[hamburglar]

Where I work there is an incident team that handles things like creating a master ticket, starting a call bridge, getting the on-calls into the bridge, keeping track of what teams (and who from those teams) have been brought in, manages the call (keeping chatter down and focused when there are 100 people in a call is important), periodically comments on the master ticket with status and a list of impacted teams, marks down milestone times like when the impact started, when it was detected, mitigated, root cause found, etc. This person is also responsible for stuff like when they hear you want to engage team X, they'll go track down an on-call for you, or summarizing known impact for the outward-facing status pages, etc. They also create the postmortem template and follow up with all involved teams to get them to contribute their detailed impact statement there.

Edit: sometimes when it's a really gnarly problem and there are huge numbers of people on the call, the set of people who are actively trying to come up with mitigations and need to just be able to talk freely at each other will break off into a less noisy call and leave a representative to relay status to the main call.