this is going to give you problems… iphone is extremely limited with what it can detect and work with. it would be best to find a friend with an android phone and ask them to scan your card / badge with taginfo
the T5577 is a 125khz chip (click the link auto-generated when i type T5577 to learn more) and the magic mifare chip is a 13.56mhz knock-off chinese cheat of a chip that emulates a legit mifare classic 1k from NXP, but with the added ability to change the ID number… real mifare chips can’t change the ID.