Number of conjugacy classes need not determine conjugacy class size statistics for groups of prime-fifth order

Statement
Let $$p$$ be a prime number. It is possible to have two groups $$P_1$$ and $$P_2$$, both of order $$p^5$$, such that $$P_1$$ and $$P_2$$ have the same fact about::number of conjugacy classes but have different conjugacy class size statistics.

Related facts

 * Nilpotency class and order need not determine conjugacy class size statistics for groups of prime-fifth order

Case $$p = 2$$
The three Hall-Senior families (equivalence classes up to isoclinism) $$\Gamma_6, \Gamma_7, \Gamma_8$$ all have the same number of conjugacy classes, namely 11. However, the families $$\Gamma_6$$ and $$\Gamma_7$$ have different conjugacy class size statistics from the family $$\Gamma_8$$:


 * The families $$\Gamma_6$$ and $$\Gamma_7$$, both comprising groups of nilpotency class three, comprise five groups in total, such as holomorph of Z8. The conjugacy class size statistics of each of these groups are the same, namely: 2 of size 1, 3 of size 2, 6 of size 4.
 * The family $$\Gamma_8$$ comprises the three maximal class groups, namely dihedral group:D32, semidihedral group:SD32, generalized quaternion group:Q32, all of nilpotency class four. The conjugacy class size statistics of each of these groups are the same, namely: 2 of size 1, 7 of size 2, 2 of size 8.