"biggest" doesn't not mean most people support it. That's not how most democracies work - they have proportional representation, so they have many parties, and the biggest one may still only (as in this case) have a small percentage of the vote (in this case, 25%[0])

[0] https://en.wikipedia.org/wiki/Opinion_polling_for_the_next_G...

It's not fringe, but it is extremist. I think you're mixing up definitions.

it's not supported by most, it has 25% max.

The word has many interpretations. You've touched upon just one (and the most fallacious: ad populum) of them.

The masses can be extreme if they are:

- wrong

- deviates sharply from historical norms

- undergoing mass psychosis

Defining extremists to be "the people with unpopular positions" is defining extremists to be "those with positions most dislike." AfD are extreme because of what their positions are, separate from who does and does not support them.

> AfD are extreme because of what their positions are

Then show us their extreme positions! Their official party program is actually quite tame.

a cursory Google search reveals that they deny anthropogenic climate change, reject the idea of women in the workplace, and wish to deny marriage rights to homosexuals

They are conservative and have a few idiots and extremist people in their ranks yes, but that doesn't make the party as a whole extremist.

I never heard about their women-workspace-denial.

And being against marriage of homosexuals was the majority opinion from the beginning of time until around 10 years ago so you can hardly count that as extremist.