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It's not entirely trivial, but here's the sketch of the proof if you would like to finish it yourself. Note that people usually denote complex numbers by $\mathbb C$: (1) Every irreducible represe …

I haven't heard this question before, but I would approach it in a following way: you know some basic relations between irreducible representations of a groups — e.g. their # is the # of conjugacy cl …

There's a very famous group, the largest sporadic simple finite group, sometimes called a monster whose size is quoted below. What's the explanation that the primes appearing in it, #{Monster} = 2 …

There are lots of good points in other answers, so I want to to add one specific thing about why representations are uniquely defined by their characters. Irreducible representations are uniquely det …