Adding to the already well given answer. GroupCoordinator receives the partition assignment from the consumer group leader and all the consumers receive their partition assignments from GroupCoordinator.
So GroupCoordinator asks the GroupLeader to decide the partition assignment based upon the https://kafka.apache.org/documentation/#consumerconfigs_partition.assignment.strategy and receives the same info back. Coordinator later passes the information to the other consumers in the group (excluding leader).
And every consumer knows only about it's own partition assignment. Though group leader knows about all the partitions assigned to different consumers in group.
PS: The first consumer from the group to connect to the broker (Group Coordinator) automatically becomes the group leader.