Done this. Good question but I don't think it's the most helpful way of thinking about it.

Every new recruit brings their own assumptions about how organizations / employment / etc. work and many of those assumptions won't be visible until after a while. This is especially true for managers.

I found Charles Handy's thinking about four types of organisational culture very helpful and I wish I'd found it earlier in the process.

AI summary: Charles Handy identified four types of organizational cultures: Power Culture, where decision-making is centralized among a few; Role Culture, which is based on defined roles and responsibilities; Task Culture, focused on teamwork to achieve specific goals; and Person Culture, where individual interests take precedence over the organization.

Basically, 15>50 is very likely to involve a shift from one of these to another one and making that open and explicit could help you a lot (including understanding how the role of senior managers needs to change).

The book is Understanding Organisations from 1976 but still valuable.

Good luck!