## Construction of the fourfold cover of the Mathieu group $$M_{22}$$.(English)Zbl 0805.20014

Summary: We give an explicit construction for the two faithful, irreducible, 16- dimensional representations of $$4 \cdot M_{22}$$ over the field $$\text{GF}(49)$$. Then we extend them to the 32-dimensional representation of $$4 \cdot M_{22} : 2$$ over $$\text{GF}(7)$$. Explicit matrices are given.