All members can hide their contact information (email and phone number) from other members of the group. You can do this by going into the group, then press the 3 dots (more) > contact information and select only visible for administrators. This is a per-group setting, so you can hide your contact information in some groups while still sharing it with members in other groups.
Administrators can also hide their contact information from group members the same way. Only the contact person is unable to do so.
When an administrator adds you to a group you will be asked if you wish members in that group to see your contact information. Until you have accepted the group invitation, only administrators will be able to see it.
The administrator of the group can also chose to hide the members contact information on behalf of the whole group by going to the group settings (the three dots in the menu) and select this.