Show that any Group of order 2907 is not a simple group? 2907= 3*3*17*19 I've started with the Sylow 19-subgroup, then the 17-subgroups and finally the 3-subgroups but i couldn't proceed in the proof to find the nontrivial normal subgroup! Please help.
Suppose the $19$-Sylow subgroup(s) isn't(aren't) normal. Are there enough elements left over for the $17$-Sylow subgroup(s) to not be normal? And vice versa.