Question

what is all groups of order up to 12?

Answer 1

well there are a bunch of them

Answer 2

prime order has to be cyclic, copies of
\[\mathbb{Z_p}\]

Answer 3

that takes care of 2,3,5, 7, 11

Answer 4

two of order 4, namely Klien 4 aka
\[\mathbb{Z_2}\times\mathbb{Z_2}\] and also
\[\mathbb{Z_4}\]

Answer 5

for order 6 you have \(S_3\) as well as \(\mathbb{Z_6}\)

Answer 6

how about symmetric group and others group that have order 12

Answer 7

ohh..thanks.. thats all?

Answer 8

oh no there are plenty more.
rather than me trying to remember them all, probably easiest to google

Answer 9

order 8 there are 4
quaternions, \(\mathbb{Z_8}\) and \(\mathbb{Z_4}\times \mathbb{Z_2}\) and \(\mathbb{Z_2}\times \mathbb{Z_2}\times \mathbb{Z_2}\)

Answer 10

let me find a link

Answer 11

ok try here lists all i think
http://en.wikipedia.org/wiki/List_of_small_groups

Answer 12

thank you so much..^^