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I need an example of a finite group $G$ such that

1) the number of Sylow $p$-subgroup of $G$ is $1$ for all $p\neq 2$

2) the number of Sylow $2$-subgroup of $G$ is $3$.

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What are their motivations with these questions? – MathOverview Mar 22 '13 at 16:05
What do you need the group for? What are your thoughts on how one might construct one? – Tobias Kildetoft Mar 22 '13 at 16:05
Try the smallest possible example!! – user641 Mar 22 '13 at 16:07
To follow up on @SteveD's comment, (2) tells you that the group is non-abelian. Think of the non-abelian (small) group(s) you know. – Andreas Caranti Mar 22 '13 at 16:12

Hints (in the correct order): any finite abelian group, non-abelian group of order $\,6\,$ ...

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I take OP wants a single group that satisfies both conditions. – Andreas Caranti Mar 22 '13 at 16:28
Ok, then only the second hinted one (the smallest non-abelian group) – DonAntonio Mar 22 '13 at 16:31

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