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Dec 26, 2015 at 12:25 comment added YCor yes, extraspecial groups are covered by my answer.
Dec 26, 2015 at 12:20 comment added Yakov Any extraspecial group of order $>p^3$ satisfies this condition.
Dec 20, 2015 at 20:50 comment added YCor Every group is an epimorphic image of itself. So no 2-generator group answers the question.
Dec 20, 2015 at 20:35 review Late answers
Dec 20, 2015 at 20:41
Dec 20, 2015 at 20:08 history answered Yakov CC BY-SA 3.0