I am currently going through a past exam paper for a group theory module and am unable to answer the following section of a question. The copy of my lecture notes doesn't seem to have a section on soluble groups but I would still like to know that if i am given the character table of this group
The how would i determine whether the group is:
- soluble?
- Simple?
- Isomorphic to a subgroup of $GL(n, \mathbb{C})$?
Any help would be much appreciated and thanks in advance