPD stats.

Though subterranean sex crime has stayed roughly flat, much of it is driven by a handful of persistent pervs, largely undeterred from striking time after time thanks to light sentences and the lack of a mechanism to bar them for good, as The Post exclusively reported in March.

Those creeps include Jesus Ayala, a 64-year-old registered sex offender with more than a half-dozen subway busts to his name.

The latest came when he allegedly groped a 14-year-old girl aboard a 1 train on the afternoon of April 23 — just over a month after he was featured in a Post roundup of the subway system’s “Dirty Dozen” worst sex criminals.

“These perverts aren’t using the subway to get around,” fumed one police source. “They are victimizing riders to get off.”

For many frustrated cops, that can make their hunt for subway creeps feel more like catch-and-release.

And for female members of the plainclothes teams, the job can put them on a collision course with the deviants, who sometimes unwittingly mistake the undercovers for civilians and target them.

But most anti-crime cops try to focus on the good they’re doing, protecting New Yorkers just trying to get to and from their jobs, schools and homes.

“I hate to say it’s fun, but it’s rewarding when you actually catch someone who’s a sexual offender,” said Officer Frank Gandolfi, a six-year NYPD vet. “It’s rewarding.”

The men and women on the anti-crime team at Transit District 4 — one of 12 transit districts across the NYPD, each with at least one anti-crime squad — are an unglamorous bunch for an unglamorous job.

Their crisp dress blues left hanging at home, these cops wear T-shirts and jeans as they squeeze onto a few couches and chairs for roll call in a cramped room at TD4’s Union Square base.

“Let’s go over a few recent crimes,” Dedvukaj, TD4’s special operations lieutenant, says as he passes around fliers showing a man wanted for recently grabbing a woman’s rear aboard a 6 train shuttling between Bleecker Street and Astor Place.

Dedvukaj didn’t yet have a name to put to that face, but as the cops fanned out into the depths of Union Square, they committed it to memory, alongside the mental images of the recidivists they’re always on alert for, and the telltale signs that allow them to pick out new deviants.

“See that guy with the hoodie on, next to the stairs?” Detective Marquis Cross quietly asks on the uptown 4/5/6 platform. “He’s watching for women wearing skirts.”

Cross had never seen the creep before, but his behavior was a dead giveaway: He’d spent several minutes sneaking peeks from the foot of the stairs, letting trains roll by on both the local and express tracks.

“That was his sole purpose,” said Cross, with the NYPD for a dozen years and the anti-crime team for eight. “Numerous trains came in and passed and he was still doing the same thing.”

Disturbing though it may be, the man wasn’t doing anything illegal, so Cross and his partner, Jose Calle-Palomeque, move on down the platform, looking for trouble — of which there’s no shortage.

Between the start of 2018 and late April 2019, there were 334 arrests in transit for sex crimes across the five boroughs, with 71 percent of them coming in Manhattan, according to NYPD statistics.

‘I describe it as hunting. That’s what it really is.’

As trains roll in, Cross and Calle-Palomeque keep an eye out for men boarding a little too closely behind women for comfort — even by the packed-to-the-gills standards of any rush-hour ride.

“Mostly it’s on the crowded trains we see this kind of stuff,” said Gratton, who used to work anti-crime but is now out of the main NYPD Transit office. “The 4/5/6. The 7 out of Queens. The 2/3.”

“They [subway pervs] tend to use the stations where they can loop around without going above ground.”

So the anti-crime teams spend much of their shifts tracing the same circuits — in the case of Cross and Calle-Palomeque, hopping an uptown train to Grand Central, patrolling through the station and onto the downtown platform, riding back to Union Square, then repeating.

Between the surging crushes of commuters, attempts to minimize detection by slightly spacing out and sometimes snap decisions on whether to board a given train, partners sometimes become separated on the platform.

“If I don’t see him, I’ll whistle,” Cross said of Calle-Palomeque.

That whistle’s meaning? “Get on the train.”

“I describe it as hunting. That’s what it really is,” said one cop on the team. “You’re hunting and sometimes you become the prey.”

The officer, who asked that her name not be printed, told The Post that she had her first brush with subway sex assault long before she signed on with New York’s Finest.

“This guy [was] grinding up on me,” she recalled of her run-in aboard a Bronx train while attending college in the ’90s. “I wasn’t that exposed to these things, so it was totally shocking to me.

“Then, it happened a few more times.”

The memories propelled her into the NYPD, where she was “trained to hunt these guys,” to help women made to feel like she had — but even her badge and that training couldn’t save her from becoming a victim again in 2016 when she was patrolling in plainclothes.

“The train came in and someone just came up behind me and grabbed me,” she said. “I felt the hand on my behind.”

As the seconds dragged by like hours, she waited for her training to kick in.

“I thought I would have the Wonder Woman reaction, but it wasn’t like that,” she said. “I froze. Then I yelled out. He ran. My partner was able to catch up to the guy and he was arrested.”

It reminded the cop of why she joined the fight — and just how much ground there is left to win.

“As a woman, I identify with the victims and I feel I have the upper hand,” she said.

“I used to ask them, ‘Has anything unusual happened?,’ but I had to curtail that question,” she said, explaining how some straphangers have become so inured to the assaults, they write them off as coming with the territory of their commutes. “They now chalk it up to riding the subway in New York City, which is sad, but it makes me feel like my work is that much more important.

“I become the hunted, but that doesn’t stop me.”

None of the anti-crime cops are immune, however, to the hurdles they face coming into the lives of victimized straphangers at their most vulnerable.

“We are plainclothes officers … walking up to random women,” said Dedvukaj. “Sometimes they don’t believe we are officers.”

That skepticism, though understandable, can make or break an arrest for misdemeanors like forcible touching, for which the victim must formally complain to move the case forward.

On the day of The Post’s ride-along, Cross pulled aside one female straphanger who he believed was the victim of a subway groper.

But the woman, already spooked and dubious that Cross was really NYPD, went on her way.

She found a uniformed cop at Grand Central, who assured her that Cross was true blue, and put her back in touch with him.

Fortunately, Cross and Calle-Palomeque trusted their instincts and had snapped photos of her assailant — who was nabbed Tuesday for the crime, shortly after TD4 spotted him preparing to violate another straphanger, police sources said.

Jermaine Hampton, a registered Level 1 sex offender who’s no stranger to transit, will be charged with felony persistent sexual abuse, sources said.

The system of turnstile justice that finds many familiar faces arrested time and time again has led NYPD brass up to Commissioner James O’Neill to push for stronger penalties, including possible lifetime bans from MTA property.

That freedom for recidivist riders to return repeatedly has left many transit cops feeling frustrated and helpless — particularly because it means they have to sit back and wait for the pervs to victimize someone else before they can legally take action.

“It’s the same guys over and over and over,” said the female team member. “Sometimes within days they’re right back out there.

“I also have two daughters and I don’t want them to have to deal with this,” she said. “Hopefully things will turn around where they’ll put some teeth onto the law.”