Do Lizardfolk unarmed attacks have a weapon specialization group?

The Lizardfolk ancestry grants an unarmed attack, and two more can be gained with ancestry feats. These three attacks are described as follows:

You have a claw unarmed attack that deals 1d4 slashing damage and has the agile and finesse traits.

You gain a fangs unarmed attack that deals 1d8 piercing damage.

You gain a tail unarmed attack that deals 1d6 bludgeoning damage and has the sweep trait.

Then the Iruxi Unarmed Cunning feat comes along and explicitly allows you to apply the critical specialization effect for the above attacks. It does nothing else, and it is concise enough to quote entirely:

You make the most of your iruxi unarmed attacks. Whenever you score a critical hit with a claw or an unarmed attack you gained from a lizardfolk ancestry feat, you apply the unarmed attack’s critical specialization effect.

Critical specialization effects are defined by the attack’s group, and there isn’t a default group. These Lizardfolk attacks don’t have a group, so there is nothing to apply.

So is this feat useless? Or is there a general rule that I don’t know, like "every weapon or unarmed attack with no group listed is in the brawling group"? What am I missing?

Further thoughts: Some spells or activities grant unarmed attacks and specifically state their group, and some don’t. The Advanced Player’s Guide replaces the Tusk Orc feat, which grants an attack without group or traits, with one that grants an attack WITH a group and traits – so somebody must have wanted to clear that up, but the Lizardfolk feats didn’t get an update. And then all weapons in the rule book have a group, but not all armors. It all seems like if Paizo wanted an attack to have a group, they would have said so.