It is highly unlikely that there is no management agreement, because the strata manager would be breaching the law. Section 27 of the Act provides that the manager must be appointed by an instrument in writing authorised by a resolution at a general meeting of the OC.
Also if there were no agreement, then the strata manager couldn’t be paid.
An EC has to have a Chair, a Secretary and a Treasurer. Under section 29 of the Act, those functions can be delegated to the strata manager, but even if they are, the Chair, Secretary and Treasurer (the EC members) can also exercise those functions.
If the functions have been delegated to the strata manager, this must be set out in the management agreement, section 29(1).
No offence, but your co-owners sound a bit silly.