NEW CANAAN — The Jazzholes surprise people in two ways: First, they are a classic rock cover band, not a jazz ensemble. Second, the six-piece unit — whose lineup includes a publisher, a financial consultant and a managing director at a beverage investment firm — does not fit the rock ’n’ roll image.

“I don’t look like I’m in a rock band,” said John Nesbett, a New Canaan resident, and founder and president of a local investor services firm. “We’ve only just begun to play in New Canaan and everybody has a very similar expression. They say, ‘That’s so interesting,’ but they’re really expecting that we’ll suck.”

But according to Nesbett, the group’s keyboardist, expectations are soon dashed once the band leans into its set, which on an average night might include hits — with deep cuts mixed in — by the Velvet Underground, the Doors, the Rolling Stones and other usual suspects in the classic rock canon.

“Usually people are pleasantly surprised when we do very studied renditions of these songs. We really do try to do it justice, because it’s great music,” Nesbett said.

Though they’ve only recently begun to play in the area, the Jazzholes have local roots, or otherwise met in college. Nesbett and bassist Paul McDaniel studied at Connecticut College together and reside in New Canaan. Drummer Chris Fischer is a New Canaan native who now lives in Ridgefield, as does acoustic guitarist and percussionist Jason Camillos. Lead guitarist Tony Verbeck grew up with Nesbett in Darien and now lives in New Jersey. Guitarist Peter Schellbach studied with Camillos at Princeton University.

“It’s a tangled web. We’re connected from way back,” Nesbett said.

On Saturday, the Jazzholes will play a benefit Saturday for Ridgefield’s Aldrich Museum of Contemporary Art at the Heights at Brother Vic’s in South Salem, N.Y.

According to Camillos, the bandmates have been playing together since at least the 1990s.

“We’ve been playing together as a band for more than 20 years. Right out of college we kind of all came together,” Camillos said.

“We didn’t find each other on Craigslist, which is what happens with most bands. Usually, you have these personalities and you’re trying to make them click, but we are truly the best of friends and it goes back to our teenage years. And so that translates to the music,” Nesbett said.

Earlier iterations of the band went by the monikers Crazy Chester and Nez, wrote original music and were active on the New York City bar scene, playing venues around Manhattan with a shifting lineup of musicians.

The band adopted the name the Jazzholes when its current roster began to coalesce as a show of their sense of humor.

“When we were first playing as a band we were just throwing out names and it just kind of stuck,” Camillos said.

They continue to play shows regularly in venues in Long Island and Connecticut, and they have a standing gig at the Red Lion in Greenwich Village.

After two decades of playing, the group has learned to adapt to the surprise of its new listeners, embracing their distinctly non-rock ’n’ roll look and misleading name.

“We’ve talked about changing the name a hundred times and we never do,” Camillos said. “It causes confusion, so whenever we’re being billed for a show we make sure the words rock ’n’ roll are in there.”

justin.papp@scni.com; @justinjpapp1