Either a gerund or an infinitive would work here:
The other option is hearing a music band.
The other option is to hear a music band.
Can you say 'group of music'? No. That makes no sense at all. You can say 'a group of students' (many students gathered together), 'a group of friends' (many friends gathered together) ... but 'a group of music' (??) - surely you can see that's nonsense! You could possibly say 'a group of musicians', but it would be more usual to make a compound noun and say 'music group'. When we make a compound noun (xy) , the principal noun (y) says what something is: a group, while the first noun (x) specifies what kind of 'y' it is - in this case, the type of group that plays music. (As opposed to a dance group, a drama group and so on).