Thread: direct products

List, once each, all the groups of order 288 as direct products of p-groups.

So i know 288 = 2^5 *3^2

but I'm sure what exactly this question wants...how many there will be...

Originally Posted by CarmineCortez

List, once each, all the groups of order 288 as direct products of p-groups.

So i know 288 = 2^5 *3^2

but I'm sure what exactly this question wants...how many there will be...

There are 1,045 different groups up to isomorphism of order 288. I sincerely doubt a lot anyone could ask any student to list them all...

Now, perhaps all the ABELIAN groups of order 288 could be a much more reasonable request...and still: there are 14 different non-isomorphic abelian groups of this order, but these already are lots easier to list.
Check which one of the above option were you actually required to answer, and if it is the first one may the gods and goddesses have mercy on you.

Tonio