Direct product of two semi-direct products

  • #1
24
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Homework Statement:
I need to find the number of elements and conjugacy classes for the direct product.
Relevant Equations:
$$G=(C_7:C_3\ )\times(C_{13}:C_3\ )$$
After finding the number of elements for this group, how do I extend the argument to $$p,q\equiv1\left(mod\ 3\right)$$, where $$G=(C_p:C_3\ )\times(C_q:C_3\ )$$


Any help appreciated.
 

Answers and Replies

  • #3
24
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$$C_7 : C_3$$ is a semi-direct product.

$$C_p$$ is as described. A prime, congruent to 1 mod 3.
 
Last edited:

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