Mutliplication table of quotient groups

[gotmilk04]

Homework Statement

Write the multiplication table of C_{6}/C_{3}
and identify it as a familiar group.

Homework Equations

The Attempt at a Solution

C_{6}={1,\omega,\omega^2,\omega^3,\omega^4,\omega^5}
C₃={1,\omega,\omega^2}
The cosets are C₃ and \omega^3C₃
I just need help making the multiplication table.

 

[rasmhop]

I'm assuming C_n and C^n both refer to the cyclic group of order n, since that's the impression I get from your post.

if you meant for C_6 to be generated by \omega, then you should have C_3 = \{1,\omega^2,\omega^4\} because otherwise C_3 is not a group. Then the cosets should be C_3, \omega C_3.

What exactly are you having trouble with? As you said yourself the group C_6/C_3 has exactly two elements (C_3 and \omega C_3), so the following four are the possible products you need to compute and insert in the multiplication table:
C_3 \times C_3
C_3 \times \omega C_3
\omega C_3 \times C_3
\omega C_3 \times \omega C_3