Direct product of two semi-direct products

Cairo
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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.
 
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What is ##C_p## and what is ##C_7:C_3##?
 
$$C_7 : C_3$$ is a semi-direct product.

$$C_p$$ is as described. A prime, congruent to 1 mod 3.
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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