Bufo
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The answer is no. But I'm supposed to solve this using basics of isomorphism (without any application of Sylow's theorem).
Suppose such a group exists. Then of course it's non-Abelian.
I know there are cyclic subgroups of order 3 or 13 (actually both, because possibly I'm allowed to use this particular implication of Sylow's theorem).
Suppose such a group exists. Then of course it's non-Abelian.
I know there are cyclic subgroups of order 3 or 13 (actually both, because possibly I'm allowed to use this particular implication of Sylow's theorem).