Direct product of two irreducible representations of a finite group can be decomposed into a direct sum of irreducible representations. So, starting from a single faithful irreducible representation, is it possible generate every other irreducible representation by successively taking direct products?(adsbygoogle = window.adsbygoogle || []).push({});

My second question is (if it makes sense), can we have a finite group in which none of the irreducible representations are faithful?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Direct product of faithful representations into direct sum

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**