Uniqueness of the equality prime in Theorem A

Determine whether the prime p=17 is the only prime for which equality holds in Theorem A, namely whether every finite solvable group G with p^2 dividing |G| satisfies k(G)>(49p+7)/60 unless p=17 and G is the specified group F_{17}^2\rtimes 2O.

Background

Theorem A establishes that if p is prime and G is a finite solvable group with p^2 dividing |G|, then k(G)\geq(49p+7)/60, with equality for p=17 and G=F_{17}^2\rtimes2O. The paper observes that integrality restricts possible equality cases to primes p congruent to 17 modulo 60, but the known equality example at p=17 does not determine whether any other primes can also attain the bound.

The unresolved issue is therefore the classification of all primes and groups achieving equality in the universal lower bound of Theorem A. The question asks specifically whether the known prime p=17 is unique.