Do Lizardfolk unarmed attacks have a weapon specialization group?

Question

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.

Answer 1

It should (almost definitely) be Brawling

Basically all unarmed attacks are Brawling group, and we have this section describing the Fist entry in the weapons table

Table 6–6: Unarmed Attacks lists the statistics for an unarmed attack with a fist, though you’ll usually use the same statistics for attacks made with any other parts of your body. Certain ancestry feats, class features, and spells give access to special, more powerful unarmed attacks. Details for those unarmed attacks are provided in the abilities that grant them.

Lacking guidance to use other statistics (eg your claw lists its own damage and traits), we can only assume that the other mandatory statistics of the 'default' unarmed attack also apply to these given unarmed attacks.

Not including a Group was a mistake

Unfortunately, Lizardfolk are only covered (so far) in the Character Guide, which has come under less scrutiny than the PHB. Leaving out the weapon group was an honest mistake, judging by the plethora of similar abilities that include the Group. Because of this, we have no way of definitively citing RAW.