The cast of Republican candidates appearing during Thursday’s prime-time presidential primary debate will be one of the most diverse lineups for either party. But one key demographic will be missing.

The Fox News rules that limited debate participation to the top 10 contenders in the five most recent national polls relegated Carly Fiorina — the lone woman in the GOP field this year — to the second-tier debate that the network will hold several hours before the main event in Cleveland.

“I think @CarlyFiorina is the Firefly of candidates,” Republican strategist Rick Wilson tweeted Monday, referring to the cult science fiction show axed after one season. “Fan favorite, network doesn’t get it, beloved after.”

Fiorina’s statement after the final lineup was announced Tuesday struck a careful tone. “I look forward to answering questions on Thursday in Cleveland,” she said, referring to the undercard event.

Republicans argued that they did not set the qualification standards that limited participation or set the rules that kept the race’s only woman off the main stage. But in a year when Hillary Rodham Clinton dominates the Democratic contest, some wonder whether the GOP could be haunted by the image of an all-male lineup at its first debate.

In 2012, President Obama won the women’s vote by 11 points. An election postmortem commissioned by the GOP noted “growing unrest within the community of Republican women frustrated by the Party’s negative image among women.”

Sabrina Schaeffer, executive director of the Independent Women’s Forum, a conservative think tank, said Fiorina’s absence from the main stage will be felt. “From the perspective of women voters, I think it’s really disappointing” she said.

Schaeffer said Fiorina would bring to the debate “the ability to talk about workplace regulations and challenges that women and their families are facing in a way the other candidates can’t.”

She added, “I think that overall it’s important to have someone on the right capable of talking about pay equity and paid leave mandates and child care, and she’s able to do that very effectively. Without her voice up there, they won’t have as robust a conversation about those issues.”

That’s not the only unique role Fiorina would have filled. As the GOP primary field’s only woman, Fiorina says she’s been able to aggressively attack Clinton in a way she says her male rivals cannot without risking the sexism charges that have dogged Republican candidates in recent campaigns. A man facing a female opponent next fall might hold back. She wouldn’t.

“In order to beat Hillary Clinton, we have to have a nominee on our side who is willing to throw every punch,” Fiorina told the crowd at New Hampshire’s Voters First Forum Monday night.

Fiorina’s campaign showcases her origin story: Her rise from secretary to the top spot at Hewlett-Packard in 1999 — making her the first female chief executive of a Fortune 100 company and drawing national attention.

Her gender has afforded her some unique opportunities to be seen and heard on the campaign trail. Earlier this year, she headlined a Conservative Political Action Conference panel titled “Countering the ‘War on Women’ Lie.” In June, she delivered a major speech on “the state of women in America.”And she has spoken to more GOP women’s groups in early primary states most of the other candidates combined.

But where Clinton highlights institutional gender discrimination and private sector pay disparity, Fiorina downplays those factors, pointing more often to outdated government seniority rules or union interference. The distinctive message Fiorina brings to the race, one shaped in large part by her experience as a woman, is central to her candidacy. At the same time, her supporters say that didn’t entitle her to a spot on the debate stage.

“Carly would be the first to say there should be a level playing field. No special favors because she happens to be a woman,” said Katie Packer Gage, a deputy campaign manager for Mitt Romney’s 2012 presidential bid and co-founder of the all-female consulting firm Burling Glass Consulting. “I don’t think gender in and of itself is a qualification. . . . I certainly don’t think it makes Hillary Clinton qualified because she happens to be a woman.”

Democrats don’t think Fiorina’s gender makes a difference either. “No matter which Republicans are on the stage, women won’t be represented, because each and every of the Republican contenders wants to turn back the clock for women,” said Holly Shulman, a spokeswoman for the Democratic National Committee.

Clinton’s campaign has been embraced by liberal women donors and supporters to an unprecedented extent, with the campaign reporting last month that 61 percent of its donors so far had been women. Clinton reported raising $45.7 million in the first 21/2 months of her campaign.

In a hypothetical general election contest between Republican Jeb Bush and Clinton, a Washington Post-ABC News poll last month found women preferred the former secretary of state over her GOP opponent by an even larger margin than they had supported the Democratic ticket in 2012, giving her a 15-point lead over Bush.

Fiorina’s candidacy has failed to draw significant support among women in her own party. In the most recent Post poll, Fiorina was at the bottom of the list, with less than 1 percent support among both men and women.

In some ways, Fiorina has tied her own fortunes to Clinton’s poll dominance, painting herself as the conservative counterpoint. She has highlighted similarities in the covers of the early editions of their similarly titled books — Fiorina’s “Tough Choices” and Clinton’s “Hard Choices” — both of which featured portraits of smiling, carefully arranged blond women. She has joked that the former first lady has copied key elements of her message.

On the trail, Clinton regularly refers to her granddaughter, her hair-coloring routine and her late mother, who was abandoned as a child. Fiorina has also very publicly tapped into her personal experience this year: She wrote candidly in her new book, “Rising to the Challenge,” released as her campaign began, about the pain of losing her stepdaughter to addiction, her fight against breast cancer and her marriage.

In person, Fiorina seems to connect with voters. She has received rave reviews for her speeches before small gatherings, especially in the early primary states of Iowa and New Hampshire and at the big cattle-call events like June’s Faith and Freedom Coalition conference in the District. There, Fiorina was treated like a star by women who waited in the hallway outside the ballroom where she spoke. They beamed as they reached to shake her hand, snapped photos with her and told her how much they admired her.

Her struggle to translate her connections on the campaign trail into success at the ballot box isn’t a new one. Fiorina’s 2010 Senate bid, her first political campaign, ended in a double-digit loss to Sen. Barbara Boxer (D-Calif.). Earlier this month, she reported raising $1.4 million since launching her presidential campaign, with a super PAC — CARLY for America — supporting her candidacy, reporting $3.4 million in donations. Both hauls are dwarfed by the eight-figure totals reported by the top contenders. The positive national exposure a solid debate performance can bring — and the surge in donations that often accompanies that sort of exposure — is a boost the Fiorina campaign could have used.

Space on the main stage this week might not have guaranteed the spotlight anyway. Republican strategist Ron Bonjean predicted that Donald Trump would so overshadow others during the debate that Fiorina’s absence would “not be a big deal this time.”

“The hope is that she will continue to campaign and keep up a serious effort to break into the top 10 because the field will thin out over time and her perseverance could pay off,” Bonjean said. “Republicans will need to win over the majority of female voters this time around, and she could help. Whether she could actually get the nomination or be part of a ticket as vice president is an important thought that should be out there for voters to consider.”