Decomposition Matrix for the projective Characters S₂8, p=11

In this work, we compute the decomposition matrix to the spin characteristics of S₂8 for a given field of characteristic p=11, the connections between the irreducible modular spin characters and the irreducible spin characters of S₂8. The technique employed in this study is (r, r ̅) -inducing, which creates projective characters for S₂8 by using the projective characters of S₂7. Maple was used to seeing all available columns and then choosing the potentially appropriate columns of them. In order to explore irreducible modular spin characteristics, general correlations and theorems will be discovered as a result of this research.