Using sqldf and standard sql to get the maximum values grouped by another variable
https://cran.r-project.org/web/packages/sqldf/sqldf.pdf
library(sqldf)
sqldf("select max(Value),Gene from df1 group by Gene")
or
Using the excellent Hmisc package for a groupby application of function (max)
https://www.rdocumentation.org/packages/Hmisc/versions/4.0-3/topics/summarize
library(Hmisc)
summarize(df1$Value,df1$Gene,max)