I am new to statistics and currently got a dataset which contains 80 dependent variables and 1 independent variable with 2 groups. MANOVA has a p-value of >0.6 on this dataset. But when I use linear discriminant analysis, two groups can be separated perfectly(almost 100%). Is this result possible?

What I understand for MANOVA is that larger p-value means less different between two groups. Then how can data be separated perfectly if there is no different?