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Question Number 194058 by Mastermind last updated on 27/Jun/23

$$\mathrm{Ques}.1$$$$\mathrm{Let}\mathrm{G}={\mathrm{C}}_5\times {\mathrm{C}}_{25}\times {\mathrm{C}}_{625}.\mathrm{Determine}$$$$\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{elements}\mathrm{of}\mathrm{each}\mathrm{order}\mathrm{in}\mathrm{G}$$$$$$$$\mathrm{Ques}.2$$$$\mathrm{List}\mathrm{the}\mathrm{abelian}\mathrm{groups}\mathrm{of}\mathrm{order}16$$$$\mathrm{and}\mathrm{of}\mathrm{order}27\mathrm{up}\mathrm{to}\mathrm{Isomorphism}.$$$$$$$$\mathrm{Ques}.3$$$$\mathrm{Describe}\mathrm{a}\mathrm{Sylow}2-\mathrm{subgroup}\mathrm{in}{\mathrm{S}}_5,$$$$\mathrm{and}\mathrm{how}\mathrm{many}\mathrm{Sylow}2-\mathrm{subgroups}\mathrm{are}$$$$\mathrm{in}{\mathrm{S}}_5?$$

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