No need of exhausting departmental remedies

No. You can't. You represent to the Head of the department.

Notice under Section 80(c) of the Code of Civil Procedure, 1908 make it compulsory (not mandatory) to approach concerned authorities 

Consult a local prudent lawyer with relevant records for proper analyses, professional advise and necessary proceeding.

You can file writ petition since you have laready made representations those will be trated as Notices. You have to show how clearly how the powers have been abused and you suffered at the hands of such abuse.

The joint representation can be given by a trade union or by an entity representing the aggrieved employees.

If it is a general grievance, then the redressal machinery may be approached or a PIL may be filed.

The details are not enough to render more opinion.

You are not sharing as to what are the irregularities and how these are effecting labour relations.