DEMO
HTML:
<div style="float:left">
<mat-tab-group style="width:98%;">
<mat-tab>
<ng-template mat-tab-label>
<mat-icon class="example-tab-icon">thumb_up</mat-icon>
First
</ng-template>
Content 1
</mat-tab>
<mat-tab>
<ng-template mat-tab-label>
<mat-icon class="example-tab-icon">thumb_up</mat-icon>
Second
</ng-template>
Content 2
</mat-tab>
<mat-tab>
<ng-template mat-tab-label>
<mat-icon class="example-tab-icon">thumb_up</mat-icon>
Third
</ng-template>
Content 3
</mat-tab>
</mat-tab-group>
</div>
<div style="width:2%;" style="float-right; ">
<button style="position:fixed;" mat-icon-button>
<mat-icon >cancel</mat-icon>
</button>
</div>