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EXCEPTIONAL GROUPS OF ORDER
$p^6$ FOR PRIMES 
$p\geq 5$
- Part of
-
- Journal:
- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 24 February 2025, pp. 1-12
-
- Article
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The minimal faithful permutation degree
$\mu (G)$ of a finite group G is the least integer n such that G is isomorphic to a subgroup of the symmetric group 
$S_n$. If G has a normal subgroup N such that 
$\mu (G/N)> \mu (G)$, then G is exceptional. We prove that the proportion of exceptional groups of order 
$p^6$ for primes 
$p \geq 5$ is asymptotically zero. We identify 
$(11p+107)/2$ such groups and conjecture that there are no others.
