# Example of a finite group

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? –  Elias 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 $\,6\,$ ...