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What, exactly, is a Mercedes-Benz GLA45 AMG? It’s an edgy-looking thing for sure, at least from the front. And the Jupiter-red color in the model we tested looks dazzling. But then you walk around to the back and it’s, um, a small, luxury, crossover SUV thingy with a rear hatch, a place where you could park your groceries.

And yet, it’s a hatch with a you-gotta-be-kidding-me 355-horsepower, turbocharged power plant from the Benz racing division (that’s the AMG part). If getting to the supermarket in a really big hurry is your mission, this is your wagon. Call it a super crossover.

So why build a supercross in the first place? That question has already been answered by Porsche and its $50,000 Macan: because there’s a market niche for luxury-badged hatches. If somebody wants to pay two to five times the cost of the Honda Civic or a Volkswagen Golf, or even the Mercedes GLA 250 (the civilian version of the GLA45), then the industry will by all means accommodate them, as it should.

In that regard, the GLA45 is both an accommodation and an accomplishment, at least in part. Consider that the horsepower is being churned by a 2.0 liter, hand-assembled inline-4 turbocharged engine that muscles up 332-lb.-ft. of torque. The GLA45 can absolutely rip it up, going from zero to 60 miles per hour in 4.8 seconds; it has a factory-imposed maximum speed of 155 m.p.h. That puts it in the same range as, say, the much sexier BMW M3 sedan. Mercedes says that’s the most powerful regulation 4-pot on the planet, and it sure feels that way. By way of comparison, the GLA45 has 145 more horses running under it than the excellent 4-cylinder Golf GTI 4-door, although the VW lists for about half the price, and is actually quieter.

Yes, that’s right, the Golf is quieter. But it’s also likely that buyers of the GLA45 are trying to escape a quiet ride, and perhaps their children; in this Benz you can do both at warp speed. You will, of course, appreciate the all-wheel drive, the ridiculous passing acceleration, and the superb handling.

The GLA45’s transmission, a 7-speed, dual clutch number with paddle shifters, is the most fun I’ve driven recently. The cleverly designed gear shifter features three driving modes — normal, sport and manual/paddle shift. Plus, there’s an Eco setting that shuts the engine off when you are stopped at lights. There’s even a launch mode, if you’d like to do some suburban drag racing. Better yet, this transmission absolutely rips through the gears, yielding a wonderfully crazy sound in the tuned exhaust. The GLA45’s song is one of a very large, very angry hornet: zzzz, ZZZZ, ZZZZAAAHHH! I’d almost pay the $48,300 sticker just for that.

Almost. There are other things to consider. The ride, for one, which is sports-car stiff, a sensation you might not appreciate with those groceries in the back as you jounce around on city streets. The dashboard brims with aluminum air vents but also has a control panel that seems way too complicated. Do we really need a keypad? The navigation system, like so many others, begs you to try to figure it out: touchscreen or the control knob on the center console?

Still, the interior is handsome and luxurious but a bit hard-edged at the same time. The performance seats, which add $2,250 to the price, are aluminum trimmed; if done in the optional black "red cut" leather ($1,500), the look is exquisite. Add the hand-stitched performance steering wheel ($500) and you are going places in considerable style.

This conflict between mission and model, sports car and family car, makes the GLA45 a bit of a puzzler. Sure, you love the driving dynamics and that powerful engine, but do you really need or want a dynamic hatchback? In truth, it’s really a hackback. It’s exactly what you’d expect to happen when you let boys and girls of the racing division redesign the family wagon without adult supervision.