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IMC 2008 Day 1 P5 - Automorphisms of Subgroups

Source: Problem 5

July 30, 2008
group theoryabstract algebraIMCcollege contests

Problem Statement

Does there exist a finite group G G with a normal subgroup H H such that ∣Aut H∣>∣Aut G∣ |\text{Aut } H| > |\text{Aut } G|? Disprove or provide an example. Here the notation ∣Aut X∣ |\text{Aut } X| for some group X X denotes the number of isomorphisms from X X to itself.
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